EPA-600/4-76-016d
May 1976
Environmental Monitoring Series
CONTINUED RESEARCH IN MESOSCALE AIR
POLLUTION SIMULATION MODELING:
Volume 3ST • Examination of the Feasibility of
Modeling Photochemical Aerosol Dynamics
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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EPA 600/4-76-016 D
May 1976
CONTINUED RESEARCH IN MESOSCALE AIR
POLLUTION SIMULATION MODELING:
VOLUME IV - EXAMINATION OF THE FEASIBILITY OF
MODELING PHOTOCHEMICAL AEROSOL DYNAMICS
T. N. Jerskey
J. H. Seinfeld •
Systems Applications, Incorporated
950 Northgate Drive
San Rafael, California 94903
68-02-1237
Project Officer
Kenneth L. Demerjian
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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11
DISCLAIMER
This report has been reviewed by the Office of Research and
Development, U.S. Environmental Protection Agency, and approved
for publication. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
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CONTENTS
DISCLAIMER ii
LIST OF ILLUSTRATIONS v
LIST OF TABLES vii
I INTRODUCTION 1
II PHYSICAL PROCESSES INFLUENCING THE DYNAMICS OF
AEROSOLS IN PHOTOCHEMICAL SMOG 4
A. Sources and Observed Properties of
Photochemical Aerosols 4
1. Sources of Aerosols in Los Angeles 4
2. Observations of Photochemical Aerosols 7
3. S umma ry 13
B. Physical Processes Influencing Aerosol Dynamics 15
1. Homogeneous Nucleation 15
2. Heterogeneous Condensation 20
3. Coagulation 33
4. Turbulent Diffusion 42
5. Gravitational Settling 43
6. Deposition of Particles on Surfaces 45
7. Rainout and Washout of Aerosols 49
C. Summary of Important Physical Processes in
the Evolution of Photochemical Aerosols 51
1. Coagulation 54
2. Heterogeneous Condensation 55
3. Turbulent Diffusion 57
4. Gravitational Settling 57
5. Deposition of Particles on Surfaces 58
6. Washout of Aerosols 58
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IV
III CHEMICAL PROCESSES INFLUENCING THE FORMATION
OF AEROSOLS IN PHOTOCHEMICAL SMOG 60
A. The Chemical Composition of the Los Angeles Aerosol . . 60
1. The Spatial Distribution of Sulfate and Nitrate . . 61
2. The Diurnal Patterns of Sulfate and Nitrate .... 63
3. The Sulfur, Nitrogen, and Carbon Composition
of the Los Angeles Aerosol 67
4. Summary 70
B: Rates of Conversion of Sulfur, Nitrogen, and
Carbon to Aerosol 73
1. Rates of Sulfur Conversion 76
2. Rates of Nitrogen Conversion 80
3. Rates of Carbon Conversion 84
C. Possible Chemical Reactions That Influence the
Evolution of Photochemical Aerosols 88
1. Sulfate Formation 88
2. Nitrate Formation 98
3. The Generation of Organic Compounds
of Low Volatility 105
4. The Role of Water in Photochemical Aerosols .... Ill
D. Summary 114
IV MATHEMATICAL MODELING OF THE DYNAMIC BEHAVIOR OF
PHOTOCHEMICAL AEROSOLS 119
A. The Status of Aerosol Emissions Inventories 119
B. The Basic Equations of an Aerosol Model 122
C. Application of the General Equation to
Photochemical Aerosols 128
1. Mean Number Density Distribution Function 129
2. Total Mean Number Density 133
3. Total Mean Aerosol Volume 134
D. Alternative Forms of Aerosol Models 135
E. Summary 140
V RECOMMENDATIONS FOR FUTURE RESEARCH 142
REFERENCES 147
FORM 2220-1 156
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ILLUSTRATIONS
1 Comparison of Surface and Volume Distributions for
Background and Motor Vehicle Source-Enriched (Near
the Harbor Freeway) Sites ................... 9
2 Comparison of the Characteristics of Photochemical
and Nonphotochemical Urban Aerosols .............. 12
3 Development of the Volume Distribution with Time
in Los Angeles on 3 September 1969 .............. 32
4 Collision Frequency Factors 3BM f°r Particles of
Size D . and D . ........................ 37
5 The Normalized Frequency Factors B- /eBM-n as a
The Normalized Frequency Factors BBM-j i
Function of Normalized Particle Diamet
er D ./D ^ ........ 39
6 Comparison of Different Collision Mechanisms in
in the Los Angeles Aerosol ................... 41
7 Equation (42) Fitted to the "Grand Average" Data
of Blumenthal et al . (1974) .................. 46
8 Deposition Velocity and Terminal Settling Velocity
for Flow over Grass ........... ............ 48
9 The Contribution of Various Sources to the Total
Aerosol Mass in the Los Angeles Basin ............. 62
10 Diurnal Variations for Sulfate and Selected Pollutants
at West Covina on 23-24 July 1973 ............... 65
11 Diurnal Variations for Nitrate, Sulfate, and NOX at
West Covina on 23-24 July 1973 ................. 66
12 Diurnal Variations in Size Distributions for Sulfate
and Nitrate at West Covina on 23-24 July 1973 ......... 68
13 Diurnal Variations in the Ratio of Particle to Gas
Phase Sulfur .......................... 77
14 Scatter Diagram of the Sulfur Conversion Ratio in
Particles Smaller Than 0.5 ym in Diameter and Ozone ...... 81
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VI
15 The Sulfur Conversion Ratio as a' Function of the
Product of Gas Phase Ozone and Nonmethane Hydrocarbon
Concentrations ......................... 82
16 Diurnal Variations in the Ratio of Particle Phase to
Gas Phase Nitrogen (N^o + NNC^) ................ 83
17 Scatter Diagram of the Ratio of Particle to Gas Phase
Nitrogen as a Function of Ozone Level ............. 85
18 Hourly Variations of bscat, Organic Distribution Factors (fc),
Ozone, Total Particulate Matter (TP), Gaseous Hydro-
carbons (GRH), and Organics .................. 87
19 Pathways for Formation of Nitrate Aerosols
20 Extrapolation of the Vapor Pressure of Adipic Acid
to the Ambient Temperature ................... 109
21 The Light-Scattering Coefficient as a Function of
Liquid Water Content ...................... H3
22 Diurnal Patterns of Waterometer Data for Pomona--
4-5 October 1972 ........... ............. 115
23 Diurnal Patterns of Waterometer Data for Pasadena--
9 September 1972 ........................ 116
24 Diurnal Patterns of Waterometer Data for Pasadena--
20 September 1975 ....................... 117
25 Diagram of the Relationship of the Emissions Inventory
to the Total Aerosol Mass ................... 12°
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vii
TABLES
1: Physical Processes Affecting the Evolution of Aerosol
Number Density Distributions .................. 5
2 Source Contributions to Aerosol Samples from Pasadena,
California (3 September 1969). . ." ............... 8
3 Comparison of the Physical Properties of Photochemical
and Nonphotochemical Aerosols. . . ...... , ......... 11
4 Comparison of Aerosol Samples Taken from Photochemical
Smog and Other Urban and Nonurban Aerosols ........... 14
5 Rates of Conversion of Vapor Phase F^SC^ Through
Heterogeneous and Homogeneous Nucleation ..... . ...... 17
6 Parameters Used in Evaluating the Relative Importance
of Thermal Effects on Aerosol Growth by Heterogeneous
Condensation ......... . ................ 26
7 Thermodynamic Data for. Calculating the Growth Rates , .,-
and the Critical Sizes: for Growth' ............... ^
8 Estimated Rates of Change of Aerosol Number Densities
in the Urban Atmosphere ..................... 53
9 ACHEX Data for Nitrate and Sulfate in the
South Coast Basin, 1972 to 1973 ................. 64
10 NASN Data for Nitrate and Sulfate in the
South Coast Basin for 1968 ................... '64
11 Sulfate, Nitrate, and Solvent Extractable Organic
Concentrations at Three Sites During .1972 ............ 69
I
12 High-Volume Sample Concentrations Obtained on
4 October 1972 ............... " .......... 69
13 A Comparison of Theoretical and Experimental
Ammonium Values ......................... 71
14 Secondary Aerosol Organics Identified in the ACHEX ....... 72
15 Pseudo-First-Order Rate Constants for the Los Angeles Basin. . . 79
16 Diurnal Variations of Total Particulates (TP) — in yg m~3—
Organic Cerbon Fraction (OCF), and Organic Carbon
Distribution Factor (fc) .................... 86
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vlii
17 Reactions in the S02-N0x-Air System 91
18 S02 Oxidation Reactions in Photochemical Smog 94
19 Chemical Equilibria in the S02-NH3-H20-C02 System ....... 96
20 Major Homogeneous Reactions Involving Nitric Acid in
Photochemical Smog 102
21 Aqueous Reactions of Nitrogen Oxides 104
22 Studies Reporting Aerosol Formation for Different
Hydrocarbons upon Reaction with Ozone or Photolysis
in the Presence of NOX » . ' 106
23 Ozone-Olefin Reaction Mechanisms 110
24 Organic Aerosol Constituents Identified in
Smog Chamber Studies Ill
25 Mechanisms for Reactions of Cyclohexane Leading to
Difunctional Aliphatic Compounds 112
26 Sources of Data for an Aerosol Emissions Inventory 121
27 Significance of the Terms in the General Dynamic
Equation [Eq. (67)] 130
28 Levels of Detail in the Representation of an
Urban Aerosol Population 131
29 Functional Dependences of the Mean Number Density
Distribution Function
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I INTRODUCTION
Since photochemical smog consists of both gaseous and participate air
pollutants, a mathematical description of its dynamic behavior should ulti-
mately include both gaseous and particulate components. Such a description
is inherently more difficult for atmospheric aerosols than for gaseous air
pollutants because the specification of aerosols requires not only their
chemical composition, but also their thermodynamic state and size. In addi-
tion, because aerosol growth is often linked strongly to gas phase species
concentrations by nucleation or heterogeneous condensation processes, know-
ledge of the dynamic behavior of the gaseous species is generally required as
a component of the description of dynamic aerosol behavior.
Although the total mass of particulate pollutants in an urban atmosphere
is generally small compared with that of gaseous pollutants, aerosols can,
nevertheless, contribute significantly to visibility degradation and health
effects. Despite many years of investigation, the origins and evolution of
urban air pollution aerosols remain poorly understood in comparison to
gaseous pollutants. For this reason, virtually no studies have been pub-
lished on the mathematical modeling of urban aerosol dynamics.
The objective of our study was to assess the feasibility of developing
mathematical models for urban aerosol dynamics. For this analysis, it
was necessary to review the current state of understanding of the physical
and chemical processes responsible for aerosol properties, since the des-
cription of these processes is required for an urban aerosol model. The
study focused on aerosols that occur in photochemical air pollution—that
is, in the presence of oxides of nitrogen, hydrocarbons, and sulfur dioxide.
The mathematical modeling of such aerosols poses perhaps the most compre-
hensive problem possible associated with urban aerosol behavior, for it
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includes all of the major urban pollutants. Thus, the results of a study
of the requirements for modeling photochemical smog aerosol can be applied
to modeling problems associated with urban aerosols in general.
From the standpoint of air pollution control, a model of aerosol
evolution in the atmosphere will relate gaseous and particulate emissions
to the properties of the aerosol that are responsible for visibility im-
pairment and health hazards. Laboratory studies have shown that the effect
of suspended particulate matter on human health results from a complex
process that is not fully understood. Apparently, the particles themselves
may cause injury, as well as carrying volatile gases into the human res-
piratory system, which may also cause injury. The Task Group on Lung Dyna-
mics ("1966} reported that the most efficient penetration into the lungs was
by particles having diameters less than 1 ym. Landahl (1959) found essentially
a 100 percent retention of particles larger than 10 ym in the nose and a
substantial retention of particles larger than 2 ym.
Measurements of light scattered by aerosols have shown very high corre-
lation coefficients (M3.9) with the total volumes of aerosols in the size
range 0.1 ym < Dp < 1.0 ym. Hence, a very good measure of visibility re-
duction can be derived from a calculation of the mass in this size range
(Charlson et al., 1968, 1969; Charlson, 1969; Thielke et al., 1972; Samuels
et al., 1973).
In the mathematical modeling of urban aerosol dynamics, the following
processes must be considered:
> Emissions
- Primary particulate (natural and anthropogenic)
- Gaseous pollutant
- Background levels of particles
> Aerosol formation and growth
- Homogeneous nucleation
- Heterogeneous condensation
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- Coagulation
- Heterogeneous chemical reaction
> Atmospheric transport and diffusion
- Advection
- Turbulent and Brownian diffusion
- Settling
- Deposition on surfaces.
Chapters II and III discuss the current understanding of these pro-
cesses as they pertain to photochemical aerosols. For convenience, we
have divided the processes that influence the dynamics of urban aerosols
into physical and chemical categories. Physical processes are those that
influence the size distribution of the aerosol or its number concentration
in a unit volume of air. Chemical processes are those that influence the
chemical composition of individual particles. As we demonstrate later,
heterogeneous condensation can be classified in either category; we have
chosen to include a discussion of that phenomenon with physical processes.
In Chapter II, we examine the physical processes—that is, those that re-
sult from the diffusional motion of particles, particle collisions, or gas-
to-particle conversion. (Of course, a physical process, such as coagula-
tion, may lead to a change in the chemical constituency of the resulting
particle.) In Chapter III, we focus on homogeneous and heterogeneous chemi-
cal reactions that may influence aerosol behavior. Based on the discussions
in Chapters II and III, Chapter IV presents our initial development of mathe-
matical models of photochemical aerosol dynamics and discusses the status of
the aerosol emission inventory for Los Angeles and the additional information
required to validate the model.
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II PHYSICAL PROCESSES INFLUENCING THE DYNAMICS
OF AEROSOLS IN PHOTOCHEMICAL SMOG
Whereas the physical processes that can affect the dynamics of gaseous
pollutants are limited to those that alter concentrations in a unit volume
of air through atmospheric transport, those that influence particle behavior
are much more diverse. The objective of this chapter is to identify the
physical processes that are potentially important in aerosol dynamics and
to assess the actual significance of each process for photochemical aerosols.
Table 1 summarizes the physical processes that affect the evolution of the
aerosol in a unit volume of atmosphere. Since the importance of each of the
physical processes in Table 1 depends strongly on the size range of the
aerosol, we must identify the observed sizes of photochemical aerosols before
we can assess the significance of each process.
A. SOURCES AND OBSERVED PROPERTIES OF PHOTOCHEMICAL AEROSOLS
Atmospheric and laboratory measurements have both provided information
on the size distribution of photochemical aerosols. Much of the atmospheric
data were obtained during two major field studies sponsored by the State of
California Air Resources Board: the 1969 Pasadena smog experiment (Hidy,
1972) and the 1972 to 1973 Aerosol Characterization Study, which is called
ACHEX (Hidy et al., 1975).
1. Sources of Aerosols in Los Angeles
The sources of suspended particulate matter can be natural or anthro-
pogenic, and the aerosol itself can be primary (emitted from sources as
particles) or secondary (formed in the atmosphere as particles). Secondary
aerosols result when gaseous pollutants (or naturally occurring hydrocarbons)
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Table I
PHYSICAL PROCESSES AFFECTING THE EVOLUTION OF AEROSOL NUMBER DENSITY DISTRIBUTIONS
Process
Homogeneous nudeatlon
of a gaseous species
Heterogeneous condensation
Definition
Agglomeration of molecules to form a stable
particle
Growth of particles by diffusion of gaseous
species to the particle surface followed by
absorption or adsorption
Important Features
Coagulation
The process of collision of two particles
to form a single particle
Particles formed-in this way are very small.
High concentrations and low vapor pressures
are required to initiate homogeneous
nucleation.
The driving force for growth is the difference
between the ambient partial pressure and the
vapor pressure just above the surface of the
particle. Because the vapor pressure over a
curved surface is greater than that above a
flat surface (the Kelvin effect), there is a
critical size—on the order of O.lpm diameter--
below which a particle will not grow by
heterogeneous condensation.
Since it is a second-order process (i.e., its
rate is proportional to the square of the
local number density), high concentrations
are required for appreciable rates. Because
large particles (over 1 ym in diameter) gen-
erally do not exist in concentrations high
enough to produce appreciable rates, coagu-
lation is most important for small particles.
Different mechanisms can bring two particles
together; the efficiencies of these mechanisms
depend on the sizes of the two particles.
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Table 1 (Concluded)
Process
Brownlan diffusion
Turbulent diffusion
Gravitational settling
Definition
Deposition
Ralnout 1n clouds
Washout under clouds
Diffusion of particles as a result of colli-
sions with gas molecules
Motion of particles with the turbulent
airflow
Settling of particles due to gravity
Important Features
Loss occuring when particles cross stream-
lines and deposit on surfaces, such as
grass
Loss of particles through their role as
condensation nuclei in clouds
Scavenging of particles by falling rain-
drops
Brownlan diffusivity depends on particle
size; it is most important for small par-
ticles.
Turbulent diffusion of aerosols can be
treated analogously to that of gaseous species.
This is important only for large particles
(over 10 ym in diameter); it is the mechanism
primarily responsible for the cutoff of the
aerosol size spectrum at the upper end of the
particle size range.
Deposition is primarily important for par-
ticles larger than 1 pm in diameter.
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form products that can homogeneously nucleate or heterogeneousty condense
at ambient temperatures.
Table 2 shows an approximate aerosol inventory for Los Angeles.
Primary and secondary anthropogenic sources have been estimated to contri-
bute nearly two-thirds of the total aerosol mass in Los Angeles. Half of
the anthropogenic contribution has been estimated to result from gas-to-
particle conversion. Hence, an "emission inventory" for photochemical
aerosols must include an inventory of gaseous species potentially conver-
tible to the particulate phase.
Of prime interest in this chapter are the size distributions asso-
ciated with the aerosol sources. Figure 1 shows the surface area and
volume distributions measured during 1972 at four sites in the Los Angeles
area. The Hunter-Liggett site is characteristic of a remote land site; the
Harbor Freeway, of a motor vehicle dominated site; Goldstone, of a remote
desert location; and Pt. Argue!lo, of a site dominated by a marine aerosol.
As Figure 1 shows, the differences in the size distributions of the aerosols
at the four sites are clearly evident. The motor vehicle exhaust aerosol
has large numbers of particles that have diameters less than 0.1 ym, whereas
the marine and natural continental aerosol particles are concentrated in the
size range larger than 1.0 urn diameter.
2« Observations of Photochemical Aerosols
Once the major sources of photochemical aerosols have been identified,
one can infer information about the physical properties important in the
evolution of the aerosol from its measured size distributions. As noted
earlier, the richest source.of data on the properties of photochemical
aerosols are the 1969 and 1972 to 1973 Aerosol Characterization Study
conducted in Los Angeles.
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8
Table 2
SOURCE CONTRIBUTIONS TO AEROSOL SAMPLES
FROM PASADENA, CALIFORNIA (3 SEPTEMBER 1969)
Source
Natural background
Primary
Sea salt
Soil dust
Secondary
Organic vapors from plants
Ammonia
Hydrogen sulfide
Man-made
Primary
Automobile exhaust
Tire dust
Cement dust (roads and construction)
Fuel oil fly ash
Diesel exhaust
Aircraft exhaust
Industrial emissions
Percentage
Secondary
Sulfur dioxide -
Nitrogen oxides
Organic vapors -
Total
sulf ate
> nitrate
particulate
1.3%
11.4
Unknown
Unknown
Unknown
8.2
0.8
1.7
0.1
1.8
2.7
7.3
* 0.1
26.7
>72.3
Source: Friedlander (1973).
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5000
4000
3000
2000
1000
o
A
V
O
LOCATION
HUNTER-LIGGETT
HARBOR FREEWAY
GOLDSTONE
PT. ARGUELLO
TIME(PST)
1500
1920
1500
1830
DATE
9/14
9/27
11/1
11/9
St(i.m2/cm3)
292
3475
181
89.7
bscat x 10
0.788
0.789
0.71
0.587
4 I*'1)
400
300
200
TOO
0.3 0.6 1.0
Particle Diameter--urn
o
60
50
40
30
20
10
T
LOCATION TIME(PST) DATE
O HUNTER-LIGGETT 1500 9/14
A HARBOR FREEWAY 1920 9/27
V GOLDSTONE 1500 11/1
O PT. ARGUELLO 1830 11/9
39.8
52.3
12.4
53.7
(84)
SPRAY)
(MOTOR VEHICLE EMISSION)
0.01 0.03 0.06 0.1 0.3 0.6 1.0 3.0 6.0 10
Source: Hidyetal. (1973a). Part1c1e ^^ter-wm
30 50
FIGURE 1. COMPARISON OF SURFACE AND VQLUME DISTRIBUTIONS FQR BACKGROUND ANQ
. MOTOR VEHICLE SOURCE-ENRICHED (NEAR THE HARBOR FREEWAY) SITES
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10
Laboratory and field studies have elucidated certain differences
between photochemical and nonphotochemical urban aerosols. Table 3 sum-
marizes some of the conclusions based on available studies. Whitby et al.
(1972) analyzed the number, surface area, and volume distributions of 342
size distributions measured during the 1969 study. The grand average
number, surface area, and volume distributions, normalized to the total
number, surface area, and volume, respectively, are shown in Figure 2(a).
Figure 2(b) compares the volume distribution measured in Los Angeles with
that measured in urban and rural locations where photochemical reactions
were not expected to be important. The bimodel size distribution appears
to be universal; however, the characteristics of the fraction in the size
range 0.1 £ Dp £ 1.0 ym indicate that these particles are apparently of a
different origin in the Los Angeles aerosol than in the other aerosols
studied. In Los Angeles, the peak in the submicron fraction occurs consis-
tently around 0.25 ym diameter and reaches a maximum number density in phase
with the peak in solar radiation. In contrast, the submicron fraction of
the volume distribution in the Minneapolis aerosol is more skewed than that
of the Los Angeles aerosol and peaks at abo'ut 0.8 ym at about 8 a.m. during
the morning traffic. In all cases, the large particle fraction, with a peak
above 1.0 ym, is attributable to local, naturally occurring particles, such
as dust and sea spray.
The peak in the total particulate concentration in Minneapolis was
nearly an order of magnitude larger than the peak in the Los Angeles aerosol.
Husar et al. (1972) suggested the following reasoning: The probability that
a particle whose diameter is less than 0.1 ym will collide with another the
same size is less than that of collision with a particle in the size range
0.1 £ Dp £ 1.0 ym. Therefore, the total number of particles in Los Angeles
is less than that in Minneapolis because the Aitken nuclei produced by com-
bustion and homogeneous nucleation are more effectively removed in Los
Angeles through coagulation with the larger number of particles in the size
range 0.1 £ Dp <_ 1.0 ym.
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Table 3
COMPARISON OF THE PHYSICAL PROPERTIES
OF PHOTOCHEMICAL AND NON PHOTOCHEMICAL AEROSOLS
Photochemical Nonphotochemical
Aerosol Aerosol
Property (Los Angeles) (Minneapolis)
Average number 1.14 x 10 cm 2.1-6.6 x 10 cm"3
density
(Whitby et al., 1972)
Daily peak number ^2 x 10 cm" %2 x 10 cm"
density
Volume arithmetic 0.086 ym 0.09-0.11 ym
mean diameter
(Whitby et al., 1972)
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12
> Q
.001
100
.01 -I I
Particle Diameter--pm
(a) Grand Average Number, Surface Area, and Volume Distribution
of Los Angeles Smog
100
90
80
70
"g 60
I"
30
20
10
I I I I I I I I | 1 I TTTTTT] ~~I I I I I I I l|"
L.A. 1969,342 RUNS
MPLS.(CLARK,I965) 56RUNS
MPLS.(PETERSON,I967) 45' 7 RUNS
COLORADO. 1970,3 RUNS
SEATTLE(NOLL)
JAENICKE a JUNGE0967)
• OKITA (1955}
T T
\ i.i i i nil \i \i i.
0.01
0.1 I 10
Particle Diameter--um
100
(b) Comparison of Volume Distributions Measured by Several Investigators
1n Different Locations
C \
Source: Whitby et al.. (1972).
FIGURE 2. COMPARISON OF THE CHARACTERISTICS
OF PHOTOCHEMICAL AND NONPHOTOCHEMICAL
URBAN AEROSOLS
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13
The chemical composition of the Los Angeles aerosol also provides
evidence that the physical mechanisms responsible for the evolution of the
aerosol differ from those in areas where photochemistry was not expected to
be important. Table 4 presents the concentrations of benzene-soluble organ-
ics, sulfates, and nitrates for 24-hour averaged aerosol samples obtained
from the U.S. National Air Surveillance Network. The data indicate substan-
tially larger concentrations of benzene-soluble organics and nitrates in the
Los Angeles and Riverside aerosols than those observed in other areas. In
the Riverside sample, the large nitrate concentration may be due to photo-
chemical transformations of NOX to nitrogen aerosol compounds or to sources
of aerosols containing nitrogen compounds in the vicinity of the sampling
site. For comparison, the fifth entry in the table is a sample taken from
San Nicholas Island during Santa Ana conditions (meteorological conditions
that place the island downwind of Los Angeles). In this sample, the nitrate
and benzene soluble organic concentrations were higher than those normally
found in samples taken from the island.
3. Summary
The sources and observations of photochemical aerosols can be summarized
as follows:
> Sources of aerosols in Los Angeles are both natural and anthro-
pogenic, but the largest fraction of aerosol mass is attributable
to motor vehicle emissions.
> One-third to one-half of the aerosol mass has been attributed
to gas-to-particle conversions in the atmosphere. The mass
accumulates predominantly in the size range of 0.1 to 1.0 ym
diameter.
> The maximum number density in the Los Angeles aerosol occurs
in phase with solar radiation. In contrast, the concentration
of nonphotochemical aerosols follows the diurnal pattern of
the sources of particulate matter.
> The fraction of the aerosol that is composed of organics or
nitrates is higher in the Los Angeles aerosol than in nonphoto-
chemical aerosols, and it increases as the photochemical products
in the atmosphere increase.
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Table 4
COMPARISON OF AEROSOL SAMPLES TAKEN FROM PHOTOCHEMICAL SMOG AND OTHER URBAN AND NONURBAN AEROSOLS
Benzene Soluble
Sulfate
Nitrate
Sample
Downtown Los Angeles (1968)
Downtown Los Angeles (1966)
Riverside, California
(Summer-Fall 1968)
San Nicholas Island coastal
and ocean (1956-1957)
San Nicholas Island (1956-
1957) aged Los Angeles
Urban (1966-1967)
25 stations
Nonurban (1966-1967)
riasb
(ug m-3)
213
119
82
69
110
102
40.0
pg m-3
30.4
15.2
4.9
3.6
10.1
6.7
2.2
Percent
14.2%
12.8
6.0
5.2
9.2
6.6
5.4
ug m~3
16.0
14.0
8.3
8.4
9.3
10.1
5.29
Percent
7.5%
11.8
10.1
12.2
8.4
9.9
13.1
ug m-3
9.4
13.0
11.7
,2.8
5.4
2.4
0.85
Percent
4.4%
10.9
14.3
2.9
4.9
2.4
2.1
Reference
Cadle (1966), Colucci et al.
(1969)
U.S. Public Health Service
(1968)
Lundgren (1969)
Holzworth (1959)
Holzworth (1959)
Ludwig et al . (1970)
Ludwig et al . (1970)
15 stations
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15
B. PHYSICAL PROCESSES INFLUENCING AEROSOL DYNAMICS
In this section, we consider each of the processes listed in Table 1
to assess its importance to the rate of formation of photochemical aerosols.
In Section II-C, we estimate the relative magnitude of the effect each
process has on the aerosol size distribution and present sample calculations.
1. Homogeneous Nucleation
As indicated by estimates of gas-to-particle conversion in photochemical
smog, secondary aerosols are responsible for a substantial fraction—as much
as one-half—of the total aerosol mass. The conversion of gaseous species
to the particulate phase can occur both in the absence and in the presence of
foreign nuclei. Homogeneous nucleation refers to the spontaneous formation
of stable nuclei from gas molecules. For a detailed treatment of the thermo-
dynamics and kinetics of homogeneous nucleation of single species, we refer
the reader to Hidy and Brock (1970). Stauffer et al. (1973) and Kiang et al.
(1973) have reviewed the homogeneous nucleation of several species, which is
called heteromolecular nucleation.
In cloud physics, it is generally assumed that even at the high super-
saturations that occur in clouds, homogeneous nucleation of water vapor is
negligible compared with condensation on preexisting particles. In photo-
chemical smog, the primary candidates for heteromolecular nucleation are
sulfuric acid, high-molecular-weight organic species, and water.
The importance of the conversion of S02 to sulfate aerosol in photo-
chemical smog has long been recognized. In this conversion, the basic pro-
cess appears to be the homogeneous oxidation of-S02 to 503, followed by a
rapid reaction of S03 with water, producing a molecule of sulfuric acid.
The sulfuric acid molecule then participates in either of two processes:
(1) Water molecules may homogeneously nucleate around the sulfuric acid
molecule, at an observed ratio of about five molecules of water per molecule
of H$04, or (2) the H2S04 molecule may diffuse to an existing stable
-------
16
particle and heterogeneously condense. Since sulfuric acid is super-
saturated in the concentration range of parts per hundred billion, it
thus rapidly follows one of these two paths. Rates of photooxidation of
S02 in air have been measured by Hall (1953), Gerhard and Johnstone (1955),
Renzetti and Doyle (I960), and Quon et al. (1971). Quon et al . measured
a pseudo-first-order rate constant of 5 x 10~6 sec~^ . At S02 levels
typical of air pollution episodes (0.65 ppm), the rate of formation of sul-
furic acid by photooxidation of S02 (in the absence of hydrocarbons and
NOX) is 3 x TO'3 ppb sec'1, or 1.31 x 10~4 g cnr3 sec-"1 of sulfuric acid.
Table 5 shows comparisons of the rates of mass conversion of H2S04
by homogeneous nucleation and by diffusion to the surface of 0.1 ym diameter
particles at a particle concentration of 105 cm~3 for various concentrations
of sulfuric acid vapor. The homogeneous nucleation rates are those calcu-
lated for various concentrations of H2S04 vapor by Doyle (1961). To obtain
these rates, we multiplied the nuclei formation rates obtained by Doyle by the
number of molecules of ^504 per nuclei and the weight of a molecule of
A detailed discussion of solutions to the kinetic equations for homo-
geneous nucleation has been given by Hidy and Brock (1970). In the classi-
cal theory of particle generation by nucleation, the rate of formation of
clusters of k molecules is assumed to be dominated by collisions between
single molecules and clusters of molecules and by the evaporation of single
molecules from the clusters. The interaction of particles is assumed to be
negligible.
No general analytic solution to the differential equations for the rate
of change of clusters in the presence of a saturated vapor has been obtained,
but solutions have been found for the steady-state distribution of clusters
of k molecules. In this cases the rate of nucleation is given by an equation
of the form
exp
-------
17
Table 5
RATES OF CONVERSION OF VAPOR PHASE H2S04
THROUGH HETEROGENEOUS AND HOMOGENEOUS NUCLEATION*
H2S04 Gas Phase ,, , F .. Homogeneous Heterogeneous
Concentration
(pbb)
1.3
0.13
1.3 x 10"2
1.3 x 10"3
1.3 x 10"4
1.3 x 10"5
Molecules
per Nucleus
5
11
18
41
118
298
nu ic rr a<- u i un
of H2S04
0.357
0.320
0.280
0.248
0.220
0.186
Rate
(gsec-1 cm-3)
4.3 x 10~8
1.7 x 10"11
3.6 x 10"15
8.1 x 10"23
4.6 x 10~40
1.64 x 10"60
Rate
(gsec-1 cm-3)
1.6 x 10"11
1.6 x 10~12
1.6 x 10"13
1.6 x 10~14
1.6 x 10"15
1.6 x 10'16
*Homogeneous nucleation rates were calculated by Doyle (1961) for a binary system
of H2S04 and water vapor at 25°C and 50 percent relative humidity.
-------
18
where AG* is the free energy of formation of the nucleus and 1° is a
function that depends on the properties of the molecular species comprising
the clusters and the concentrations of their vapors.
Doyle (1961) adapted the model of Reiss (1950) for the determination
of self-nucleation rates in binary systems to determine the rate of forma-
tion of nuclei in the sulfuric acid and water system. To calculate the
rate of formation, I, at given concentrations of sulfuric acid vapor and
water vapor, Doyle first determined the location of the activation barrier
(that is, the minimum number of molecules for which an aggregate of molecules
is stable). The activation barrier can be found by determining the free
energy for which an aggregate of 2n-| moles of 1^0 and 2n2 moles of ^864
is stable as follows:
Ar 2 (2 1 \ , 2 (2 1 \ , n2
Ab = nn I yn - u-, 1 + n0l y0- u0 / + TTYL)_ ,
I \ I I / L^ e. el p
where
2 2
n, and n2 = the number of moles of H^O and I^SO^,
in the liquid phase, respectively,
2 2
y, and y2 = the chemical potentials of ^0 and H2S04,
respectively,
Y = the surface tension of the droplet,
D = the droplet diameter.
P
From the expression obtained by Reiss (1950), Doyle calculated the
function 1°, which is a function of the properties of the two components
of the system and the size of and surface energy of the embryo. The homo-
geneous nucleation rates given in Table 5 are uncertain by three or four
orders of magnitude because of the inadequate data for partial pressures
of sulfuric acid over its aqueous solution. Additional uncertainties in
the results can be attributed to the model used.
-------
19
In computing the heterogeneous condensation rates in Table 5, we
assumed that the rate of condensation is controlled by the rate of diffu-
sion of gaseous ^804 to the particles. The maximum rate of diffusion
occurs when the concentration of the condensing material in the aerosol
is negligible. In such a case, the rate of mass transfer of ^$04 per
unit volume of atmosphere to a monodispersed aerosol of diameter Dp and
number density N in an atmosphere with a partial pressure p^ of ^804 is
, 2irDMp DN
M = P °°
dt RT
where
M = the molecular weight of the condensing species,
D = the molecular diffusivity of the condensing species
in air }
R = the gas constant,
T^ = the ambient temperature.
We computed the rates shown in Table 5 on the basis of the following
values: Dp = 10"5 cm, D = 0.5 cm2 sec'1, M.= 98 g mole-1, T^ = 298°K,
and N = 105 cnr3.
Note that at F^SCty concentration levels below about 0.1 ppb, the rate
of loss of H2S04 by heterogeneous condensation exceeds that of homogeneous
nucleation. At the clean air photooxidation rate of S02 of 1.3 x 10~14 g cm'3
sec~l reported earlier, if we assume that this rate is balanced by hetero-
geneous condensation, the contribution of homogeneous nucleation to the rate
of loss of H2S04 is completely negligible. Under these conditions, the con-
centration of H2S04 in the gas phase would be about 10~3 ppb.
-------
20
In general, at typical ^04 levels in the urban atmosphere
-3 ppb), homogeneous nucleation can be neglected, compared with
heterogeneous condensation, as a mechanism for the conversion of gases
to the particulate phase. If S02 concentrations were to reach values in
the range of 60 ppm, as they do in concentrated plumes, then homogeneous
nucleation of the 1^04 formed might be expected to become important;
otherwise, homogeneous nucleation can be neglected in the formulation of
an urban-scale dynamic model for aerosols.
2. Heterogeneous Condensation
Growth by heterogeneous condensation is thus an important mechanism
in photochemical aerosol dynamics. In fact, that part of the aerosol mass
attributable to gas-to-particle conversion processes is basically the re-
sult of heterogeneous condensation. The theory of the growth of multicompo-
nent liquid droplets by vapor diffusion is reasonably well developed
(Fukuta and Walter, 1970). In applying the theory to photochemical aerosols,
the major problem is that the physical state and chemical composition of the
aerosols are often unknown. It is possible that some photochemical smog
aerosols exist as solid particles, for example, containing high-molecular-
weight organics that are solids at normal atmospheric temperatures and
pressures. At present, there are no adequate theories to explain the growth
of particles of this type, and the available experimental data on the true
physical state of these particles are so scarce that it is not clear what
the theoretical needs are. Therefore, in this section, we consider the theo-
retical aspects of growth of liquid droplets only. In this discussion, we
cite some empirical results obtained experimentally by Heisler and
Friedlander (1974).
a. Theoretical Relations for Diffusion-Controlled Heterogeneous
Condensation
When the growth of a particle is controlled by diffusion of a single
gaseous condensing species to the particle surface, the rate of change of
particle volume is given by
-------
21
where pL is the density of the droplet and ps is the partial pressure of
the condensing species in the vapor just above the droplet surface. The
critical parameter controlling droplet growth is ps at given values of Dp
and p^. The partial pressure of the condensing species at the droplet
surface differs from that for the pure liquid species at TM for several
reasons:
> The temperature at the droplet surface is higher than T^
because of the heat released by condensation of the vapor.
Since TS > T^, ps is greater than the vapor pressure at Tm.
> The surface tension associated with a curved surface in-
creases the amount of energy required to form that surface
from the vapor phase. The particle curvature has the ef-
fect, therefore, of increasing the vapor pressure of the
species over a curved surface beyond that over a flat
surface. The phenomenon is known as the Kelvin effect.
> The droplet may consist of several species, in which case
ps is the vapor pressure of the condensing species over a
solution. The effect is that the vapor pressure over the
solution is lower than that over the pure condensing
species. This phenomenon is called the solute effect.
To estimate their possible importance in controlling the rate of growth
of aerosol particles by heterogeneous condensation, we briefly consider
each of these effects below.
-------
22
Assuming that the droplet is at temperature Ts, the rate of loss of
energy from the droplet to the atmosphere is given by*
a? • ^ a? •
(3)
where L1 is the latent heat of condensation (in solution) and k is the
thermal conductivity of air. From Eqs. (2) and (3), the surface temperature
can be related to the partial pressure by
T
Ts -
DML1
(4)
if the heat of condensation of the pure species, L, is approximately con-
stant over the temperature range T^ to Ts, the Clausius-Clapeyron equation
can be integrated to give
LM /I
fT T
If the exponent is small and TST ~ T^, then
(5)
^-i ,
=1
(6)
The Kelvin-Gibbs relation for the vapor pressure at equilibrium over
a curved surface of a pure component is
/4aV
ps = ps exp
I
\
(7)
where p^ is the vapor pressure over a flat surface of pure species at Ts,
a is the surface tension, and V, is the molar volume of the species in the
liquid.
*In writing this relationship, we assume that the characteristic time
for the conduction of heat in the droplet is much shorter than that
for changes in ambient conditions. The characteristic time is estimated
as t = D?/a, where a = kL/PLCpL is the thermal diffusivity of the
droplet. A typical value of t is 10~6 sec for a 015 ym diameter drop
nf
-------
23
The vapor pressure over a solution can be related to that of the pure
component at the same temperature by Raoult's law:
PS =
(8)
where Y-J is the activity coefficient of species i, x-j is the mole fraction
of species i in the solution, and ps. is the vapor pressure of the pure
species i.
Equations (2), (4), (6), (7), and (8) can be combined to give the
following expression for the rate of growth of a two-component droplet by
diffusion of one component, species i, to the droplet:
dv
dt
2irD
PL
RT
CO
_DMp°(T
S -
4-
J
Y.X. exp (
LL'M .. x
kRT2 '1"1
L
RT Dr
^ 00 |
expf
\
J
4aVL \
RT Dn )
k « p/ J
(9)
where S = p (T )/p°(T ) is the saturation ratio. We note that in deriving
OO CO S QO
Eq. (9) we assumed that the Kelvin effect is not altered in the presence
of a solution; that is, that Eq. (7) holds for the vapor pressure over a
solution droplet as well as for a droplet of pure species i.
We note from Eq. (9) that growth ceases when
r4aV,
(10)
or, alternatively, when
4aV,
RT an
(ID
-------
24
Thus, there is generally a critical particle size below which growth
does not occur. We also note that two phenomena act in opposite directions
in governing the rate of condensation. The Kelvin effect increases the
vapor pressure over that of the flat solution, whereas the solute effect
decreases the vapor pressure over that of the pure solution. Growth does
not occur if Dp is too small or if YiX-j is sufficiently large.
The foregoing development can be extended to include multi component
droplets. If there are K condensing species, the rate of change of the
mass of a particle is the sum of the contributions from the K species:
dm 1
dt 2, dt
(12)
where
dm.. 27:0
dt~ = RT
iJ-(p, -Pi.)
(13)
The derivation of the expression for p-j (Ts) is analogous to that
for ps(Ts) for the single component system, except that the vapor pressure
of species i depends on the concentrations of the other N-l species in
the particle. The resulting relation is
(TS) =
L.M.
kir
v
z
v
i - Pi
J J/
(14)
Equations (9), (12)s (13), and (14) are general expressions for conden-
sation growth relations that involve all three effects cited earlier (the
Kelvin effect, the solute effect, and energy transport due to the latent
-------
25
heat of condensation). The next step in the analysis of the growth of
aerosols by condensation is to estimate the relative importance of each
effect on the overall rate of growth of a typical atmospheric aerosol.
We consider thermal effects first.
Thermal effects are embodied in the second term of the denominator of
Eq. (9). Thus, the relative sizes of the two terms in the denominator pro-
vide an indication of the importance of thermal effects in relation to dif-
fusive transport. Data typical of organic acids (see Table 6) indicate that
the magnitude of the first term in the denominator of Eq. (9) is about a
factor of 1C)5 larger than the second term. Thus, it appears that thermal
effects are unimportant in governing aerosol growth rates by heterogeneous
condensation; that is, the particle can be considered to be .at a temperature
of T . In that case, Eq. (9) becomes
dv
dt
S - yixi
4aVL
P'J
(15)
The analogous relation for a multicomponent droplet is
dv
dt
RT
exp
P /J
(16)
b. Theoretical Relations for Reaction-Controlled Heterogeneous
Condensation
The alternative to heterogeneous condensation growth controlled by
vapor diffusion is growth controlled by heterogeneous chemical reaction.
-------
26
Table 6
PARAMETERS USED IN EVALUATING THE RELATIVE IMPORTANCE
OF THERMAL EFFECTS ON AEROSOL GROWTH
BY HETEROGENEOUS CONDENSATION
Parameter Value Remarks
k 2.62 x 103 ergs cm"1 sec"1 V1
T 300°K
oo
2 -1
D 0.07 cm sec Estimated value
typical of organic
acids (Dreisbach,
1959)
a 26.25 dyne cnf Estimated for organic
acids
R 8.31 x 107 ergs mole"1 °K"]
L,L' 6.8 x 109 ergs g Value typical of
organic acids
(Dreisbach, 1959)
V, 150 crn mole" Estimate
D 10"5 cm
p°(Tj 2.6 x 10~2 dyne cm"2 Adi pic acid
-------
27
In this case, vapor diffusion is rapid compared with the rate of consumption
of the condensing species by chemical reaction in the particle, and the
overall rate of heterogeneous condensation is equal to the heterogeneous
reaction rate. We can develop the general form of a growth law as follows.
Let c denote the concentration of the diffusing gaseous species. Then,
in the steady state, c is governed by
(17)
dp
where p is the radial position in the vapor (p = 0 is the particle center
and p = D /2 is the particle radius). The boundary conditions on c are
c = c» » P + "
(18)
n -
U dp
P=D /2
)2 = I D3pkc , p = Dp/2
The second boundary condition states that the flux of the condensing
species at the particle surface is equal to the rate of consumption of the
species by first-order reaction in the volume of the particle (k is the
first-order rate constant). Thus, this problem describes the case in which
the rate of condensation is controlled by a volume reaction in the particle.
The rate at which the vapor species condenses on the particle is
p
where = kDp/12D. When reaction controls the rate, we expect « 1. This
rate is directly related to the rate of change of the particle volume. Thus,
in this case,
-------
28
(20)
in contrast to the case of vapor diffusion controlling in which, as we
have already seen,
If a surface reaction controls the rate of growth, the above boundary
condition at p = D /2 is replaced by
= k'c § (22)
P=Dp/2
where k' is a surface reaction rate constant. In that case, it can be
shown that the growth law is of the form
(23)
c. Experimental Studies of Heterogeneous Condensation Growth
of Photochemical Aerosols
There are two sources of data on the growth of aerosols by heterogeneous
condensation: laboratory investigations and ambient field studies. In this
subsection, we briefly summarize some of the available data from both sources
In a laboratory study, Heisler and Friedlander (1974) compared experi-
mentally observed rates of growth with theoretical aerosol growth laws. The
objective of their study was to determine whether it is possible to infer
the dominant mechanism of growth from experimentally observed aerosol growth.
In analyzing their data, Heisler and Friedlander assumed that the basic
multicomponent growth law was
-------
dv
dt
where
*l
RT (1 + J>Kn)
si-
29
(24)
a =
1.333 + 0.71Kn~
1 + Kn
-1
(25)
and where Kn = 2x/Dp--the particle Knudsen number--is the ratio of the mean
free path of the gas to the particle radius. In the limit as Kn -* 0,
Eq. (24) reduces to Eq. (16). The factor (1 + jiKn) in Eq. (25) is the result
of an attempt to extend empirically the validity of Eq. (16) to the regime
of the intermediate Knudsen number.
The main objective of the Heisler and Friedlander study was to deter-
mine whether the growth relation given by Eq. (24) was capable of repre-
senting experimentally observed growth rates. In particular, the investi-
gators wanted to see if experimental growth rates were proportional to DD
2 3
(rather than Dp, indicating a surface reaction, or Dp, indicating a volume
reaction). If these rates were found proportional to Dp, the growth rate
would then indicate a diffusion-controlled mechanism. For the purposes
of analyzing their data and determining whether dv/dt -v Dp, Heisler and
Friedlander assumed that the mole fraction of species i remained constant
in time and that the saturation ratio remained constant and near unity.
By expanding the exponential in Eq. (24), they obtained the following ap-
proximate growth relation:
dt
(26)
where A is a function of particle composition and saturation ratio but is
assumed to be constant.
-------
30
Heisler and Friedlander made a linear least-square fit of their data
plotted in the form of (1 + £Kn)(dv/dt) versus D Their results indicate
that a growth law of the form of Eq. (26) is capable of representing the
data and that it predicts a minimum particle size for growth of about 0.25 ym
If we assume that the condensing species are primarily hydrocarbons, then we
can use Eq. (11) and the data given in Table 6 to show that
2.5 x 10"2
for the experimental conditions reported by Heisler and Friedlander. Hence,
in this experiment, the gaseous species that diffused to the particles were
only slightly supersaturated and were very likely unsaturated (since yi*i is
less than 1, in general).
The assumptions invoked to reduce Eq. (24) to Eq. (26) lead to a funda-
mental change in the nature of the growth law. Equation (26) predicts that
as long as Dp > D* a particle will grow, whereas Eq. (24) predicts that if
a particle continues to grow, a point will be reached when growth will cease.
This cessation occurs when the partial pressure of the dissolved species
above the particle equals the ambient vapor pressure of that species:
<27>
If we assume that the mole fraction of the condensing species in the particle
is small and that S-j is always near unity, then the equilibrium size pre-
dicted by Eq. (27) will not be reached, and a growth law similar to Eq. (26)
will be obtained. Therefore, the following is an important question: In
the description of photochemical aerosol growth by condensation, is it neces-
sary to account for the change in composition of the particle, and hence in
the vapor pressure over the surface of the particle, with time, or is it
-------
31
acceptable to neglect this change? The resolution of this question requires
a comparison of theoretical predictions with experimental observations. In
a recent study, Heisler (1975) attempted to reproduce the size distribution
of aerosols observed in the Los Angeles smog using a growth relationship of
the form
2 *
Good agreement with the data was found when A, t,. = 0.236 ym , D -i = 0.055 ym,
2 * ' T P
Aptf = 0.581 ym , D £ = 0.240 ym, where tf represents the duration of aerosol
growth. The growth relationship above represents the growth of two gaseous
species onto the particulate phase. The smallest critical size (D -, = 0.055 ym)
might result from the conversion of secondary sulfur, although the growth rela-
tionship of the form given by Eq. (26) has never been tested for sulfates.
It is interesting to compare the empirical constants with those calculated
on the basis of thermodynamic data of the gaseous species which may be diffus-
ing to the particles. If we assume the two species above to be sulfuric acid
formed in the gas phase and the organic acid CgH,gCOOH formed in the gas phase,
then the data necessary to calculate the rate of particle growth and the criti-
cal size are given in Table 1. For sulfuric acid we calculate that
_o o -1 * -5
A, = 2.76 x 10 ym sec and D , =1.91 x 10 ym and for the organic acid
? ? -1 6 -1
A9 = 4.40 x 10 ym sec and Dn9 = 2.86 x 10 ym. If the actual growth time
-52 -1
was 5 hours in Heisler's model (Heisler, 1975) then A-, = 1.3 x 10 ym sec
-52-1
and Ap = 3.2 x 10 ym sec . Hence, the theoretical values indicate a more
rapid rate of growth than was measured and critical sizes which are much smaller
than the values determined by Heisler.
The second source of aerosol data is atmospheric monitoring. Several
volume distributions measured at various times on 3 September 1969 by Whitby
et al. (1972) are shown in Figure 3. The diameter at which the mode of the
volume distribution is located does not appear to vary appreciably, although
-------
LOS ANGELES,
SEPT. 3,19 69
0.0!
PARTICLE DIAMETER, D
Source: Whltby et al . (1972).
FIGURE 3. DEVELOPMENT OF THE VOLUME DISTRIBUTION WITH TIME
IN LOS ANGELES ON 3 SEPTEMBER 1969
-------
Table 7 33
THERMODYNAMIC DATA FOR CALCULATING THE GROWTH RATES
AND THE CRITICAL SIZES FOR GROWTH
Value for Value for
Parameter H2S04 C8H18COOH
Mi 98 g mole"1 159 g mole"
D.J 0.07 cn^sec"1 0.07 ci/sec"1
P.. 1.3 x 10"3 dynes cm"2 5.92 x 10"1 dynes cm"2
p. 1.87 g cm"3 0.94 g cm~3
Si 23 0.349
rixi o.i o.i
1 -2
a. 52 dynes cm 26.25 dynes cm
V, 52.5 crAole"1 169 aAole"1
Li
the total aerosol volume changes substantially during the day. Husar,
Whitby, and Liu (1972) showed that diffusion-controlled growth (i.e.,
9v/3t ^ Dp) results in growth for which the location of the mode in the volume
distribution does not change appreciably in time.
Although the results shown in Figure 3 are interesting, other data (in
particular, the 1972 ACHEX data) do not support the symmetry or the consistent
location of the mode in the volume distribution. There does not now appear to
be sufficient evidence to characterize the structure of the mode of the volume
distribution in the 0.1 < Dp < 1.0 ym diameter size range. Certainly, the
characteristics of this mode--in particular, its behavior with time—should
provide evidence of the nature of the gas-to-particle conversion process
occurring in the atmosphere.
3. Coagulation
Coagulation can result from any of several mechanisms that bring
particles together: (1) Brownian motion, (2) turbulent shear, (3) gravita-
tional settling, and (4) electrostatic attraction. The objective of this
section is to assess the importance of each mechanism, and of coagulation
in general, to the dynamics of photochemical aerosols.
-------
In a spatially homogeneous aerosol, the size distribution function
n(Dp,t), is defined so that n(Dp,t)dDp is the number of particles with dia-
meters in the range Dp to Dp + dDp. The rate of disappearance of particles
of diameter Dp as a result of collision with particles of diameter Dp can
be expressed in terms of the size distribution function as
0(Dp,Dp) n(Dp,t) n(Dp,t)
where g(Dp,Dp) is the collision frequency factor in (crn^ see'"'). Thus, the
rate of change of the size distribution function at diameter Dp due to colli
sion with all other particles is
n(Vt}
The different mechanisms of coagulation are reflected in the functional
form of 3(Dp,Dp). If we define Mj(Dpj,t) as the number density of particles
Ni(DD,-,t) in the discrete size range Dn^ to D . + AD .
J rj (JJ pj |JJ
n
[Note that n(Dp,t) is a size distribution function expressed in units of
ynH cm~3, whereas N-j(Dp,t) is a number density in cm~3j We can use
Eq. (28) to estimate the rate of disappearance of particles in certain
size ranges due to coagulation once 3 has been specified. Note that L-j
o 1
is expressed in units of cm~0 sec .
-------
35
a. Coagulation Due to Brownian Motion
In Brownian coagulation, the particle collisions result from the random
particle motions induced by collisions with molecules of the gas. The man-
ner in which motion is imparted to a particle depends on the size of the
particle relative to the mean free path of the gas, i.e. on the particle
Knudsen number, Kn = 2X/D .
When the particle Knudsen number is small, Kn < 0.1, the particle is
in the so-called continuum regime, where the particle is large enough rela-
tive to the mean free path of the gas that the gas appears as a continuum
to the particle. Assuming that particles are hard spheres, the collision
frequency factor can be written as
' <29>
where D.. is the sum of the Brownian diffusivities of particles of diam-
1 J
eters D . and D.;D.. = D.+D.; and M. . is the symmetry number, defined
as
1 i = -r
9 J ' J 5
1 , 1 f j .
Using the Stokes-Einstein diffusivity for a particle of diameter D .,
D. = kT
where k is Boltzman's constant and y is the viscosity of the gas, we
obtain the collision frequency factor for coagulation in the continuum
regime
In this regime both particles must be larger than about 0.5 ym diameter.
When both particle Knudsen numbers are large (Kn > 10, or D < 0.01
then the particles are in the so-called free molecular regime. In the
-------
36
transition regime, when K - 1, the approaching particles are engaged in
gas-particle collisions but not frequently enough for the diffusion equa-
tion to be applicable, as in the continuum regime. Husar (1969) has sum-
marized the form of the collision frequency factor covering the range from
the continuum regime to the free molecule regime. The collision frequency
factor for arbitrary Kn may be expressed in the form,
«BM =
where the correction factor,
_ _
ij 1+AKn.,
' J
and where the collision Knudsen number is defined as
The effective mean free path A., should be calculated from
' J
3Dij
> = J
ij v
ij
where V-- = /v• v.' , where v. and v- are the mean molecular velocities.
i j "i J ' J
The parameter A in Y-- is called the linear extrapolation distance. Tabu-
lated values of \ as a function of Kn are given by Husar based on the work
of Sahni. The tabulated values can be fit by the following relations:
0.515 Kn + 0.71 0 < Kn < 0.30
A =
0.153 an Kn + 1.043 0.30 £ Kn < 2.0 (32)
1.33 - 0.355 Kn'1 2.0 < Kn
< 00
The collision frequency factors obtained from Eq. (31) are shown in
Figure 4 for the size range 0.002 ym < D < 10 ym. The bottom heavy line
in Figure 4 represents the collision frequency factor for equal size par-
ticles and exhibits a rather weak size dependence over the entire range of
particle sizes. In the free molecule regime the collision frequency factor
-------
37
10
- ^- EQUAL SIZE PARTICLES
10
-10
- FREE i
MOLECULAR
|- REGIME '
TRANSITION
REGIME
SLIP, CONTINUUM
REGIME
.002
i mini i i mini i i i mill I 'i I n
.01
O.I
Dp. (ym)
1.0
10
FIGURE 4. COLLISON FREQUENCY FACTORS 6DM FOR PARTICLES
OF SIZE D . AND D .
BM
Source: Husar (1971).
-------
38
depends strongly on the ratio of the sizes of the two particles, D ./D ..
To illustrate this dependence further, Figure 5 shows the normalized
collision frequency factor,
BBM = 3BM. .j^BM^.
versus the particle size ratio, D ./D .. In the continuum regime 3'
increases roughly linearly with D ./D , , whereas in the free molecule regime,
3gM approaches a quadratic dependence on D ./D . . The collision regime for
two unequal size particles is determined essentially by the size of the
larger particle.
b. Coagulation Due to Turbulent Shear
When particles exist in a turbulent fluid, the motion of fluid eddies
brings particles in contact with each other. If the characteristic length
scale of the eddies is larger than a characteristic particle size (which
is always the case in the atmosphere), the following two processes can be
responsible for collisions between particles:
> Spatial variations of the fluid velocities result in
different velocities of neighboring particles.
> Particles—because of their inertia—may not follow
fluid streamlines.
In the first case, collisions can occur between particles of equal or
unequal size, whereas the second mechanism is restricted to different
sized particles, since particles of equal size in close proximity have
equal inertia in the same direction.
Saffman and Turner (1956) formulated a theory of coagulation due to
turbulent shear. They derived an expression for the collision frequency
factor in the form
(33)
-------
39
CQ
CO.
CQ
00.
FREE MOLECULA
REGIME
CONTINUUM
REGIME
Dp > 0.5
10
10
100
Source: Husar (1971).
FIGURE 5. THE NORMALIZED FREQUENCY FACTORS &BM--/&BM.. AS A FUNCTION
OF NORMALIZED PARTICLE DIAMETER Dpj/Dpi 1J n
-------
40
where e is the local rate of energy dissipation in the small-scale turbu-
lence and v is the kinematic viscosity of the fluid. In this derivation,
they neglected the effect of the particles on the velocity field.
c. Coagulation Due to Sedimentation
Coagulation can occur when particles of different masses are settling
at their terminal velocities. The collision frequency factor in the limit
as Dp-j/Dpj ->• 0 can be written as (Friedlander, 1964)
5S - 8
where qs- is the terminal settling velocity of particle j:
J
(34)
<35>
In this equation, p is the particle density. At 20°C,
(1.3 x 109)
9 9
D . - D .
PJ Pi
(36)
2 2
In Eqs. (34) through (36), we assume that Dp1- » Dp-.
d. Coagulation Due to Electrostatic Attraction
The effect of electrostatic forces on coagulation rates is difficult
to assess, but we do not expect it to be significant in urban atmospheres.
e. Summary
The calculated collision parameters for the three mechanisms described
above for the collisions of a 2 ym (from Hidy, 1973b') and a 0.2 ym diameter
particle with particles of size Dpj are plotted in Figure 6. It is apparent
that in the submicron size range collisions are dominated by the relative
-------
10
0.)
Source: H1dy (1973b).
Particle Radius, 0 /2—vm
(a) Collision of a Particle Whose Diameter
is 2 ym with Particles of Various Sizes
TURBULENT SHEAR
em2 sec"')
0.01
1.0
Particle Radius, D J2—vm
10.0
(b) Collision of a Particle Whose Diameter
is 0.2 ym with Particles of Various Sizes
FIGURE 6. COMPARISON OF DIFFERENT COLLISION MECHANISMS IN THE LOS ANGELES AEROSOL
-------
motion of particles due to their thermal velocities. For energy dissipation
rates typical of ground-level atmospheric turbulence (e = 1000 cm2 sec~^),
turbulent coagulation becomes important for particles whose diameters are
larger than 1 ym. An overall assessment of the role of coagulation in the
atmosphere follows at the end of this chapter.
4. Turbulent Diffusion
We expect to find that turbulent diffusion is an important process
shaping the distribution of particles found in the atmosphere. In par-
ticular, the mixing of emissions from the ground, both the gaseous emis-
sions and primary particulate emissions, probably depends upon the sta-
bility of the atmosphere and the intensity of the turbulence in the mixed
layer of the atmosphere.
Turbulent diffusion transports particles in all three coordinate
directions. In the lowest layer of the atmosphere, turbulent diffusion
in the vertical (z) direction is of primary interest. If we use an eddy
diffusivity, Kzz, to characterize vertical turbulent diffusion, then the
rate of change of the total particle number density in a unit volume of
air can be written as
2
LTD = Kzz ~~2 s (37)
oZ
where, for the purpose of estimation, we assume that K is constant.
2
In the atmosphere, the turbulent diffusivity may range from 10 to
105 cm2 sec'1, depending on the proximity to the ground and the local
hydrostatic stability. To calculate L-j-p, we need an estimate of
82N/9z2.
In the following subsection, we discuss the formulation of an expres-
sion for N(z) using a simple model and field data on the distribution of
particle concentrations with height. We then use this expression for N(z)
to calculate 82N/8z2 in Eq. (37).
-------
43
5. Gravitational Settling
Sedimentation, which is expected to be unimportant for particles
whose diameters are less than 10 ym, provides an effective cutoff of the
spectrum for particles larger than 50 ym in diameter. The rate of loss
of particles per unit volume and time can be expressed as
LGS ' 'Is f • <38>
where qs is the settling velocity and N is the total number density in the
size range of interest. Assuming the Stokes law for the terminal velocity,
we find that Eq. (38) becomes
L6S - -0.32 x 106 DJ; f (39)
for particles of unit density in air at 20°C.
To calculate the rate of loss of particles from a unit volume of
atmosphere by sedimentation, we must determine the gradient of the particle
concentration in Eq. (39). Data are available that give the variation of
particle concentration with altitude (Blifford and Ringer, 1969; Weickmann,
1955; Meszaros, 1969; Blumenthal et al., 1974). The fluctuations in the
measurements from point to point and with altitude make it difficult to
calculate a meaningful distribution of the particle number density from
these field data. We therefore seek a simple way of estimating the particle
density as a function of height in the atmosphere for use in estimating
LGS and LTD-
Hidy (1972) has proposed a simple model of the height distribution of
total particle number density in the atmosphere. In his formulation, the
following assumptions were required to obtain the distribution:
-------
44
> A quasi-stationary state exists in the particle distribu-
tion, that is, 3N/9t = 0.
> The dominant physical processes affecting the distribution
are turbulent diffusion and Brownian coagulation.
> The turbulent diffusivity has a constant value through the
mixed layer.
These assumptions lead to the following differential equation for the
particle distribution with height:
Hr - Y * = 0 , (40)
dy2
where
x = N/N0,
y = z/H,
N, NQ = the particle number densities at any height
z and at z = 0, respectively,
H = a characteristic vertical length scale,
Y = an empirically determined constant that depends
on the meteorological parameters and the ground-
level concentration.
To formulate boundary conditions on Eq. (40), Hidy assumed that the concen-
tration approaches a constant value as the distance from the ground be-
comes large. If one assumes that the concentration at the ground is con-
stant, NQ, then the boundary conditions become
x = 1 at y = 0
and (41)
f = 0 as y + -
-------
45
A simple analytic solution to Eq. (40) with the boundary conditions given
by Eq. (41) is
(42)
where y' =
The assumptions made in obtaining Eq. (42) represent a gross oversim-
plification of the dynamics of urban aerosols. However, one might expect
coagulation and turbulent diffusion to be the dominant mechanisms controlling
the concentration of particles near the ground, particularly in source-
enriched areas. Equation (42), with the adjustable parameter y', can approxv
mate the vertical distribution of particulate matter in the lower 1000 to
2000 feet of the atmosphere quite well. In Figure 7, we fitted the "grand
average" distribution of condensation nuclei measured by Blumenthal et al.
(1974) over El Monte, California. Below 2000 feet, Eq. (42) approximates
the distribution of the condensation nuclei quite well. Thus, we use
Eq. (42) to estimate aN/sz and 82N/9z2.
6. Deposition of Particles on Surfaces
The deposition of particles can occur through sedimentation, Brownian
diffusion, or impaction. Impaction occurs when, because of its inertia,
a particle is unable to follow the streamlines of air around an obstacle
and is intercepted by the object. The removal of particles through impac-
tion on an object can be defined in terms of a pseudo-deposition velocity
qq. The loss of particles per unit surface area of the object per unit
time can then be expressed as
(43)
-------
46
3000
- A
0>
V
+>
JC
at
2000
1000
I I
O
AO
A
A "GRAND AVERAGE"
• CONDENSATION NUCLEI
DISTRIBUTION OVER
EL MONTE
O EQUATION (42)
O A
234 56 78 9 10
Number Density
x 104 cm'3
FIGURE 7. EQUATION (42) FITTED TO THE "GRAND AVERAGE" DATA
OF BLUMENTHAL ET AL. (1974)
-------
47
where N is the number density of particles in the size range corresponding
to the deposition velocity q .
The transfer of aerosol particles from the turbulent atmosphere to an
underlying boundary depends upon the flow near the surface, as well as upon
the nature of the surface itself. Particles are transferred through a turbu-
lent boundary layer whose transport properties depend on the eddy motion of
the turbulence. Near the surface, the particles move through a laminar sub-
layer, where the thermal motion of the particles becomes important.
Figure 8 presents values of qg measured in a wind tunnel over a flat
surface roughened with grass. In this figure, the terminal velocity of
particles of unit density falling through air at 20°C has also been in-
cluded to illustrate that the pseudo-deposition velocity of a particle is
generally larger than the sedimentation velocity of a particle of the same
size. The increase in qg for particles smaller than 0.1 ym diameter might
be expected from the increased mobility of small particles in the laminar
sublayer.
Other factors, such as electrical charge and reentrainment of particles
that have deposited on a surface, affect the magnitude of qg. The relative
importance of inertia! effects, electrical charging, and reentrainment has
been examined in a series of wind tunnel experiments with single conifer
needles and conifer trees (Langer, 1965; Rosinski and Nagamoto, 1965).
Langer (1965) observed no detectable effect of electrical charge on deposi-
tion losses for 2 ym diameter ZnS particles in simulated winds of 1.2 to
1.6 m sec'1. In addition, Rosinski and Nagamoto (1965) observed that the
rate of deposition on surfaces depends on the amount of material previously
deposited on the surface; that is, the cohesive properties of the depositing
material have a strong influence on the pseudo-deposition velocity.
It is apparent that the particle losses due to deposition strongly
depend on the particle composition, the properties of the surface on which
-------
48
mill—i i i uiiii—T-TT
i i i ii ml i i i /mil i i 111 ml r i 111 in
10 1 . 10
Particle Diameter—um
Source: Chamberlain (1967).
FIGURE 8. DEPOSITION VELOCITY AND TERMINAL SETTLING VELOCITY
FOR FLOW OVER GRASS
-------
49
material deposits, the surface roughness, and the wind speed. Hence, for
the purposes of an order-of-magnitude estimate of deposition rates, we use
below the results of Chamberlain (1967) to estimate qg.
To compare the rate of loss from a unit volume of atmosphere due to
the deposition of particles on a surface with other loss mechanisms, we
must calculate the total loss on the surface boundary of the volume of
interest. That is, the loss of particles by deposition per unit time per
unit volume is given by
LD - L* , (44)
where A denotes the surface area of obstacles bounding the volume, V, of
interest. It is apparent then that the relative importance of depositional
losses depends upon the buildings and the vegetation present in the
modeling region.
7. Rainout and Washout of Aerosols
Precipitation can remove aerosols by two methods. Rainout involves
the various processes taking place within a cloud that lead to the forma-
tion of raindrops. Washout refers to the removal of aerosols below the
cloud by falling hydrometeors. In generals rainout is not an important
process for the removal of urban aerosols because cloud formation takes
place at elevations above the urban polluted layer.
The efficiency of removal of aerosols by washout depends on the size
distributions of the aerosol and the raindrops, the solubility of the
aerosol in water, and the total rainfall. The rate of removal of particles
by collision with raindrops can be written as (Hidy, 1973b)
• -"V / f (DP1 + Dr> "s"V MVV' Sr dDr ' (45)
0
-------
where gr(Dr) is the size distribution function for the raindrops and Er
represents the collection efficiency of aerosol particles in the size range
D . to D . + dD . with raindrops in the size range D to D + dD .
Langmuir and Blodgett (1946) obtained theoretical expressions for the
collection efficiency of point masses flowing around spheres for the poten-
tial flow regime by incorporating the solution of Lamb (1932) for the po-
tential flow around a sphere. If we assume that the raindrop is at rest
and consider the flow around the droplet, the efficiency of collection of
point mass aerosol particles by the raindrop is
E „ (46)
r (Stk + 0.25T
for Stk >_ 0.2, where the Stokes number, Stk, is equivalent to the ratio of
the stop distance to the characteristic radius of the collecting sphere,
defined by
Here, qsr is the terminal velocity of the falling raindrop, y is the
viscosity of air, and p is the density of the aerosol particle.
Simple corrections to Eq. (46) are possible for aerosol particles of
a finite diameter for two extreme cases: (1) when the inertia of a par-
ticle is so large that it moved in a straight line (Stk » 1) and (2) when
a particle possesses no inertia and moves along a streamline (Stk = 0).
For the former cases one must consider the increase in the classical cross
section for particle collisions, that is (Fuchs, 1964),
-------
51
and the corrected collision efficiency becomes
, 2 • C48)
(Stk + 0.25T
,, +/
If the terminal velocity of the raindrop is on the order of 4m sec"^ , the
restriction Stk >_0.2 limits the application of Eq. (48) to Dp > 1.0 ym
if Dr = 0.05 cm and the aerosol particles have unit density. For small
particles that diffuse to the raindrop, Slinn (1967) calculated the collec-
tion efficiency to be
c __ Q_ 4k
Er ~ D -
where k denotes Boltzmann's constant, y is the viscosity of air, and T is
the temperature.
C. SUMMARY OF IMPORTANT PHYSICAL PROCESSES IN THE EVOLUTION
OF PHOTOCHEMICAL AEROSOLS
In this chapter, we have discussed the importance of the following
physical processes to the dynamics of photochemical aerosols:
> Homogeneous nucleation
> Heterogeneous condensation
> Coagulation
> Turbulent diffusion
> Gravitational settling
> Deposition on surfaces
> Washout.
With respect to homogeneous nucleation and heterogeneous condensation, the
number density of particles in the atmosphere is sufficient to accommodate
the condensation of supersaturated gaseous species; thus, homogeneous nuclea-
tion can be neglected relative to heterogeneous condensation.
-------
52
Observations of the Los Angeles aerosol indicate that the aerosol
volume in the diameter size range 0.1 ym < Dp < 1.0 ym grows at the rate
of 10 to 40 ym3 cnT3-hr (Husar, Whitby, and Liu, 1972). Two possible mech-
anisms responsible for this growth are heterogeneous condensation and coagu-
lation. Coagulation of particles in the size range 0.1 to 1.0 ym diameter
with particles of size 0.05 ym at respective number densities of 102 and 105
cm"3 and at a collision frequency factor of 10~^ cm3 sec'l would transfer
00]
mass into the 0.1 to 1.0 ym size range at a rate of only 0.25 ym cm hr .
Thus, coagulation cannot be responsible for the observed rate of volume
increase of photochemical aerosols; heterogeneous condensation is the pri-
mary growth mechanism for photochemical aerosols.
For the purposes of formulating a model of the evolution of the par-
ticle number density distribution, n(Dp,t), we would like to know the rela-
tive order of magnitude of the processes that remove or add particles from
the infinitesimal size range Dp to Dp + dDp containing the infinitesimal
number of particles dN = n(Dp,t)dDp. To estimate the rate at which particles
are transferred into and out of these size ranges, we divided the particle size
spectrum into three size ranges: Dp < 0.1 ym, 0.1 < Dp < 1.0 ym, and
Dp > 1.0 ym, in which the number densities were assumed to be:
D < 0.1 ym 0.1 < D < 1.0 ym D > 1.0 ym
105 cm"3 102 cm"3 TO'1 cm"3
For each of these broad size ranges, we assumed that the particle sizes
were (for the purposes of these calculations) 0.05 ym, 0.5 ym, and 5.0 ym,
respectively. Table 8 summarizes the results of these calculations.
-------
53
Table 8
ESTIMATED RATES OF CHANGE OF AEROSOL NUMBER DENSITIES
IN THE URBAN ATMOSPHERE
(In Particles per Cubic Centimeter per Second)
Size Range
Process Dpj < 0.1 ym* 0.1 ym <_ Dpi <_ 1.0 ymf Dpi > 1.0 ym§
Heterogeneous
condensation** (Sulfate)
4 -5
50 percent conversion 10 1 10
3 fi
10 percent conversion 10 0.1 10
2 -7
1 percent conversion 10 0.01 10
Heterogeneous 3 7
condensation (hydrocarbons) 10 0.01 10"
Coagulation
Brownian 1 10 10
Turbulent (e = 103 cm2 sec"3) 10"3 10"3 10~4
Sedimentation (D . = 10 ym) 10"4 10"8 10"9
r J
Turbulent diffusion ^ fi
(DT= 105 cm2 sec-1) 1 10" J 10"°
Gravitational settling 10~5 10"6 10"7
Deposition on surfaces0 103 (A/V) (A/V) 10"1 (A/V)
WashoutA TO"4 10"8 10"4
* Assuming that Dp-j = 0.05 ym for all particles and that the number density is
105 cm-3.
Assuming that Dpi = 0.5 ym for all particles and that the number density is
102 cm-3.
Assuming that Dpi = 5 ym for all particles and that the number density is
10-1 cm-3.
**
Percentage conversions of 0.3 ppm S0?.
tt
Rate of condensation of 5 ppb of adipic acid.
^The quantity (A/V) represents the ratio of the obstacle surface area and the
volume of interest (A/V has the units cm'1).
Assuming that the raindrops are 1 mm in diameter at a number density of 10~3 cm~3.
-------
54
Because of the approximations made in estimating the order of magni-
tude of the physical processes listed in Table 8, some care must be taken
in drawing conclusions from the results included in this table. The as-
sumptions we made to determine the order of magnitude of the turbulent dif-
fusion term should give lower values than expected (we discuss this subse-
quently). We conclude from these results that for the length scales and
the time scales for which an aerosol model will be developed, heterogeneous
condensation and turbulent diffusion are the mechanisms that play dominant
roles in the evolution of the spatial and size distribution of the aerosol.
In the following subsections, we summarize the equations and numbers used
in the calculation of the values in Table 8.
1. Coagulation
We used Eq. (28) to calculate the loss rate of particles of sizes
ranging from Dpj to Dpj + dDpj that collide with others in the size range
Dpj to Dpj + dDpj for collisions due to Brownian motion, turbulent shear,
or differential sedimentation.
a. Brownian Coagulation
Since most particles are in the size range Dp < 0.1 ym, the rate of
transfer of particles into or out of the size range Dp to Dp + dDp due to
collisions with other particles is greatest for collisions with particles
of radius less than 0.1 ym. For each size range, we used Eqs. (28) and
(32) to calculate the rate of transfer through Brownian coagulation with
y = 1.83 x 10-4 g cm'1 sec'1, k = 1.38 x 10~16 ergs Vs T = 300°K, and
D < 0.1 ym 0.1 ym < D < 1.0 ym D > 1.0 ym
D . = D . = 0.05 ym D . = 0.5 ym D . = 0.05 ym
N. = N. = 105 cm"3 D , = 0.05 ym D , = 5 ym
' J HJ r J
N1 = 102 cm"3 N1 = 10"1 cm"3
N. = 105 cm"3 N. = 105 cm"3
-------
55
b. Turbulent Shear
Similarly, collisions due to turbulent shear occur primarily with
particles of diameter Dp < 0.1 pm. We used Eq. (33) for the calculation
with Eq. (28). The local rate of energy dissipation in the small-scale
turbulence had the value 1000 cm2 sec"3 and v = 0.1 cm^ sec'^. The par-
ticle diameters and the number density were the same as those used for the
calculation of Brownian coagulation.
c. Differential Sedimentation
We used the collision parameter in Eq. (36) in Eq. (28) to calculate
the loss due to differential sedimentation. Because of the rapid increase
in collision rate with particle diameter (^DD), we assumed that Dn- = 10 ym
. ~^ ^J
for this calculation and that Nj = 10"' cm"-3. The values of the particle
diameter and number density in each size range were the same as those used
in the previous calculations.
2. Heterogeneous Condensation
To calculate the rate of loss of particles from a given size range
due to gas-to-particle conversion, we assumed that the loss rate is pro-
portional to the rate of change of particle size in each size range and
the number of particles in the size range. We calculated the loss rate
due to condensation on particles in the size range Dpi to Dpl- + dDpl- from
Lc = Ni D
pi
dD
dt
where we obtained the rate of particle growth from Eq. (15).
rate from a given size range by condensation is then
(50)
The loss
4DMp
LC~ PLRT~Dpi
4aV,
S - YxexplFrD
PL
(51)
-------
56
for the growth of a binary droplet.
We calculated the order of magnitude of the loss for the conversion
of sulfuric acid and adipic acid as indicated in Table 8. The three
numbers listed for ^04 represent the conversion of 50, 10, and 1 percent
of a 0.3 ppm concentration of S02- The other values used in the calcula-
tion were:
D = 0.07 cm2 sec'1,
M = 98 g mole'1,
Ps(TJ = K3 x 10~3 dynes cm~2 (D°yle> 1961),
p|_ = 1.87 g cnr3,
To, = 300 °K,
Yx =1,
a = 52 dynes cnr1 [International Critical Tables (1928)].
We also calculated the rate of loss of particles due to diffusion of
adipic acid to the surface of the particle. Because adipic acid does not
appear to be saturated for reasonable gas phase concentrations, we calcu-
lated a maximum value for the rate of diffusion; that is, we assumed that
the concentration of adipic acid in the droplet was zero, x = 0. We as-
sumed a concentration of adipic acid of 5 ppb, corresponding to roughly a
10 percent conversion of all reactive hydrocarbons. The values of the
other quantities used in the calculation were
D = 0.07 cm2 sec'1,
M = 150 g mole'1s
p°(Tj = 2.6 x 10~2 dynes cnr2,
PL = 0.94 g cm~3,
T = 300 °K.
00
-------
57
3. Turbulent Diffusion
We calculated the values listed in Table 8 for the removal rate of
particles from a unit volume of atmosphere due to turbulent diffusion at
z = 0 from Eqs. (37) and (42) with K2Z = 105 cm2 sec'1 and Y' = 5 x 10'6
cm~^. Unfortunately, the technique we employed to calculate the order of
magnitude of the turbulent diffusion term relies on a smoothed function of
time-averaged data. In the real atmosphere, the distribution of the par-
ticle concentration is not monotonic as we represented it, and the transport
of mass due to diffusion from one volume element to another is far greater
than our calculations indicate. Therefore, in formulating a model, we will
retain the turbulent diffusion term along with the diffusion-controlled
growth term.
4. Gravitational Settling
We calculated the order of magnitude of losses from a unit volume of
atmosphere by gravitational settling for particles of unit density in air
at 20°C using Eq. (39). To compute the gradient of the particle number
density, we used Eq. (47) and the concentration data reported by
Blumenthal et al. (1974), For the data shown in Figure 7, we found the
parameter y' to be 5 x 10~^ cm" .
The data actually apply only to sizes smaller than 0.1 ym, the size
range that contains most of the number density. However, there are little
reliable data on the vertical distribution of larger particles; therefore,
for the purposes of this calculation, we assumed that Eq. (42). can also be
applied to larger particles. We calculated the loss of particles from a
unit volume of air due to sedimentation from Eqs. (39) and (42) at z = 0
or
LGS = 3.2 DJ;N0 (52)
using values of Dp and Ng given previously for each size range.
-------
58
5. Deposition of Particles on Surfaces
To calculate the losses of particles per unit volume per unit time
due to deposition, we used Eqs. (43) and (44). From the data of Chamberlain
(1967), we computed the following deposition velocities:
D = 0.05 ym , q = 2.7 x 10"2 cm sec" ,
-2 -1
D = 0.5 ym , q = 4 x 10 cm sec ,
D = 5.0 ym , q = 1.0 cm sec~ ,
It is apparent from the results of our calculations that losses due
to deposition on surfaces are important only when the obstacle surface
area is large. Such situations might arise in forested areas or in urban
areas where buildings are tall and closely spaced. However, in general,
for the modeling regions of interest, A/V « 1 cm" , and deposition losses
can be neglected in comparison with other processes shaping the aerosol
concentration in the atmosphere.
6. Washout of Aerosols
To calculate the effect of washout on the concentration of particles
of diameter Dp in the atmosphere, we assumed that we can consider the prop-
erties of all droplets to be given by the properties of an average size
droplet of diameter D"r = 0.05 cm. Under this assumption, for "Dr » Dp, we
can rewrite Eq. (45)
-------
59
where all functions outside of the integral are evaluated for the raindrop
of mean diameter Dr. For the purposes of the calculations presented in
Table 8, we assumed that the total concentration of raindrops was 10~3 cm~^
and that the terminal velocity of the raindrops was approximated by
qsr(Dr) = 4m sec . For submicron aerosol particles, we calculated the col-
lection efficiency from Eq. (49); and for aerosol particles with diameters
greater than 1.0 ym, we calculated the collection efficiency from Eq. (48).
We used the molecular viscosity of air at 20°C in Eqs. (47) and (49), and
we assumed that the density of the aerosol particles was that of water.
-------
III CHEMICAL PROCESSES INFLUENCING THE FORMATION
OF AEROSOLS IN PHOTOCHEMICAL SMOG
The physical processes that influence photochemical aerosols mainly
determine the size distribution of the aerosol. Although heterogeneous
condensation could equally well be classified as a chemical process, we
chose to include it in the discussion of physical processes because of its
strong influence on the aerosol size distribution. In this chapter, we
briefly consider those aspects of aerosol chemistry which are important
in the study of photochemical aerosols. Our main objective in this exami-
nation is to summarize what is currently known and to indicate what is un-
known about the chemistry of photochemical aerosols. This discussion is
intended not as an exhaustive survey of photochemical aerosol chemistry,
but rather as an analysis of the chemical information ultimately required
in formulating a dynamic model for photochemical aerosols.
We first summarize experimental measurements of the chemical composi-
tion of the Los Angeles aerosol, with particular emphasis on compounds of
sulfur, nitrogen, and carbon. Then we discuss the apparent rates of con-
version of gaseous sulfur, nitrogen, and carbon to the corresponding par-
ticulate forms. Finally, we speculate on the homogeneous and heterogeneous
reaction mechanisms that might account for the observed rates of atmospheric
conversion and the species found in the particulate phase.
A. THE CHEMICAL COMPOSITION OF THE LOS ANGELES AEROSOL
The 1969 and 1972 to 1973 Los Angeles aerosol characterization studies
provided considerable data on the chemical composition of aerosols in photo-
chemical smog [see, for example, Hidy and Friedlander (1971), Miller et al.
(1972), Friedlander (1973), Hidyet al. (1975)]. On the basis
-------
61
of the data from these studies, one can represent the composition of
typical photochemical aerosols in a IT diagram as in Figure 9. This pie
diagram represents the collected aerosol mass equilibrated to air at less
than 50 percent relative humidity based on 1969 and earlier results. The
upper half of the figure shows secondary constituents, and the lower half,
primary constituents. Although this figure indicates that nitrate comprises
only about 2 percent of the aerosol mass, most data now indicate a nitrate
concentration of 10 to 20 percent. Thus, roughly one-half of the aerosol
mass is a result of secondary conversions of gaseous species. In addition,
compounds of sulfur, nitrogen, and carbon are of prime importance in the
secondary fraction of photochemical aerosols.
In this section, we summarize recent data on the composition of the Los
Angeles aerosol, focusing particular attention on compounds of sulfur, nitro-
gen, and carbon. The objective of the summary is to ascertain typical aerosol
constituencies and, thus, to provide background for a discussion of chemical
processes important in aerosol dynamics.
1. The Spatial Distribution of Sulfate and Nitrate
Sulfur oxide emissions in the Los Angeles basin basically originate
from the following:
Source Percent
Stationary sources (power plants) 49%
Sulfur recovery plants 20
Transportation 15
Petroleum refining 12
Although sulfur oxide emissions appear almost totally as S02, in the atmos-
phere S02 can be oxidized to sulfate ($04). Measured annual averages indi-
cate that sulfate levels are rather uniformly distributed over the Los
Angeles basin and that they range from 9 to 15 yg m~^. Average ambient
S02/S04 ratios vary from about 3 or 4 in coastal areas to about 1.5 to 2
1n the inland areas. Since the concentration of $64 is relatively uniform
-------
r-NO~(2%)
-CEMENT
DUST -
CONSTRUCTION (2%)
Source: Hidy et al. (1975).
FIGURE 9. THE CONTRIBUTION OF VARIOUS SOURCES
TO THE TOTAL AEROSOL MASS IN THE LOS ANGELES BASIN
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63
spatially, this variation in ratio probably reflects the fact that most of
the S02 sources are located in the coastal regions and that S02 is diluted
and dispersed as it is carried eastward. The uniformity of $04 levels
probably indicates a general balance between dilution effects'and the oxi-
dation of S02 to $64. The average sulfate background level in Los Angeles
has been estimated as 4 yg m . Thus, of the typical 9 to 15 yg m~3 annual
average sulfate, only about 5 to 11 yg m~3 originate from man-made sources.
Table 9 shows 24-hour average high-volume sample data from the ACHEX
obtained at different times during the 1972 to 1973 period. Table 10 shows
similar data, obtained from the National Air Surveillance Network (NASN) in
1968, based on 26 sampling periods at each location. These data tend to
confirm the following (Appel et al., 1974):
> Nitrate and sulfate together often comprised more than
15 percent of the total aerosol mass in Los Angeles on a
24-hour average basis.
> Twenty-four-hour average values of sulfate and nitrate in
Los Angeles were on the order of 15 yg m~^ and 10 yg m~3,
respectively.
2. The Diurnal Patterns of Sulfate and Nitrate
Figure 10 shows the diurnal pattern of sulfate, total carbon, ozone,
and $02 at West Covina on 23-24 July 1973. The diurnal behavior of sulfate
parallels that of the other pollutants shown. Figure 11 shows the diurnal
variation of sulfate, nitrate, and NOX for the same location and time period.
In contrast to sulfate, the diurnal behavior of total nitrate mass typically
exhibits its maximum in the morning, close to the maximum in NOX. At first
glance, this observation seems inconsistent with the observation that nitrate
levels increase as the air travels eastward. However, an examination of
the diurnal behavior of the size distributions of sulfate and nitrate pro-
vides some insight into this problem.
-------
Table 9
ACHEX DATA FOR NITRATE AND SULFATE IN THE SOUTH COAST BASIN
1972 TO 1973
(24-Hour Average Values)
Sampling
Location
Harbor Freeway
Dominguez Hills
Pasadena
West Covina
Pomona
1972
1973
Rubidoux
Riverside
No. of
Episodes
2
2
6
5
5
2
3
9
6.3
4.1
6.5
8.2
19.8
7.9
31.5
15.2
Percent
of Mass
5.6%
3.1
9.0
4.5
14.6
4.8
12.5
13.4
5.7
17.8
7.0
21.8
9.6
11.5
10.7
7.7
Percent
of Mass
5.1%
13.6
9.7
12.0
7.1
7.0
4.2
6.8
* Analyses of high-volume samples collected on Whatman-41 filters during
July to October periods.
Source: Appel et al. (1974).
Table 10
NASN DATA FOR NITRATE AND SULFATE
IN THE SOUTH COAST BASIN FOR 1968
(Annual 24-Hour Average Values*"1")
Nitrate
Sulfate
Sampling
Location
Long Beach
Los Angeles
Ontario
Riverside
»
5.7
7.7
9.1
10.2
Percent
of Mass
5.0%
6.0
7.9
8.8
12.7
10.2
9.0
8.3
Percent
of Mass
11. IX
7.9
7.8
7.2
* From air quality data for 1968 obtained L>y the National Air Surveillance
Network and contributing state and local networks, EPAS Research Triangle
Park (1972).
Data were based on the geometric mean of 26 24-hour sampling periods.
Source: Appel et al. (1974).
-------
65
CO
I
75 -,
50-
25-
0
so:
01
O.
O.
0.4-
0.2-
60 n
40-
.a
a.
OL
14 16 18 20 22
22 24 2
6 8 10 12
Time of Day (PST)
Source: Appel et al. (1974).
FIGURE 10. DIURNAL VARIATIONS FOR SULFATE AND SELECTED POLLUTANTS
AT WEST COVINA ON 23-24 JULY 1973
-------
CO
I
E
Dl
50-
40-
30-
20-
10-
• N03
-— so:
i
._.—i
22 24 2 4 6 8 10 12 14 16 18 20 22
£
Q.
Q.
0.
0.
0.
3-,
2-
1-
•
1 1 1
22 24 2
Nfl
— MO
i
4
i
i
6 e
! 1
f
\ 1
0 12 14 16 18 20
i
22
Time of Day (PST)
Source: Appel et al. (1974).
FIGURE 11. DIURNAL VARIATIONS FOR NITRATE, SULFATE, AND NO
AT WEST COVINA ON 23-24 JULY 1973 '
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67
Figure 12 shows the diurnal variations in concentration of the total
nitrate and sulfate masses and of only those particles less than 0.5 ym in
diameter at West Covina on 23-24 July 1973. The total sulfate level reached
a maximum at about 1600 hours, probably as a result of the transport to West
Covina of particles produced earlier in the day in the western regions of
.the basin. The increased fraction of sulfur contained in particles whose
diameters were less than 0.5 ym reflects the fact that freshly produced
sulfate is generally associated with particles smaller than 0.5 ym. From the
curves for total nitrate mass concentration and nitrate mass concentration of
particles smaller than 0.5 ym in diameter, it is clear that the early morning
nitrate peak was associated mainly with particles larger than 0.5 ym. The
decrease in the total nitrate mass concentration was due to transport away
from the site. Although the peak in the curve for nitrate particles smaller
than 0.5 ym is not pronounced, during the late morning and afternoon the
fraction of nitrate particles that are smaller than 0.5 ym increased sub-
stantially. Apparently, later in the day nitrate is produced on particles
smaller than 0.5 ym. The implication is that there may exist two nitrate-
forming mechanisms: one in the early morning associated with particles
larger than 0.5 ym and one later in the day associated with particles smaller
than 0.5 ym. The sulfate and nitrate size distributions in aged aerosols
are rather similar, even though the original mechanisms of incorporation may
be quite different.
Mass median particle diameters determined during the ACHEX for sulfate
and nitrate fall in the ranges of 0.3 to 0.4 ym and 0.6 to 1.2 ym, respectively.
3. Sulfur, Nitrogen, and Carbon Composition of the Los Angeles Aerosol
Table 11 summarizes sulfates nitrate, and solvent extractable organic
concentrations at three sites in the South Coast air basin during 1972.
Table 12 shows additional data obtained from an analysis of 24-hour average
high-volume filter samples during the 1972 program.
-------
oo
I
701
60-
50-
40-
30-
20-
10-
0
NO
SO
I I
22 24
i
2
i
6
I
8
I
10
I
12
I
14
I
16
18 20
I
22
Time of Day (PST)
Source: Appel et al. (1974)
FIGURE 12. DIURNAL VARIATIONS IN SIZE DISTRIBUTIONS FOR SULFATE
AND NITRATE AT WEST COVINA ON 23-24 JULY 1973
cr>
oo
-------
Table 11
SULFATE, NITRATE, AND SOLVENT EXTRACTABLE ORGANIC CONCENTRATIONS
AT THREE SITES DURING 1972
(In
r3)
69
Site
Pasadena
April 1972
Summer/Fall 1972
Total
80
69.1 ± 7.7
Sulfate
9.
6.
45 ±
11 ±
1.41
1.6
0.
5.
Nitrate
69
76
± 0.097
± 0.44
Solvent
Extractable
Organic*
3.3 ± 0.2
Riverside
April 1972
Summer/Fall 1972
Pomona
October 1972
154 ± 5 11.2 ± 1.7
110 ± 12.7 8.22 ± 2.1
126.4 ± 14.4
9.71 ± 2.9
0.486 ± 0.075 5.79 ± 0.58
16.6 ± 1.4 4.7 ± 0.2
18.0 ± 1.6 5.4 ± 0.4
* Cyclohexane extractable.
Source: Hidy, et al. (1975)
Table 12
HIGH-VOLUME SAMPLE CONCENTRATIONS OBTAINED
(In yg m~3)
4 OCTOBER 1972
Sample
Fasadena
Rmona
N03
so]j2
CEO*
NH+
(NO; + so!)/NHlj
^ s t
Mass
N0~/Pb
S0'2/Pb
NOo/mass
SO^ /mass
7.19
3.9
3.1
4.17
2.7 (3
69.5
4.73
2.56
0.103
0.056
± 0.54
± 0.1
± 0.2
± 0.4
.2)
± 7.6
13.1 ± 1.
6.2 ± 1.
4.8 ± 0.
6.39 ± 0.
3.0 (3.2)
137.0 ± 15.
7.66
3.63
0.096
0.044
4
5
4
32
0
* Cyclohexane extractable organics.
Source: Hidy, et al. (1975)
Riverside
15.4 ± 1.2
5.8 ± 1.4
4.8 ± 0.2
6.61 ± 0.33
3.2 (3.2)
134.0 ± 15.0
8.7
3.28
0.115
0.043
-------
In the ACHEX, investigators found that the predominant compounds of
sulfate and nitrate are (NfykSCty and N^NOs, respectively (Appel et al ,
^ _i_
1974).* Table 13 compares the observed levels of NH4 in the aerosol with
the amounts calculated, assuming that all the sulfate and nitrate were pre-
sent as ammonium salts. For the South Coast air basin, the observed NH^
ranged from 62 to 103 percent of the calculated values, with an average of
85 percent. These data suggest that, except near important sources of sul-
fate, ammonium salts are the predominant sulfate and nitrate compounds.
The general level of NH^ is about 10 yg nr3. The main source of gaseous
NH3 in Los Angeles is feed-lot emissions. For the data in Table 12, the
measured NH4 is roughly equivalent stoichiometrically to that needed to
balance Sfy and NO^ for ammonium salts.
Aerosol organics were identified in the ACHEX (Hidy et al., 1975).
Table 14 summarizes organic compounds identified at Pasadena on 22 September
1975 and at West Covina on 24 July 1974. The organics can be classified
according to di functional aliphatic compounds, monofunctional aromatic com-
pounds and oxygenated compounds derived from terpenes. The compounds listed
in Table 14 represent secondary organics (not listed). Grosjean and Fried-
lander (1975) estimated that secondary organics contribute 80 percent—and
in some cases as much as 95 percent—of the total aerosol organics. Subse-
quently, we discuss mechanisms that might explain the occurrence of many of
the compounds in Table 14.
4. Summary
In this section, we have summarized some available data relating to
the chemical composition of the Los Angeles aerosol. Although a great deal
concerning the composition of photochemical aerosols is still unknown, sev-
eral general conclusions can be drawn on the basis of the data obtained to
date.
* Craig et al. (1974) identified seven separate chemical species of sulfur in
aerosol samples from California: $03, S04, S02, SOJ5, S^, and two kinds of
sulfides. However, sulfates were generally the dominant species.
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71
Table 13
A COMPARISON OF THEORETICAL AND EXPERIMENTAL AMMONIUM VALUES*
Sampling
Location
Harbor Freeway
Pasadena
West Covina
Pomona
1972
1973
Riverside
Rubidoux
Dominguez Hills
No. of
Samples
2
6
4
5
2
7
3
2
Expected NH4
Based on_
N03 and $04
Present^
4.0
4.0
10.3
8.9
6.6
7.9
15.5
7.9
Observed
as Percent of
Expected
103%
82
76
94
75
93
73
62
* Analyses of high-volume samples collected on Whatman-41 filters.
* Assuming the composition (NH4)2S04 and NH4N03.
Source: Appel et al. (1974).
-------
72
Table 14
SECONDARY AEROSOL ORGANICS IDENTIFIED IN THE ACHEX
Di functional Aliphatic Compounds
(1) X - (CH?) - Y
n
X
COOH
COOH
COOH
COOH
or
COH
COM
COH
COOH
or
COH
COH
COOH
n = 3, 4, 5
Y
CH2OH
COH
COOH
CH2ONO
CH2ON02
CH2OH
COH
COONO
CON02
COONO
COON00
COOH CH2ON02
(2) Others
CH2OH - CH = C(COOH)CHO
CH2OH - CH2 - CH = C(COOH) - CHO
CHO - CH.= CH - CH(CH3)CHO
CH2OH - CH = CH - CH = C(CH3)CHO
Monofunctional Aromatic Compounds
(1) CgH5 - (CH2) - COOH , n = 0, ls 2, 3
(2) C2H5CH5OH
Sources: Hidy et al. (1975).
Schuetzle et al. (1973).
-------
73
About 50 percent of the aerosol mass can be attributed to gas-to-
particle conversion processes. Of the fraction of the aerosol that is
secondary material, the important constituents are sulfate, nitrate, and
organics. Since there are no major primary sources of sulfate and nitrate,
except possibly for motor vehicles, the quantities in the aerosol are the
result of gas-to-particle conversions. It is more difficult to estimate
the relative contributions of primary and secondary sources to particulate
carbon, although Grosjean and Friedlander (1975) estimated that organics
resulting from conversion of photochemical products represent about 80
percent, and sometimes as high as 90 to 95 percent, of the total particulate
carbon (in the submicron size range). Under the assumption that NO^ and
$04 are present as ammonium salts, the NH4 level can be calculated. Measure-
ments indicate that ammonium salts may account for as much as 90 percent of
the nitrate and sulfate. Considerably less is known about the species com-
prising the organic particulate fraction than about sulfate and nitrate.
A profile of a "typical" submicron photochemical aerosol particle
might show the following composition:
> Ammonium sulfate
> Ammonium nitrate
> Oxygenated organic species
> Water
> Primary material (e.g., leads salt).
B. RATES OF CONVERSION OF SULFUR, NITROGEN, AND CARBON TO AEROSOL
In representing the rates of conversion of sulfur, nitrogen,
and carbon to the particulate phase, it is useful to define a measure of
the relative amounts of the species in the gaseous and particulate phases
at any time and location. Two ways of representing this distribution be-
tween gaseous and particulate phases have been used. The first is the so
called distribution factor, which is the ratio of the mass of the species
in the particulate phase to the total mass of the species in the gaseous
-------
74
and participate phases. For example, one can define the distribution
factors for sulfur, nitrogen, and carbon as follows (Grosjean and Fried-
lander, 1975):
> Sulfur distribution factor
5 [S02] + [S0~]
where
[SO^] = particulate sulfate concentrations, expressed
as S02, in yg
m
-3
[$02] = gas phase S02 concentrations, in yg m
> Nitrogen distribution factor
[N0~]
f N =
-3
[NO 1 + [NOI]
X 0
where
[N05] = particulate nitrate concentration, expressed
as N02> in yg m~3s
[NOX] = gas phase NO + N02 concentration, expressed
v;a$:N02» in yg m~3.
Carborr""distM4:!^ffiF factor
:5'c- icg] + icp]
where
-------
75
[Cp] = particulate organic concentrations in \\g m~°,
as carbon,
[Ca] = gas phase reactive hydrocarbons, converted
-3
from ppm CH. to carbon in pg m = total
hydrocarbons (including oxygenates), as CH4
- ([CH4] + [C2H2]).*
(One might wish to restrict [Cg] to only aerosol-forming
hydrocarbons. However, available data, both on which hydro-
carbons lead to aerosol formation and on the concentrations
of these hydrocarbons, are incomplete.)
The alternative to using the distribution factor for representing
the gaseous-particulate fractions of species is simply the ratio of the
mass of the species in the particulate phase to that in the gaseous phase.
For example, we can define the following ratios:
9c =
9 "
9r =
In g§ and g^, the concentrations can be expressed in terms of SC^ and N02,
or simply sulfur and nitrogen. The mass ratios are related to the distribu-
tion functions by relations such as
9S
f „ =
9S + 1
* Grosjean and Friedlander did not measure the concentration of benzene,
which is also unreactive, although if it were known, its concentration
would also be subtracted from that of the total hydrocarbons.
-------
76
thus, data reported in terms of §5 can be readily converted into fs, and
vice versa. If one is interested in the degree of chemical conversion, the
distribution factor is a more revealing measure than the mass ratio.
There are two potential sources of data on the rates of conversion of
sulfur-, nitrogen-, and carbon-containing species to the particulate phase:
ambient monitoring and laboratory studies. In this section, we confine our
attention to ambient monitoring data because there are virtually no avail-
able laboratory data available from which the desired ratio of conversion
can be inferred.
1. Rates of Sulfur Conversion
Figure 13 shows the diurnal patterns of the ratio of particulate sulfur
to total gas phase sulfur for four locations during four periods in 1973.
The sites,which are presented in their order from west to east., include one
source-enriched site (Dominguez Hills) and three receptor sites. Close to
a strong S02 source, gs was about 0.2, whereas at the receptor sites it
reached values as high as 0.6. Ignoring S02 losses, we found that g^ = 0.6
corresponds to a conversion of gaseous $62 of about 35 percent. On the basis
of the travel time from the source area to the receptor areas, one can esti-
mate an approximate rate of conversion from data as those given in Figure 13.
Roberts and Friedlander (1974) estimated gas-to-particle conversion
rates for sulfur on the basis of measurements of the particulate to gas phase
sulfur ratio near major stationary sources and downwind of these sources
along known air trajectories. They assumed that the conversion of S02 to
particulate sulfate is a first-order process in S02 and that [S02]/[Sj],
where [Sj] is the total concentration of sulfur, is independent of both
height above the ground and time and depends only on distance along a tra-
jectory. Then the first-order rate constant for the conversion of S02 could
be estimated from the following equation:
-------
77
0.4-,
to 0.2
01
4-5 OCTOBER 1973
1 1 1
I 1 I i 1 i I I i
0.4-n
oo
01 0.2
WEST COVINA
23-24 JULY 1973
1
I I 1 I I
1 1 1 I i 1 1
0.4-
a? 0.2 -
0
POMONA
16-17 AUGUST 1973
1 1 i i 1 1
1 I
1 1
0.4 -,
0.2-
0
RUBIDOUX
24-25 SEPTEMBER 1973
i i i i i i r 11 i i I I
22 24 2 4 6 8 10 12 14 16 18 20 22
Time of Day (PST)
Source: Appel et al. (1974).
FIGURE 13. DIURNAL VARIATIONS IN THE RATIO
OF PARTICLE TO GAS PHASE SULFUR
-------
78
start end
end start
[S0]
\ ^
H[S02] )
aW'
I ST
f H[S02]
dT
(53)
where
"start" and "end"
AT
va and vg
WST
WST
a
the beginning and termination,
respectively, of an air trajectory,
the duration of time of the tra-
jectory,
the deposition velocities for loss
of aerosol sulfur and S02, respec-
tively, to the ground,
the mixing height,
the area source emission rate for
total sulfur,
the area source emission rate for
motor vehicles only,
the ratio of aerosol sulfur to
total sulfur in auto exhaust.
To determine the value of k for a particular trajectory, Roberts and
Friedlander solved Eq. (53) iteratively by first assuming a value of k and
using the hourly average measured values of [SC^J and [Sy] to evaluate the
integral and to compute [SC^l/fSj] at the end of the trajectory. They then
compared the calculated value of [SC^l/tSj] at the end of the trajectory
with the measured value and adjusted k until a match was achieved.
Table 15 shows the k values that Roberts and Friedlander calculated
for three days in July 1973. The Alamitos Bay area contains two large
power plants, and the El Segundo area has two power plants and a refinery.
As indicated, an initial value of 0.97 was assumed for the [S02]/[Sj] ratios
-------
Table 15
PSEUDO-FIRST-ORDER RATE CONSTANTS
FOR THE LOS ANGELES BASIN*
79
Date Time of Arrival at
(1973) Pasadena (PST)
July 10 1300
1400
1500
1600
July 25 1400
1500
1600
July 26 1200
1300
1400
1500
(percent per hour)
1.2
3.0
9.0
13.0
12.8
8.2
8.8
4.3
5.6
7.6
4.7
Starting
Location
El Segundo
El Segundo
El Segundo
El Segundo
Alamitos Bay
El Segundo
El Segundo
Alamitos Bay
Alamitos Bay
Alamitos Bay
Alamitos Bay
* Assuming that
3[S00]
[soj
= 0.97
start
Source: Roberts and Friedlander (1974).
-------
80
near these two sources. The calculated values of k vary considerably, indi-
cating a dependence of k on other meteorological and chemical parameters in
the atmosphere.
It is of interest to determine whether a correlation exists between the
rate of conversion of S02 to sulfate and other quantities in the photochemical
smog system. Since ozone is generally taken as a measure of the intensity of
photochemical smog, one can examine the dependence of the conversion on ozone
level. Figure 14 shows a plot of Sp/Sg versus 63 for several sampling periods
at three locations. In this figure, Sp refers only to particulate sulfur in
particles smaller than 0.5 ym in diameter. As this figure indicates, an ap-
proximate correlation appears to exist between Sp/Sg and the 0^ level.
As we discuss in the next section, one path proposed for the oxidation
of S02 is that of reaction with a product of the reaction of ozone and ole-
fins. Assuming that the concentration of the product responsible for the
oxidation is proportional to [(^HOlefin], the ratio of Sp (less than 0.5 ym)
to Sg can be plotted as function of [03][Olefin] for monitoring data. Be-
cause the total gas phase olefin concentration was not available, this corre-
lation must be presented as Sp/Sg versus the product of the 03 concentrations
and the total nonmethane hydrocarbon concentration (assuming that olefin
levels are proportional to total hydrocarbon levels). Figure 15 shows a
correlation of this type prepared from the ACHEX study. The correlation
does not appear to be superior to that constructed on the basis of 03 alone.
2. Rates of Nitrogen Conversion
Figure 16 shows the diurnal patterns of the ratio of particulate nitro-
gen (Np) to total gaseous nitrogen (Ng) at three locations on three days.
The Np/Ng ratios are generally lower than those of Sp/Sg, although on
5-6 September 1973 in Rubidoux, values of Np/Ng exceeding 0.6 were observed.
There appears to be a stronger variation of Sp/Sg with location in the basin;
this is consistent with the observations of the spatial variation of the
total particulate mass of sulfate and nitrate.
-------
0.3 -
0.2-
in
o
V
oo
cn
0.1 -
0
n©
i
0.1
9
Source: Appel et al. (1974).
©
0.2 0.3
03--ppm
Q
WEST COVINA
. o 7/23-24/73
a 7/24-25/73
° 7/26/73
POMONA
® 8/16-17/73
RUBIDOUX
N> 9/18-15/73
i
0.4
I
0.5
FIGURE 14. SCATTER DIAGRAM OF THE SULFUR CONVERSION RATIO
IN PARTICLES SMALLER THAN 0.5 ym IN DIAMETER AND OZONE
oo
-------
o.s r-
0.2
0.1
a a
so
0.68
AA
J_
WEST COVINA
O 7/23-24/73
S 7/24-25/73
n 7/26/73
POMONA
O 8/16-17/73
RUBIDOUX
•
-------
83
0.4 -,
0.2 -
0
West Covina
July 26, 1973
i i
tn
E-
\_x
p.
0.4 _,
0.2 -
Pomona
Aug. 16-17, 1973
T T
i r
H
fe
0.6
0.4 -
hD
0.2 -
Rubidoux
Sep. 5-6,
0_
1 I
22 24
1973
ill i i i i i
2 4 6 8 10 12 14 16 18 20 2
Time of Day (PST)
Source: Appel et al. (1974)
FIGURE 16. DIURNAL VARIATIONS IN THE RATIO OF
PARTICLE PHASE TO GAS PHASE NITROGEN (NNQ + NNQ ).
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84
Less is known about the rate of conversion of NOX to nitrate than
about that of S0£ to sulfate. Appel et al. (1974) explored the relationship
between Np/Ng and ozone levels at several locations during 1973; Figure 17
presents their results. Although a correlation is not evident, the overall
trend of the data suggests that particulate nitrate levels may be inversely
related to 63 levels. The data in Figure 17 might be explained on the basis
of a nitrate conversion mechanism that is most efficient when photochemical
smog intensity is low. We have already seen that there appear to be two
mechanisms for nitrate conversion: one for early morning and one for after-
noon. The early morning mechanism, involving mainly particles larger than
0.5 ym in diameter, may involve absorption of NOX into liquid droplets. The
wide range of Np/Ng values at the low 63 levels of Figure 17 might reflect
the effect of relative humidity and early morning absorption of gaseous NOX.
3. Rates of Carbon Conversion
Table 16 presents total particulate concentrations, organic carbon
fractions (the fraction of the total particulate weight due to organics), and
the organic distribution factors (frj determined on six days in 1973 by Gros-
jean and Friedlander (1975). As indicated in this table, their results show
that the measured organic carbon fractions (OCF) were always substantial,
reaching a level as high as 0.43. Figure 18 presents the hourly variations
of organics, total particulate matter, bscat, fc> [03], and reactive hydro-
carbons on 25 July 1973. Grosjean and Friedlander observed two maxima in
the OCF and f^ curves. The second peak is closely related to [03] and is
probably the result of the conversion of gas phase hydrocarbons to aerosols.
The first peak in OCF and f^ probably reflects a more direct conversion of
primary emissions.
In summary, although only about 3 percent of the organic gases are con-
verted to aerosols, this material comprises about 30 percent of the total
aerosol mass. The estimated rates of conversion of total organic gases is
thus less than 2 percent per hour. Since most of the secondary organic
-------
ro
o
0.5 i
0.4 -
0.3 -
0.2 _
0.1 -
0 -
o
o
£2
O O
© D©
I
0.1
Source: Appel et al. (1974).
I
0.2
I
0.3
Np(TF)/Ng
WEST COVINA
O 7/23-24/73
ED 7/24-25/73
0 7/26/73
POMONA
O 9/16-17/73
RUBIDOUX
•$• 9/5-6/73
I
0.4
0.5
FIGURE 17. SCATTER DIAGRAM OF THE RATIO OF PARTICLE TO GAS PHASE NITROGEN
AS A FUNCTION OF OZONE LEVEL
-------
Table 16
DIURNAL VARIATIONS OF TOTAL PARTICIPATES (TP)--IN vg m-3—
ORGANIC CARBON FRACTION (OCF),
AND ORGANIC CARBON DISTRIBUTION. FACTOR (fc)
May 16 June 19
TP
99
123
116
183
180
172
130
119
117
87
84
TP
225
179
149
136
104
OCF
0.255
0.248
0.050
0.160
0.270
0.248
0.215
0.274
0.240
0.090
..
July 10
OCF
0.266
0.221
0.164
0.220
0.131
x 102
2.5
3.0
0.6
2.9
4.8
4.3
2.4
3.1
2.9
0.8
—
x 102
3.3
2.35
1.55
2.1
1.0
TP
158
152
128
97
89
88
108
144
119
96
TP
106
148
154
116
101
75
OCF
0.338
0.367
0.292
0.535
0.398
0.394
0.430
0.198
0.159
0.202
July 12
OCF
0.154
0.182
0.123
0.267
0.205
0.112
fc2
x 10^
2.4
2.9
3.4
5.8
3.9
3.7
4.0
2.4
2.0
2.15
fc2
x }Q*
1.4
2.35
1.75
3.0
2.1
0.9
TP
126
128
144
153
168
238
214
296
303
232
184
131
90
46
TP
52
103
192
61
53
OCF
0.178
0.221
0.241
0.343
0.212
0.058
0.151
0.277
0.350
0.428
0.317
0.158
0.281
0.141
October
OCF
0.229
0.112
0.156
0.177
0.108
S
x 10^
2.1
1.6
2.0
3.65
2.9
0.9
2.1
3.85
5.15
6.15
4.95
2.0
2.. 3 5
0.6
17
fc2
x 10Z
0.42
0.79
2.05
0.88
0.66
Note: The sampling periods were as follows:.
,, May 16 1 hour, 7:00 to 18:00 (11 samples).
> June 19 1 hour. 6:30 to 16:30 (10 samples).
> juiy 10 1 hour, 12:30 to 17:30 (5 samples).
> July 12 8:00 to 12:00, 12:00 to 14:00, 14:00 to 16:00,
16:00 to 18:00, 18:00 to 20:00, and 20:00 to
24:00 (6 samples).
> July 25 0:00 to 6:30, then 1 hour, 6:30 to 17:30,
17:30 to 19:30, and 19:30 to 24:00 (14 samples).
> October 17—8:00 to 10:00, 10:00 to 12:00, 12:00 to 13:00,
13:00 to 1S:00, and 15:00 to 17:00 (5 samples).
Source: Grosjean and FHedlander (1975).
-------
87
L 0.8
U 0.6
L0.4 o"
6:30 12:30 16:30
Time, PDT
Source: Grosjean and Fried!ander (1975)
20:30
24:00
to
o
en
D
i
I
FIGURE 18. HOURLY VARIATIONS OF bscat, ORGANIC DISTRIBUTION FACTORS (f ),
OZONE, TOTAL PARTICULATE MATTER (TP), GASEOUS c
HYDROCARBONS (GRH), AND ORGANICS.
-------
species identified in the aerosol are difunctional aliphatic and monofunc-
tional aromatic compounds, it is possible to identify likely olefinic pre-
cursors, as discussed later.
C. POSSIBLE CHEMICAL REACTIONS THAT INFLUENCE THE EVOLUTION
OF PHOTOCHEMICAL AEROSOLS
Up to this point, we have reviewed the observations made by several
investigators on the chemical composition and rates of formation of photo-
chemical aerosols. The objective of this review has been to provide a
basis upon which to determine the chemical processes responsible for photo-
chemical aerosol formation. In this section, we discuss the current under-
standing of these chemical processes. The treatment is divided into sulfate
formation, nitrate formation, and the generation of organic compounds of
low volatility.
1. Sulfate Formation
There are basically two paths by which S02 can be converted to partic-
ulate sulfate:
> Gas phase reactions lead to the formation of $03, which
rapidly combines with water to give H2S04- The H2S04
formed in the gas phase can then dissolve in existing
droplets or serve as embryonic nuclei for molecular
clusters of water molecules.
> Sulfur dioxide dissolves in aerosol droplets, wherein
it is subsequently oxidized to sulfate. The oxidation
requires a catalyst, and two types of catalysts have
been identified and studied—dissolved NH3 and metal
salts.
-------
89
a. Gas Phase Formation of Sulfate
Surveys of gas phase atmospheric reactions involving S0? have been carried
out by Urone and Schroeder (1969), Katz and Gale (1970), Bufalini (1971),
Urone et al. (1971), and Calvert (1974). Compared with the wealth
of available laboratory smog chamber data on hydrocarbon-NO systems,
}\
there are at present relatively few studies on irradiated mixtures of hydro-
carbon-NO -SQ9 systems (Wilson and Levy, 1970; Wilson et al., 1971; Calvert,
/\ £-
1973; Smith and Urone, 1974). The lack of smog chamber studies involving
SOp can apparently be attributed to two factors. First, investigators have
generally felt that it is necessary to understand the chemistry of hydrocarbon-
NO mixtures before proceeding to the more complex hydrocarbon-NO -S09
X X £.
systems. Second, when S09 is added to hydrocarbon-NO systems, irradiation
L- y\
often results in pronounced aerosol formation, which has been viewed as un-
desirable in laboratory studies. Thus, even at this time, not enough
laboratory data are available to test thoroughly proposed mechanisms for SOp
photooxidation chemistry. Some uncertainty still exists as to the predominant
paths for homogeneous oxidation of S0? in the atmosphere (Cox and Penkett,
1971; Sidebottom et al., 1972; Davis et al., 1974; Calvert, 1974;
Wood et al., 1974).
It has been suggested that heterogeneous paths may account for the for-
mation of most of the photochemical sulfate aerosol observed in the atmosphere
under certain conditions (Goetz and Pueschel, 1967; Urone et al., 1968). How-
ever, if, as it is generally agreed, SO- is primarily responsible for the
heterogeneous formation of sulfate, the homogeneous oxidation of SO^ to SO-
becomes a key step in the sulfate formation process. In addition, smog
chamber experiments have shown that significant rates of S02 oxidation can
be achieved in the absence of any apparent heterogeneous paths. Once SO^ is
produced, nuclei can be formed via the following reactions:
S03 + H20 -» H2S04
H2S04 - (n - 1)H20 + H20
-------
90
In the absence of foreign nuclei, the acid embryos represented as
nH20 are formed initially as very small particles, on the order of 10 A
in size. With other aerosol particles present, it is likely that molecules
of H2$04 will condense on existing particles as opposed to undergoing
heteromolecular nucleation with water molecules.
The Photochemistry of SO,,. The photooxidation of SO,, alone or in mix-
tures of SOp and oxygen proceeds slowly relative to observed atmospheric
rates (Hall, 1953; Gerhard and Johnstone, 1955; Renzetti and Doyle, 1959;
Rao et al., 1969; Okuda et al., 1969). We will not review the photochemistry
of SOp here. The interested reader is referred to Rao et al. (1969),
Okuda et al. (1969), and Bufalini (1971) for details.
SOo-NO -Air Mixtures. The principal reactions occurring in the
^ ^Q •--—-••
S09-N0 -air system are listed in Table 17. Although Reaction 1 cannot
C. X
compete with the primary ozone formation reaction O+O^+M+O^+M
in the depletion of oxygen atoms, Reaction 1 is apparently the most
important SOp oxidation reaction in SOp-NO -air systems. Several invest-
igators have suggested that Reactions 4-6 might be important S02 removal paths.
Although Jaffee and Klein (1966) reported a rate constant for Reaction 5
of 3.7 x 10"3 I mole"1 sec'1 at 24°C, data reported by Boreskov and
Illarionov (1940) indicates that the rate constant is almost six orders of
magnitude smaller. Sidebottom et al. (1972) estimated that Reaction 5
should have a low activation energy and a high preexponential factor; how-
ever, more recent data of Daubendiek and Calvert (1974) set an upper limit
on the rate constant at 25 x 10"5 ppm'1 min"1. Daubendiek and Calvert (1973)
-8 -1
also indicated that the rate constant of Reaction 6 is 1.7 x 10 ppm
nrin~ . Reaction 7, suggested by Wilson and Levy (1972), has not been
substantiated, although Urone and Schroeder (1971) obtained a white crystal-
line solid with empirical formula SN05 in their experiments with S02 and N02
in dry air. Rate constant data for reactions such as Reaction 7 are not
available and would probably be difficult to estimate. In summary, Reactions
4 through 7 apparently play an unimportant role in the S09-N0 - air system,
-------
Table 17
REACTIONS IN THE SCL-NO -AIR SYSTEM
c. X
Rate Constant at
No.
1.
2,
3.
4.
5.
6.
7.
8.
9.
10.
Reaction
0(3P) + SO- + M + SO- + M
L. *3
o + so2 + 3so2 + so3 + so2
°3 + S02 * S03 + °2
S02 + N02 + S03 + NO
2332
SO + NO -, SO + NO
C- L- \J \J i. *T
S09 + N0v •> (SO-) (NO ) solid
£ A O X
so + o3 -»• 3so2 + o2
SO + 0- •* S09 + 09
O L. L.
SO- + 0 -»• SO. + Q9
O L, £.
25°C, ppm~l min~
3 x 10~5*
1 x 10"3*
3 x-10"7
9 x ID'14
25 x 10"5
1.7 x 10"8
—
0.1
no
7.3 x 104
Reference
Garvin and Hampson (1974)
Mulcahy et al. (1967)
Davis et al. (1974)
Boreskov and Illarionov (1940)
Daubendiek and Calvert (1973)
Daubendiek and Calvert (1973)
Levy et al. (1970)
Levy et al. (1970)
Garvin and Hampson (1974)
* -2 -1
ppm min
-------
92
Reactions 8-10 participate in the reconversion of SO and SO., to SO
Urone and Smith (1974) observed a decrease in SOp oxidation rate"at high
initial N02 levels. Reaction 10 may be rapid enough to account for these
observations.
SO^-Hydrocarbon-Mixtures. The direct reaction of S00 and hydro-
£. d.
carbons tias been studied since 1950 (Dainton and Ivin, 1950). Recently,
Badcock et al. (1971) conducted a series of experiments on the S02~hydrocarbon
system in which they used laser excitation to populate the excited triplet
state of S02 (see also Sidebottom et al., 1971). They suggested that the
S02-hydrocarbon reaction is either an insertion of the form
3S02 + RH -*• RS02H (11 a)
or a free radical abstraction involving a hydrogen atom:
3S02 + RH -> S02H + R . (lib)
Badcock et al. (1971) and Sidebottom et al. (1971) determined the rate con-
stants for Reactions (11 a) and (lib) and for the collisional deactivation
3S02 + RH ->• S02 + RH . (12)
Typical rate constant values for paraffins and olefins are
k,, = 512 ppnT1 min"1 (ethane) and 2.08 x 105 ppm"1 min"1 (propylene).
A recent mass spectrometric study by Penzhorn et al. (1973) provides
additional insight into the products of the S02-alkane reaction. In addi-
tion to the sulfinic and sulfonic acids identified by others (Dainton and
-------
93
Ivin, 1950), a number of adducts, including RS02R, RSR, RSOsR, and RS02SR,
were found in the products. Penzhorn et al. suggested that an initiation
step of the form of Reaction (lib) followed by
R- + S02 ->• RS02
and other propagation steps dominate the process.
S0?-N0 -Hydrocarbon-Air Mixtures. The main S09 oxidation reactions
^ ^ _.,__._._,_,__,__ ^,
(in addition to those in Table 17) in the photochemical smog system are
listed in Table 18. The products of the reactions in Table 18 are SCL, ROSCL,
or RCLSCL. All of the reactions are exothermic and are favored thermodynamically.
Most of the reactions in Table 18 have rates that are sufficiently rapid to
account for observed rates of SOp oxidation in photochemical smog (Roberts, 1975).
It has been observed that SCL is efficiently oxidized in the
presence of ozone and olefins (Cox and Penkett, 1971, 1972;
McNelis, 1974). Reactions 18, 19a and 19b represent three possible
reactions that might occur between SO,, and initial products of ozone -
olefin reactions. Based on the observations of Cox and Penkett and
McNelis it is not possible to ascertain whether the S02 oxidation is
due to reaction with the immediate ozone - olefin product or reaction
with a subsequent decomposition product such as OH.
The radical addition products, such as ROS02, should react rapidly
to generate sulfuric acid, peroxysulfuric acid, alkyl sulfates, and
mixed intermediates such as HOS02ON02. All of these species can then
ultimately lead to aerosol sulfate.
-------
94
Table 18
S02 OXIDATION REACTIONS IN PHOTOCHEMICAL SMOG
Rate Constant
No. Reaction at 25°C, ppm min Reference
13
14
15a
15b
16a
16b
17
18
19a
19b
so2
so2
so2
so2
so,
2
S09
2
RO
/
+
+
+
+
+
+
OH •>
OH 4-
H02
H02
R09
2
R09
2
+ so2 ->
\
CH2— CH. 4-
CH2
CH£
00
L
+ SO
=0-0 +
HOS02 2.65 x 103 (162°C) Gordon and Niloc (1975)
M + HOS02 + M 1.3 x 103 (pseudo second-order) Davis (1974)
+ S03 + OH 1.3 Payne et al . (1973)
-?+
•*• S02H02 6.2 x 10 not measured
+ SO- + RO 1.5* not measured
3
-> S00R00 6.2 x 10"2 not measured
2 2
ROS02
S00 -> S00 + 2CH00
232
2 -> S03 + CH20
S02 -> S03 + CH20
t An estimate based on Calvert's suggestion that Reactions 15b and 16b should
be about 1/8 as fast as Reactions 15a and 16a.
* An estimate based on the assumption that Reaction 16a should proceed about
30% faster than Reaction 15a at comparable concentrations.
-------
95
b. Sulfate Formation in Solution
The catalytic oxidation of S09 in solution is known to be promoted
+3 +2
by ammonium ions and metal ions, such as Fe and Mn . In such oxidation,
the role of NH. is essentially to buffer the solution to permit effective
absorption of SCL to form sulfurous acid and sulfite ions. The solution
chemistry of this system seems to be reasonably well understood (Scott and
Hobbs, 1967; Miller and dePena, 1971).
The important steps in the equilibrium chemistry of the SCL-hLO-NHL
system are given in Table 19.
Sulfate forms according to:
S03 + \ °2 * S04 ' (20)
Assuming that there is an excess of dissolved oxygen, we can represent the
rate of formation of sulfate ion by
bU
r
[b
dt 20 3
Miller and dePena (1971) estimated that k2Q = 3.1 x 10 sec . Ammonia
is important because it strongly governs the formation of SCL- In Table 19
we present the chemical equilibria for the SO?-NH--liquid water system,
including COp equilibria. Scott and Hobbs (1967) showed that as the
concentration of SOT increases in a droplet, the concentration of hydrogen
^ .j. =
ions increases. The increase in [H ] causes [SCL] to decrease, and the
_ *^ —
rate of production of SO^ thus decreases. This means that [S0~] approaches
a limiting value as the reaction proceeds. Calculations performed by Scott
flnd Hobbs indicate that for typical atmospheric conditions, the initial
concentration of SO^ is 500 times greater when NH3 is present than when it
-------
96
Table 19
CHEMICAL EQUILIBRIA IN THE S02-NH3-H20-C02 SYSTEM
Value of the Equi-
Equilibrium Constant librium Constant
Reaction Expression at 25°C
(S02)g
so2
(NH3)g
NH3
(C02)g
co2
H20 £ H+
+ H20 + S02
• u r\ . M
rlpU •*• n
HS03 Z H+
+ H90 £ NH,
^— O
• H20 t NHj
+ H20 ? C02
-> +
' H20 * H
HC03 * H+
+ OH-
' H20
+ HSO-
+ S03
' H20
+ OH"
' H20
+ HC03
+ C03
\, = [H+][OH"]
Khc = [S09 ' H,0]/pcn
hs 2 2 S02
Klc = [H+][HSO"]/[SO? ' H90]
1 O O L. L.
K2s = [H+][S031/[HS03]
Kha = [NH3 ' H.Ol/p^
Kla = [NHj][OH"]/[NH3 ' H20]
Kk^ = [C09 ' H00]/prn
he i
-------
97
is absent. Thus, based on Reaction 20 above, the initial rate of formation
of S04 is also increased by a factor of 500 in the presence of NH3. Not
only does the presence of NH3 increase the rate of formation of SO^, but
also the concentration of 504 formed after 24 hours in the presence of NH3
is two orders of magnitude greater than in its absence.
Ozone is quite soluble in water. Thus, dissolved 03 and S02 in water
droplets might lead to enhanced oxidation rates of S02- Penkett (1972)
found that oxidation of S02 in air at 7 ppb absorbed in water droplets, where
ambient 03 was at 5 pphm, was as fast as 13 percent per hour.
In studies in which NH3 was added to a mixture of air, S02, and sul-
furic acid embryos, Friend (1966) found a rapid production of large parti-
cles of ammonium sulfate. The following mechanism explains the experimental
results:
NH3 -> NH4 HS04 ' nH20 , (21)
NH.HSO, • nH?0 + NH, -> (NH4)9 SO, • nH?0 , (22)
3
2NH3n
H S02 -
I- H20 H
}
h 2 °2
MH4
Catalyst'
(NH4)2S04 . (23)
Reactions 21 and 22 represent the conversion of acid embryos to salt
embryos. The solution present in the salt embryos is the medium necessary
for the catalytic oxidation of S02 represented by Reaction 23.
Kiang et al. (1973) also considered the nucleation processes involved
in aerosol formation and the possible chemical reactions associated with
the formation of (NH^SO^ They suggested that the gas phase reaction
S02 --» NH3 • S02
-------
98
is followed in the presence of water by a heteromolecular nucleation of
gaseous NH^ ' Sfy and gaseous H20 into an aqueous NH3 ' S02 solution droplet:
NH3 • S02 + H20 -y Aerosol
The solution droplets may form (N^SC^ after oxidation.
Stauffer et al. (1973) suggested that in a system of low volatility
gases—such as ^$04, NH3 ' S02» NH^Cl , Nh^NC^, and organic acids--in equal
concentrations and in the presence of water vapor, the gaseous substance
with the lowest volatility nucleates first and the critical sized droplets
then act as surfaces for heteromolecular condensation (in the absence of
particles).
2. Nitrate Formation
The modes of formation of aerosol nitrates are less well understood
than those leading to sulfate. Nitrate levels in Los Angeles are observed
to peak sharply in the morning and then to increase slowly in air masses
as they move over the eastern portions of the Basin. The rapid NCU
morning buildup appears to be unrelated to the gradual increase in NO"
eastward across the Basin later in the day. In the ACHEX study no
systematic, useful relation could be established between NO^ levels and
those of 0 , NO, N02, SO" relative humidity, or noncarbonate carbon
(Hidy et al., 1975).
There is virtually no quantitative information available on the
rates of conversion of NO to NOZ in the atmosphere. A rapid transient
A O
conversion exists in conjunction with the morning influx of NO ,
/\
perhaps associated with the high humidity prevalent in the morning hours.
The second NOZ formation process is slower than that in the morning and
1s roughly comparable in rate to SOp oxidation to S07.
-------
99
Aerosol nitrates can be formed by homogeneous and heterogeneous path-
ways. Figure 19 summarizes many of these pathways. The low vapor pressure
of sulfuric acid leads to rapid homogeneous nucleation at H?SO. partial
pressures in the range 10"8 to 10"10 torr. The hydration of sulfuric acid
droplets 1s thermodynamically favored over a wide range of relative humidities
Thus, sulfuric acid formed in the gas phase can be expected to become
rapidly incorporated into the particulate phase. Although nitric acid
can be formed in the gas phase in several ways (to be discussed shortly).
the vapor pressure of nitric acid is relatively high, and homogeneous
nucleation of HNOo in a humid atmosphere is not expected to take place
under normal atmospheric conditions (Kiang et al., 1973). Nitric acid
does form certain stable complexes in sulfuric acid solutions (Gillespie
et al., 1950), and Castleman (1974) suggested that HN03 may become
incorporated in sulfuric acid droplets. It appears that the production
of aerosol nitrate must involve formation of a condensable species such
as NH.NCL in the gas phase, or the absorption of an NO species in a
T1 O X
droplet followed by chemical stabilization.
The morning nitrate mechanism, generally associated with particles
of diameter greater than 0.5 ym, probably involves absorption of NO
A
species into droplets followed by chemical reaction in the drop. The
afternoon mechanism, generally associated with particles of sizes less
than 0.5ym, probably involves gas phase oxidation of NO in photochemical
A
smog reactions followed by condensation of products such as NH4N03<
We now consider both gas and liquid phase nitrate forming mechanisms.
The objective is to identify clearly what is known and unknown concerning
NO chemistry in urban aerosols.
To assess the importance of this pathway for removal of HN03 from the gas
phase, Castleman (1974) suggested measurement of HNO- vapor pressures over
H2S04"H2°"HN03 solutions-
-------
100
NH,
- NIL
1. Gas-phase formation of HNO- from NO
0 A
2. Gas-phase formation of NH.NO- followed by condensation
of NH.NO-3 on existing droplets
3. Absorption of HN03 in droplet
4. Direct absorption of NOp in droplet
5. Direct absorption of NH- in droplet
6. Formation of organic nitrates in the gas phase followed by
condensation of the organic nitrates.
FIGURE 19. PATHWAYS FOR FORMATION OF NITRATE AEROSOLS
-------
101
a. Nitrate Formation in the Gas Phase
The reaction paths for nitrate accumulation in the particulate
phase via homogeneous steps all involve reactions of gaseous nitric
acid. Table 20 lists the major gas phase reactions involving nitric
acid. The major homogeneous sources of nitric acid in photochemical
smog are Reactions 3 and 4 in Table 20. Based on the rate constants
given in Table 20, the rates of formation of nitric acid by these
two reactions can be estimated for typical atmospheric conditions.
)2> 0.1 ppm, [H2
If we assume that [N0j= 0.1 ppm, [H90]= 104 ppm, [N90t.]= 10~3 ppm,
—7
and [OH]= 10" ppm, then the rates of formation of HON02 through
Reactions 3 and 4 are
-5 -1
R3= 5x10 ppm min
-4 -1
R.= 10 ppm min
Thus, it appears that Reaction 4 is the principal one for gaseous
HONO? formation in photochemical smog. The rate of conversion of
N02 to HON02 by Reaction 4 is of the order of 6 percent per hour.
The following reactions appear to be the principal ones involving
ammonia in the nitrate system:
NH3 + HON02 •* NH.N03 2.8 x 10"2 ppm"1 min"1 Calvert (1974)
NH3 + HNO£ -> NHiN02 2.8 x 10"2 ppm"1 min"1 Calvert (1974)
Countess and Heichlen (1973) measured the rate constant for the
reaction
NH3 + HC1 + NH4C1
-------
102
Table 20
MAJOR HOMOGENEOUS REACTIONS INVOLVING NITRIC ACID IN PHOTOCHEMICAL SMOG
Rate Constant
No. Reaction
1. NO, + NO, ->• N90C
3 2 f. 5
2. N205 -»• N03 + N02
3. N205 + H20 -> 2 HON02
4. OH + N02 -> HON02
5. OH + HNO, -»• H,0 + NO,
O £ 0
6. H00 + NO- -»• HONO, + 09
CO C. C.
7. NO + HNO, -> HN00 + NO,
322
8, HNO, + HNO, -> H50 + 2 N09
•at'25°C, ppm"1 riiin
5.6 x 103
30 min"1
5 x 10'6
104
190
2.5 x 103
2.5 x 10"4
0,2
Reference
Garvin and Hampson (1974
Garvin and Hampson (1974'
Garvin and Hampson (1974
Garvin and Hampson (1974
Garvin and Hampson (1974
Demerjian, Kerr, and
Calvert (1974)
Hecht, Seinfeld, and
Dodge (1974)
Hecht, Seinfeld, and
Dodge (1974)
-------
103
-211
as 2.8 x 10 ppm min . If the NhL - MONO reaction has a rate constant
O
of this magnitude, and if NH3 and MONO concentrations can be estimated as
1 pphm, Calvert (1974) estimated the homogeneous rate of NH.N03 formation
as 2.8 x 10"6 ppm min'1.
b. Nitrate Formation in Solution
Little is known about liquid-phase nitrate formation in atmospheric
aerosols. Liquid-phase mechanisms may be largely responsible for the
morning nitrate peak observed in Los Angeles. In this subsection we
discuss the possible chemistry leading to N03 formation in aerosol
droplets. Consider an idealized situation in which a droplet of pure
water is exposed to an atmosphere containing NO, NO^, SO,,, NH,, 0,,,
and C0?. An equilibrium situation will be established in the droplet
as the result of the dissolution of the gases and subsequent reaction
and ionization. In addition to the equilibria, sulfate and nitrate
form irreversibly by
S03 + °2 "*" S04
N02 + \ 02 •+ N0~
The equilibria in the S02-NH3-C02-H20 system: as well as the kinetics
of sulfate formation have been considered by Scott and Hobbs (1967) and
were discussed in the previous section (see Table 19). An analogous
study of NO-N02-NH3-C02-H20 equilibria and nitrate formation kinetics
has not been carried out.
Table 21 presents four reactions and their equilibrium constants
which occur subsequent to absorption of NO and NOp by a droplet. We note
that N03 can form as a result of the equilibrium established in Reaction 2
as well as by the irreversible oxidation reactions with dissolved 0^ and 0~.
At this point the relative efficiencies of the nitrate-forming reactions
are unknown.
-------
No.
Reaction
Equilibrium
Constant
Value at
25°C Reference
1. (NO) + (N09)n +
9 ^ 9
2HN0 K
. -fef
In n n
p p
NO N0
122
2. 2(N02)g + H20 ^=±: HN02 + H +
4.3 x 10D (Pick, 1920)
-
4.5 x 10 ^ (Abegg)
-------
105
3. The Generation of Organic Compounds of Low Volatility
The formation of photochemical aerosols during the irradiation of
hydrocarbon-NOx mixtures was first observed by Haagen-Smit in the early
1950s (Haagen-Smit and Fox, 1952). Since that time, a number of studies
have been performed to determine the types of hydrocarbons that lead to
aerosol formation when reacted with ozone or irradiated in the presence
of NO . Table 22 presents a summary of several of these studies. Based
A
on these studies, the following conclusions can be drawn concerning photo-
chemical aerosol formation:
> Paraffins, olefins containing fewer than five carbon atoms,
and benzene do not form aerosols.
> Five- and six-carbon monolefins form aerosols only if the
hydrocarbon is branched.
> In general, only those olefins that produce a radical with
six or more carbon atoms after rupture of the double bond
form aerosols.
> Cyclic olefins and diolefins form significantly more
aerosol than do alkenes that lead to radicals with the same
number of carbon atoms.
> Terpenes form the most aerosol of the hydrocarbons studied.
In addition to the studies cited in Table 22, investigators examined
the effect of adding S02 to hydrocarbon-03 or hydrocarbon-NOx systems.
We have already stated that S02 can be effectively oxidized by intermediates
formed in an irradiated hydrocarbon-NOx system. In many smog chamber
studies, aerosol sulfate has formed in irradiated hydrocarbon-NOx or
hydrocarbon-03 systems (Prager et al.s 1960; Stevenson et al., 1965; Schuck
and Doyle, 1959; Schuck et al., 1960; Endow et al., 1963; Harkins and Nicksic,
-------
Table 22
STUDIES REPORTING AEROSOL FORMATION FOR DIFFERENT HYDROCARBONS
UPON REACTION WITH OZONE OR PHOTOLYSIS
IN THE PRESENCE OF NOX
106
Hydrocarbon
Reference*
Monolefins
1-hexene
1-heptene
2-methyl-1-hexene
2,4,4-trimethyl-1-pentene
1-octane
1-decene
1-dodecene
Cyclic olefins
Cyclopentene
Cyclohexene
a-pinene
Diolefins
1,3-butadiene
1,5-hexadiene
1,6-heptadiene
1,7-octadiene
1,6-octadiene
2-methyl-1,5-hexadiene
Cyclopentadiene
Aromatics
Toluene
m-Xylene
2, 6, 9
2, 5, 7, 8
7
1
6
6
6
1, 3, 8
1, 3, 4, 5, 6, 7, 8, 9
3, 4, 5, 7, 8
1
1, 4, 8
7
7, 8
7
7
1
9
9
* Numbers refer to the following references:
Number
1
2
3
4
5
6
7
8
9
Reference
Prager et al. (1960)
Stevenson et al. (1965)
Groblicki and Nebel (1971)
Ripperton et al. (1972)
Wilson et al. (1972)
Hidy and Burton (1974)
O'Brien et al. 0975)
Grosjean and Friedlander (1975)
Kocmod et al. (1975)
-------
107
1965; Groblicki and Nebel, 1971; Wilson et al. 1972; Cox and Penkett, 1972;
McNeils, 1974). In a recent study, Grosjean (1975) found that the formation
of aerosol sulfate depends on the hydrocarbon type. Alkenes having less than
seven carbon atoms, which do not form organic aerosols in irradiated NOX
systems, always produce sulfate aerosols when S02 is added. Alkenes with
seven or more carbon atoms and C]-C4 diolefins form organic aerosols in the
absence of S02 and both organic and sulfate aerosols in the presence of SO?.
For Cr+ diolefins and cyclic olefins, Grosjean found no significant
b
sulfate formation, and the nature and yield of organic aerosols is
unaffected when S02 is added. Grosjean's observations with respect to
cyclohexene were, however, not substantiated by the study of
Kocmond et al. (1975), in which a substantial increase in aerosol form-
ation was observed in a system of cyclohexene-NO -SO over that in a
A A
system of cyclohexene-NO . Because the composition of the aerosol was
X
not measured in the Kocmond et al. study, it cannot be established that
there was any sulfate aerosol present, although it is highly probable
there was.
Although photochemical aerosols have been known to exist for more than
two decades, until recently no significant attempts were made to identify the
composition of the aerosols, particularly the organic fraction. Using a gas
chromatograph and mass spectrometer system, Wilson et al. (1972) analyzed the
aerosol generated from cyclohexene and a-pinene in the presence of N02- They
found that each identifiable constituent contained an organic acid functional
group. Each of these species also contained a second functional group, either
an aldehyde, an alcohol, a nitrate ester, or a ketone. O'Brien et al. (1975)
analyzed the aerosol formed from the reaction of cyclohexene and 1,7-octadiene
with ozone and found adipic acid to be a major component. Upon irradiation of
cyclohexene and 1,7-octadiene, Grosjean ("1975) found the following product
distributions:
Percent of Total
Reactant Products Organic Aerosol Mass
Cyclohexene Adipic acid 55%
Hexanoic acid nitrate 24
1,7-octadiene Adipic acid 61
Hexanoic acid nitrate 25
-------
108
One would expect that if organic acids and their derivatives were
present in the atmosphere, they would accumulate in the particulate
phase because of their very low vapor pressures at ambient temperatures.
a. Vapor Pressures of Organic Aerosol Constituents
The primary reason for the condensation of the relatively high-molecular-
weight organic acids and their derivatives is the extremely low vapor pres-
sures of these species at ambient temperatures. Unfortunately, very little
specific data are available on the vapor pressures of the organic species
(discussed above) that have recently been identified. For example, of the
major species identified by Grosjean and O'Brien et al., adipic acid is the
only one for which vapor pressure data are available. Figure 20 shows the
vapor pressure of adipic acid as a function of temperature. At 25°C, adipic
acid in the pure state is a solid, although it probably exists in solution
in aerosol particles. Now that commonly occurring organic aerosol species
have been identified, vapor pressure determinations will be quite desirable
for the purposes of predicting rates of heterogeneous condensation.
b. Reaction Mechanisms Leading to Organic Aerosol Constituents
As a result of recent identifications of several organic aerosol species
in field and laboratory smog chamber studies, we can now postulate mechanisms
that might account for the observed products.
It appears that the principal reaction responsible for the formation of
organic aerosol precursors (the species that, once formed, condense into the
particulate phase) is the ozone-olefin reaction. In Table 23 we summarize
the classical Criegee mechanism for liquid phase ozone-olefin reactions, which
has often been used to explain gas phase reactions in photochemical smog, and
the new mechanism proposed by O'Neal and Blumstein (1973). The principal as-
pect of the Criegee mechanism is the decomposition of the molozonide inter-
mediate into a carbonyl compound and a diradical, or a zwitterion. The
zwitterion can then decompose or react with other species in the system. In
the O'Neal and Blumstein mechanism, the molozonide is postulated to be in
equilibrium with two diradicals. The diradicals can then participate in
hydrogen abstraction reactions.
-------
109
1.70 1.85 2.00 2.15 2.30 2.45 2.60 2.75 .2.90 3.05 3.20 3.35 3.50
1/T--X 10~3
FIGURE 20. EXTRAPOLATION OF THE VAPOR PRESSURE
OF ADIPIC ACID TO THE AMBIENT TEMPERATURE
-------
110
Table 23
OZONE-OLEFIN REACTION MECHANISMS
Criegee mechanism
CARBONYL ZWITTERION
Hx © ®/R?
c=o + o-o-c i
1\ /K2
C—C ^
1V
MOLOZONIDE
OR
Hx© © ,
C-0-0 + 0=C
ZWITTERION CARBONYL
Hx® 0
C-O-O •
C0
HCOOR1 OR R^OOH
+ CO
O'Neal and Blumstein mechanism
°3 + „ ,- -x
/R2
oT
H
C —
0^
I
\ *' /^p
-|~'\L
\n ' '
b'
\
C
—C '
^H2CH2R3
0/
T---^^,,
1 |f | 223
0 OOH
a-KETOPEROXIDE
Jf
-c-c
—• RT-C-C-
1 I T I
HOC-O
(B-HYDROGEN ABSTRACTION)
R^C-C 0
HO CH0-CH
(a-HYOROGEN ABSTRACTION)
-, ,Q
I 2 3 21|
0 0
a KETO ALCOHOL
(Y-HYDROGEN ABSTRACTION)
-------
Ill
O'Neal and Blumstein estimated that the Criegee mechanism is more important
for ethylene and propylene, that both the Criegee and hydrogen abstraction
mechanisms are of equal importance for butenes, and that the latter mechanism
is more important for alkenes with five or more carbon atoms.
Let us now consider possible mechanisms for accounting for observed
organic aerosol species. The most effective aerosol generators have been
found to be cyclic olefins and diolefins. Two olefins in these classes that
have been studied recently in smog chamber experiments are cyclohexene and
1,7-octadiene. Table 24 summarizes the products observed in three such
studies. The major products found in these smog chamber studies were difunc-
tional aliphatic compounds. Thus, the desired mechanisms are those that will
convert cyclic olefins and diolefins to difunctional aliphatic compounds. Al-
though the reaction with ozone appears to be the major one responsible for
aerosol formation, reactions with atomic oxygen and hydroxyl radicals can also
be postulated. Table 25 presents mechanisms involving the reaction of cyclo-
hexene with 0, OH, and 03. In this table, the species that have been identified
in smog chamber studies are shown in boxes.
Table 24
ORGANIC AEROSOL CONSTITUENTS IDENTIFIED IN SMOG CHAMBER STUDIES
Cyclohexene
1,7-Octadiene
Wilson et al. (1972)
CH.OH - (CH2)~ - COOH
c. o
COH - (CH2)3 - COOH
CH2ON02 - (CH2)3 - COOH
CHO - (CH2)4 - COOH
Grosjean (1975)
COOH - (CH2)4 - COOH
COOH - (CH2)4 - CH2ON02
CH2OH - (CH2)3 - CH2OH
O'Brien et al. (1975),
Grosjean (1975)
COOH - (CH2)4 - COOH
COOH - (CH2)4 - CH2ON02
4. The Role of Water in Photochemical Aerosols
There is strong evidence that the total photochemical aerosol mass is
closely correlated with the liquid water content of the aerosol. Figure 21
-------
112
Table 25
MECHANISMS FOR REACTIONS OF CYCLOHEXENE
LEADING TO DIFUNCTIONAL ALIPHATIC COMPOUNDS
OH-
0 — Q:
CH
OH
CCH
H
CO-
+ NO .
CO-
OH
- OH
+H0i
-------
•si-
o
X
I
I
4J
(O
O
(X^HRAYLEIGH SCATTERING .
I [ I | 1
I
O POMONA (10/4-10/5)
A PASADENA (9/20)
A PASADENA (9/15)
D GOLDSTONE (11/1)
10
20
30 40 50 60 70
Liquid Water Concentration--yg m
Source: Hidy et al. 0975).
FIGURE 21. THE LIGHT-SCATTERING COEFFICIENT
AS A FUNCTION OF LIQUID WATER CONTENT
80
90
100
-------
114
shows the light-scattering coefficient as a function of aerosol liquid
water concentration at four locations during 1972. Figures 22 through 24
present the diurnal fluctuations of total aerosol mass and aerosol liquid
water concentrations of Pomona and Pasadena. In these three figures, the
data indicate that substantial changes in aerosol water content can occur
despite only small changes in relative humidity. Measurements made during
the 1972 ARB study indicate that changes in aerosol water content correspond
closely with changes in the sulfur, nitrogen, and carbon content of the
aerosol. The recent work of Ho (1975) during the 1972 ACHEX indicated that
the aerosol liquid water content may display a diurnal variation closely
linked with changes in aerosol mass and bs ^ (as seen in Figures 22 through
24). Water is probably involved in sulfate and nitrate formation in the
aerosol. At present, however, the mechanisms by which the water content of
aerosols changes with time seem to be unknown and thus constitute a key area
for future investigation.
D. SUMMARY
In this chapter, we have surveyed much of what is currently known re-
garding the chemistry of photochemical aerosols. In a description of urban
aerosol dynamics, the prediction of the chemical composition of the aerosol
requires knowledge of the details of both homogeneous and heterogeneous
chemistry. The key features of such a prediction are the description of the
rate of formation of condensible species and the composition of those species
Compared with what is known about the physical processes that influence aero-
sol dynamics, our knowledge of the chemical processes is much less developed.
From the review given in this chapter, the following major problem areas have
emerged:
> Understanding of the homogeneous oxidation of S02 in photo-
chemical smog--the important reactions and their rate con-
stants.
> Determination of the probable route of formation of sulfate
in photochemical aerosols—for example, homogeneous formation
-------
CD
3-
I
C.
O
-13
ro
S_
-------
700
BEGIN
SLIGHT HEAVY
DRIZZLE MIST
TOTAL MASS NOT RELIABLE
(DATA QUALITATIVE)
TOTAL MASS CONCENTRATION
LIQUID WATER CONCENTRATION
2400 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000
Time (PST)
Source: Hidy et al . (1975).
2200
FIGURE 23 DIURNAL PATTERNS OF WATEROMETER DATA
FOR PASADENA— 9 SEPTEMBER 1972
-------
160
140
120
n
i
f 100
c
o
4J
ra
£ 80
o
c
o
CO
03
60
40
20
0
TOTAL MASS CONCENTRATION
LIQUID WATER CONCENTRATION
1
2400
0200 0400 0600 0800 1000 1200
Time (PST)
Source: Hidy et al. (1975).
FIGURE 24. DIURNAL PATTERNS OF WATEROMETER DATA
FOR PASADENA--20 SEPTEMBER 1972
1400 1600
-------
118
of H2S04, followed by heterogeneous condensation, and
heterogeneous formation of $04 in the presence of dis-
solved NH3.
> Determination of the probable route of formation of ni-
trate in photochemical aerosols—for example, homogeneous
formation of NO^.
> Measurement of organic aerosol constituents.
> Determination of the vapor pressure of organic aerosol
constituents.
> Determination of the mechanisms of formation of organic
aerosol precursors in the laboratory.
> Elucidation of the mechanism of incorporation of liquid
water in aerosols.
-------
119
IV MATHEMATICAL MODELING OF THE DYNAMIC BEHAVIOR
OF PHOTOCHEMICAL AEROSOLS
Our purpose in the previous chapters was to review the physical and
chemical processes that govern the evolution of photochemical aerosols. In
this chapter, we first discuss the status of emissions inventories for aero-
sols, then we derive the model equations, and finally we describe the approxi-
mations that might be made in developing a model.
A. THE STATUS OF AEROSOL EMISSIONS INVENTORIES
In Chapter III, we pointed out that the analysis of aerosol data for
the Los Angeles basin indicates that roughly half of the aerosol mass can
be attributed to gas-to-particle conversions. In Figure 25, we illustrate
diagrammatically the need for a gaseous emissions inventory, as well as a
primary emissions inventory, for the aerosol model. Table 26 presents refer-
ences that can be used to compile an emissions inventory of natural and
anthropogenic primary aerosols.
The existing emissions inventories for primary particulate matter are
based on measurements made in the vicinity of the sources. On the subgrid
scale, coagulation and sedimentation will modify the size distribution of
the emissions. Hence,a microscale model will be necessary to account for
these changes in the particle size distribution function.
The gaseous emissions inventory should include the principal secondary
aerosols (such as reactive hydrocarbons, S02? and NOX) as well as gases that
play a role in transforming these gases to the particulate phase (such as
ammonia). Although source data for emissions of gaseous pollutants have been
compiled for application to photochemical smog models (Roth et al., 1974),
-------
PRIMARY PARTICULATE EMISSIONS
(ANTHROPOGENIC)
> MOTOR VEHICLES
> POWER PLANTS
> AIRCRAFT, ETC.
PRIMARY PARTICULATE EMISSIONS
(NATURAL)
> SEA
> SOIL
AEROSOL
MASS
GASEOUS
EMISSIONS OF
HYDROCARBONS
NOX
EMISSIONS
so2
EMISSIONS
GAS-TO-PARTICLE
CONVERSION
* 50%
PRIMARY
•b 50%
SECONDARY
NH3
EMISSIONS
ro
O
FIGURE 25. DIAGRAM OF THE RELATIONSHIP OF THE EMISSIONS INVENTORY TO THE AEROSOL MASS
-------
121
Table 26
SOURCES OF DATA FOR AN AEROSOL EMISSIONS INVENTORY
Emission Source
Motor Vehicles
Chemical
Size Distribution
Power plants
Sea
Soil
Miller et al. (1972)
Gangley and Springer (1974)
Hirschler et al. (1957)
Cahill and Feeney (1974)
Gatz (1974)
Miller et al. (1972)
Gatz (1974)
Miller et al. (1972)
Gatz (1974)
Miller et al. (1972)
Whitby et al. (1969)
Gartrell et al. (1974)
Gangley and Springer (1974)
Cahill and Feeney (1974)
Ter Haar (1972)
Ter Haar and Stephens (1971)
White et al. (1973)
Gartrell et al. (1974)
Woodcock (1953)
Gartrell et al. (1974)
-------
122
such inventories do not provide separate emissions data for individual
hydrocarbons. The California Department of Transportation is currently
compiling more extensive emissions inventories, and the EPA is sponsoring
an inventory that includes differentiation by hydrocarbon type.
The spatial and temporal distributions of water vapor are also impor-
tant factors in photochemical aerosol growth. During the summers of 1972
and 1973, the California Air Resources Board took three-dimensional measure-
ments of temperature and relative humidity in the Los Angeles basin; these
data are available for determining the distribution of water vapor in the
basin.
B. THE BASIC EQUATIONS OF AN AEROSOL MODEL
To develop the general equation governing the dynamics of the aerosol
in photochemical smog, we assume that the aerosol is composed of liquid drop-
lets of composition (q, C2> ..., c«) (moles/volume) of the K species present
in the aerosol. We then define n(q ,C2»... ,C|<,r,t)dc].. .dcK as the numbers
of particles per unit volume of atmosphere at location r and time t containing
between c-j and c-j + dc-j moles of species i, i = 1, 2, ..., K. We can refer
to n as the number density distribution function. The total particle number
q
density (cm ) at location r at time t is
N (r,t)
r r
= / ... / n(c1,...,c|<,r,t) dcr..dcK . (54)
It is convenient to introduce the particle volume v into the number
density distribution function. Since the volume of a particle can be ex-
pressed in terms of the molar volumes, Vj, i = 1, 2, ..., K, and the species
concentrations by
K
v = 2-r c.v. , (55)
1=1 1 1
-------
123
the particle volume v can replace one of the concentrations as an indepen-
dent variable of n; that is, n = n(q ,... ,CK_-| ,v,r,t).
If only the distribution of particles by volume is of interest, we can
define nQ(v,r,t)dv as the number of particles per unit volume of atmosphere
of volume v to v + dv at location r at time t. The distribution function
n0 is related to n by
CO CO
nQ(v,r,t) = J ...J n(c1,...,c[(_1,v,r,t) dc1...dc|<_1 . (56)
0 0
"3 -3
The total aerosol volume per unit volume of atmosphere (yirr cm" ) at
location r and time t is given by
CO
Vjr,t) = /vn0(v,r,t) dv . (57)
0
Chu and Seinfeld (1975) derived the general equation governing
n(c-|,... ,CK_-] ,v,r,t). This equation includes the effects of advection,
heterogeneous condensation, coagulation, Brownian and turbulent diffusion,
sedimentation, homogeneous nucleation, and heterogeneous chemical reaction.
In deriving the equation, one must consider the processes that influence the
total derivative of n in a unit volume of atmosphere. In particular, the
total derivative of n is
KT = rate of homogeneous nucleation + rate of coagulation + rate of washout
+ rate of rainout + rate of Brownian diffusion. (58)
Thus, the total derivative is equal to the net rate of all processes that
serve to introduce or remove particles from a unit volume of atmosphere.*
The total derivative of n can be expressed as
* Particle losses by impaction on surfaces and particle introduction from
sources are accounted for in the boundary conditions on the equation for n
-------
where
9c-j/9t = rate of change of the concentration of species
i in a particle. Changes in c-j will occur as a
result of heterogeneous condensation and chemi-
cal reaction. We can represent these two rates
by I-j(ci,...,CK_i,nisv) and Rj (c-| ,. . . ,CK_-| ,v) ,
respectively, where n-j is the gas phase concen-
tration of species i .
9v/9t = rate of change of the volume of a particle.
Changes in v will occur as a result of hetero-
geneous condensation and chemical reaction. We
can represent these two rates by
I0(c1,...,cK_1,n1,...»nL,v) and RO(C] . . . ,CK_-| ,v) ,
respectively.
9rn-/9t = rate of change of the itn coordinate location of
a particle due to advection. Thus, 9r-j/9t = u-j,
the i component of the wind velocity. Note
that 9r2/3t may differ from U3 because of sedi-
mentation. If the settling velocity of a particle
is -us, then 9r3/9t = us - us. Henceforth, we
consider us to be the net vertical velocity.
Combining Eqs. (83) and (84), we can write
K-l 3
(59)
H+ § ^7 [«l + V"] + ^[('o + Ro>"] + § ^ ("1"
homogeneous coagulation washout rainout Brownian
nucleation diffusion
-------
125
where each S on the right-hand side represents the rate of change of n
[(fc/mole)K~' ym~3 cm~3 see"'] as a result of the particular process.
The rate of homogeneous nucleation can be expressed as
Sh(c.|,... ,cK,n-|,... ,nL>v). We discussed the computation of this term in
Chapter II. The rate of change of n due to coagulation is
C = J
coag 9K
* 0 0
v cl CK-1
»CK_-J ,v,r,t) dc1...dcK_1 dv
00 00
~J •• •/ e(v,v) n(c1,... ,cK_lsv,r,
0 0
• n(c, ,...,£., -,,v,r,t) dc, ...dc,,_i dv (61)
An expression for the rate of change of the number density distribu-
tion function due to washout can be developed by analogy to that for
coagulation:
CO OO
Swashout= -•••Y(v,vr) n(cls...,cK_rv5r,t) gr(vr,r,t) dc^.dc^ d
0 0
(62)
where y(v,vr) is a collision frequency factor equal to
(3/4Tr)2/3 Tr(v2/3 + v2/3) qs(vr) Er(v,vr) in the notation of Chapter II,
and gp(v,r,t) is the number density distribution function for raindrops
at location r and time t. Thus, the total number density of raindrops at
r at time t is given by
-------
126
oo
Nn(r,t) = fg_(v,r,t) dv (63)
V ~ J v
Brownian ~ *
diffusion
3 2
* A a*n
^ 9r2
i=l i
^rainout 1S a complicated function of particle size, composition,
water vapor concentration, and turbulence within the cloud. Because this
process is unimportant in the atmospheric layer closest to the ground for
photochemical aerosols, we do not consider it further here.
Finally, the rate of change of n by Brownian diffusion is
(64)
where D(v) .is the Brownian diffusivity, a function only of particle size.
Equation (60), with Eqs. (61), (62), and (64), represents the complete
conservation equation for the aerosol number density distribution function
in a fluid. When the fluid is turbulent, the velocities in Eq. (60) contain
random components. In addition, the gas concentrations n-i > ...» n, are
random functions in a turbulent field. Consequently, n is itself a random
function. In developing the conservation equation for n in a turbulent
flow field, we follow the usual procedure of decomposing the wind velocities
into mean and random components, u"^ + u^-. Similarly, the gas phase concen-
trations and the number density distribution function can be expressed as the
sum of mean and random components, n-j = n-j + n-} and n = n + n1. Because
10 and I.j depend, in general, on the ni » these two functions must be expressed
as IQ = TO + IQ and 1^ = Tj + It. Finally, we must also write gp = g"p + gp'.
We wish to obtain an equation governing the mean value of the number
density distribution function, rf, from Eq. (60). The desired equation can
be obtained by substituting u-j = ITj + u], n = rf + n1, gp = cL + g',
IQ = TO + IQ'> and 1-j = T.J + I] into Eqs. (60) through (63) and then taking
the mean value of the resulting equation. During this operation, a number
of new dependent variables emerge that represent mean values of the product
-------
127
of two fluctuating quantities: u V , Ign' , IV, n'n1, and n'g' The first
of these variables is simply the turbulent flux of the number density
distribution and can be expressed in terms of a turbulent eddy diffusivity,
<65>
There is virtually no theory available for treating the remaining second-
order variables above. For example, Ign' represents the turbulent contri-
bution to the change of n by heterogeneous condensation. We do not expect
any of these second-order terms to be important in urban-scale aerosol
simulation.
Thus, the final general dynamic equation governing the mean number
density distribution function in the atmosphere is
.- 3 . K-l , . _ _, ,
^TT J ~ i\-1 r, r i -, r
— + V — (u".F) + V — (I- + R. )rf + — (
*\-4~ f 'iv* \ T / f Ci/^ I^T T ' i\/l
o L * ..^i o i • 1 y^ ^ d C • I d V
^«i^ T *»*» -i l_ J l_
o
T — — h-
1 = 1
V C, C., ,
^//-/
^00 0
n(c15...,cK_15v,r,t) dc^.-dc^-j dv
oo oo
[v,v) nCc,...^.. -,,v,r,t) n(c,,...,£., n,v,r,t) dc1...dc|<_1 dv
i i\~ i ~ i N— i i |N '
0 0
CO 00
//• > _
•••JY(V'V) n(cl Vl'^C't) 9r(v,r,t) dv dcr..dcK .
00 ' '
-------
12R
C. APPLICATION OF THE GENERAL EQUATION TO PHOTOCHEMICAL AEROSOLS
With the appropriate input functions, Eq. (66) constitutes a general
model capable of describing the dynamic behavior of urban aerosols. On
the basis of the discussion in Chapter II, however, certain terms in
Eq. (66) can be neglected when considering photochemical aerosols. We are
interested primarily in the evolution of photochemical aerosols in the sub-
micron size range over spatial and temporal scales comparable to those of
the SAI gas phase photochemical pollutant model. The principal conclusions
of Chapter II relative to Eq. (66) are the following:
> Brownian diffusion can be neglected relative to turbulent
diffusion.
> Homogeneous nucleation is negligible compared with hetero-
geneous condensation.
> Sedimentation is important only for particles larger than
1 ym in diameter and can be neglected here.
> Coagulation is important in shaping the size distribution
near sources. Turbulent coagulation and coagulation by
differential sedimentation may be important for particles
larger than 1 ym in diameter. In the 0.1 ym <_ Dp <_ 1 ym
range, however, coagulation can be neglected in urban-
scale models.
> Washout is an infrequent phenomenon in the region of
interest and can be neglected (if there was no rainfall
during the time periods over which the model is exercised).
Thus, Eq. (66) becomes
at JLi ar. vuf" jL, ac.
i=l T i=l n
i7 [
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129
Table 27 summarizes the significance of each term in Eq. (67).
Although most of the desired i-formation concerning photochemical
aerosols is embodied in the function n, the effort involved in computing
n may not be justified in view of the data avilable for validation. Rou-
tine monitoring of the size and chemical composition distribution of an
urban aerosol is not generally possible. On one hand, optical analyzers
(Charlson, 1969) and electrostatic devices (Whitby et al., 1972) measure
the number of particles in a given size range without regard to composition.
On the other hand, current methods of measuring chemical composition do not
differentiate particles by sizes. In addition, the objectives of an aerosol
model may not require the level of detail inherent in n. For example, the
prediction of visibility degradation requires only the total aerosol volume
concentration in the size range 0.1 to 1.0 ym diameter. Therefore, in this
section, we develop several models for urban aerosols, each involving a
different degree of complexity. The models are most easily characterized
by the function chosen to describe the aerosol population (see Table 28).
The first entry of Table 28 is the most general and detailed model,
that based on computing rT(c-],... ,CK_-] ,v,r,t) by Eq. (67). The equations
that serve as the basis for computing the other functions in Table 28 are
developed in the sections that follow.
1. Mean Number Density Distribution Function
In this subsection, we develop the general dynamic equation governing
nQ(v,r,t), the mean number density distribution function for particle size.
Integrating Eq. (67) over all compositions, we obtain
F:
0
00 00 / — \
Jf o r_ 1 3 * / 9nn\
-J f»[«Io + Ro'nJdcl-dcM -ZaM^la?:) ' (68)
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130
Table 27
SIGNIFICANCE OF THE TERMS IN THE GENERAL DYNAMIC EQUATION [Eq. (67)]
Term Comments
3n Rate of accumulation of n at location r at time t
8t IV0/mnlp)K-l vm-3 cm-3 sec-l
M .
K-l
9 --
(u.n) Advection of n. This term affects all particles
9r- i
i=l equally (having neglected sedimentation) but drops
out of the equation if an air parcel moving with
the mean flow is considered.
/^ —— (I. + R.)n Rate of change of the chemical composition of a
,-_1 °c-j L"! "! J
particle resulting from heterogeneous condensation
and chemical reaction.
|— (Tn + Rn)n| Rate of change of the volume of a particle re-
sulting from heterogeneous condensation and chem-
ical reaction. This is the dominant volume growth
term for photochemical aerosols.
Rate of change of n due to turbulent diffusion.
This term affects all particles equally.
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131
Table 28
LEVELS OF DETAIL IN THE REPRESENTATION
OF AN URBAN AEROSOL POPULATION
Term Describing the
Aerosol Population Comments
n(c,,... »CK_.| ,v,r,t) Mean number density distribution as a function
of particle chemical composition, size, loca-
tion, and time. The most detailed representa-
tion possible. Governed by Eq. (67).
nQ(v,r,t) Mean number density distribution as a function
of particle size, location, and time. Chemi-
cal composition not accounted for explicitly.
Governed by Eq. (68).
Nco(r,t) Total mean number density as a function of
location and time. Governed by Eq. (75).
V^rjt) Total mean aerosol volume per unit volume of
gas as a function of location and time. Within
the size range 0.1 ym to 1.0 ym diameter, this
quantity can be related directly to the light-
scattering coefficient and, hence, to visibility
reduction. Governed by Eq. (76).
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132
The integrand of the third term on the left-hand side represents the
rate of change of n due to changes in the species concentration within a
particle. These composition changes do not affect Fg, and this term can
be shown to equal zero.
The fourth term on the left-hand side of Eq. (68) represents the
rate of change of ng due to changes in the particle volume by hetero-
geneous condensation and chemical reaction. We recall that
^0 = "lb(c-|»-"»cK-rv'n-|'"-»\) and RQ = RQCc11...cK_-|,v). Thus, the rate
of change of particle volume by heterogeneous condensation depends on the
concentrations of the species in the particle, as well as on those of the
gaseous condensing species. Also, the rate of change of particle volume
due to heterogeneous chemical reaction depends on the species concentrations
in the particle. If we define
CO OO
J ...j IQ(C-| ,... ,
n"0(v,r,t)
I0(v,nr..JiK,r,t) = 0 0 (6g)
and
OO CO
/...jR0(c1,...,cK_1,v)n dcr..dcK_1
r\ n
, (70)
n0(v,r,t)
we can express Eq. (68) as
3
n a a r - •} a
*T + E IF7 + !» [<'o + V"o] ' E 1FT
1
-------
133
The sum IQ + RQ can be interpreted as the rate of change of the total par-
ticle volume due to heterogeneous condensation and chemical reaction; that is,
To compute IQ and RQ using Eqs. (69) and (70), we must know n and thus the
detailed chemical composition distribution of the aerosol. Clearly, this
calculation should be avoided if possible in using Eq. (71). It is desirable
to use a growth relation that can be expressed only in terms of the particle
volume and the concentrations of the gaseous condensing species. As dis-
cussed in Chapter II, Heisler and Friedlander (1974) developed empirical
growth relations of this type. Because the changing chemical compositions
of the particles are not accounted for, these growth relations are not
capable of predicting an equilibrium particle size corresponding to the ini-
tial particle composition and the gas phase concentration. However, if the
conditions of application of the model are similar to those of the experi-
ments from which the growth relations were determined, the use of these re-
lationships in atmospheric applications should be justified. If we represent
the empirical growth law as
3^= Ig(v,7rr...,\) , (73)
then Eq. (71) becomes
'n°s s r o ~i J a / ^nn
0 , ^ 8 ,-- \ + 3_ Ue - l ^ _3_ K _u
ku-i"n/ ^ii/ \ir\ "n > ^v I INi -i
at Z^ ar, vui"0' 8v TO "0 I 2^ zr. \lxii lr.
(74)
2. Total Mean Number Density
An equation governing the total mean number density N00(r,t) can be
obtained by integrating Eq. (71) over all volumes. The result is
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134
3 , 3 a / 3N
— (u".N ) = V — K.. —^1 . (75)
3r. vui «' 2-f 3r, \ 11 3r. / ^b'
We note that heterogeneous condensation does not affect the total number
of particles; it affects only their size and composition distribution.
3. Total Mean Aerosol Volume
Recalling Eq. (57), we can derive an equation governing the total
mean aerosol volume per unit volume of atmosphere Vco(r,t), by multiplying
Eq. (71) by v and then integrating over all v. The result is
8V 3 . r _ 3 ,
r
J
1=1 1 0 i=l 1
If we employ the growth law [Eq. (73)], then Eq. (76) becomes
8? 3 , r p 3 / W
3r+ E 3FT (V~} + /^.n^....^^ dv - £ ^ Kii — . (77)
i=l 1 0 i=l 1 X
Since we are most interested in the particle size (diameter) range
of 0.1 to 1.0 ym, we would like to replace the integral in Eq. (77) with
v*
I ^(v.n-j,... »nK)ng dv
where v^ and v* are the volumes corresponding to Dp = 0.1 ym and 1.0 ym,
respectively. To validate this approximation, we can estimate the quantity
of material added by condensation in the size range of v > v*. Assuming
that dv/dt -v Dp for diffusional growth, and assuming a Junge distribution
for particles above Dp = 1.0 ym, that is,
-------
135
n0(v) - D- ,
then the ratio of the mass converted on particles with Dp > 1 ym to the mass
converted on particles with 0.1 <_ Dp <_ 1 ym is
(BI)V
(— W
\dt/ * -
f D~3 dD
> v* _ J P P
< v < v* /. 0
~ ~ / D"3 dD
i p p
0.1
^0.01
One cannot obtain an equation for V that involves only V^ because of
the volume dependence of the heterogeneous condensation growth law (since
it is necessary to have n"0 to compute V^). Eq. (77) is an alternative to
Eq. (74)5since V" can always be obtained directly from Fn by using Eq. (57).
oo v
D. ALTERNATIVE FORMS OF AEROSOL MODELS
In this section, we consider certain aerosol model forms based on the
functions summarized in Table 28. The mean number density distribution
function rF(c-|,... »CK_I ,v,r,t) represents a complete description of the
aerosol distribution. By reducing the number of variables on which n de-
pends, one gains improvements in model simplicity at the cost of less detail
in the aerosol distribution. We can distinguish the possible models based
on rT according to the spatial and chemical species dependence on the distri-
bution. We consider the following cases:
> Spatial dependence
- Spatially homogeneous
- Vertically inhomogeneous
- Spatially inhomogeneous
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136
> Species dependence
- Chemically homogeneous
- Two component
- Multicomponent.
Table 29 lists the functional dependences of the nine combinations.
We note that a chemically homogeneous n may be different in principle
than r\Q. Chemical homogeneity implies that the concentrations of the
species in each particle do not vary with particle size, location, or time.
Of course, in general, the composition of particles can vary with particle
size, location, and time. In the equation governing FQ [Eq. (71)], HQ depends
on the composition distribution through the definitions of IQ and RQ. In
practice, we have noted that Ig + RQ would be replaced by an empirical,
concentration-independent growth law. Therefore, from the point of view of
implementation, a model based on n would not differ from a model based on ng.
An approximation of the multicomponent nature of a real particle can
be obtained by considering each droplet to consist of two species. How these
species should be chosen depends upon the needs of the calculation. The fol-
lowing are two possible choices:
(1) c-i = water
C2 = all species except water.
(2) c-j = condensible species (secondary aerosol)
c2 = noncondensible species (primary aerosol).
Chu and Seinfeld (1975) developed an aerosol model based on the assumption
of a two-component particle consisting of condensible and noncondensible
species. From the point of view of compromising between computational feasi-
bility and representation of as much of the detailed composition of a par-
ticle as possible, a model based on a particle of a few components should
be considered in future work. As summarized in Table 29, simplifications
in the spatial dependence of the aerosol distribution can be achieved.
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137
Table 29
FUNCTIONAL DEPENDENCES OF THE MEAN NUMBER DENSITY DISTRIBUTION FUNCTION
Spatial Dependence
Species
Dependence
Chemically
homogeneous
Two component
Spatially Vertically
Homogeneous Inhomogeneous
n"(v,t)
n"(c,v,t)
n(v,z,t)
rf(c,v,z,t)
n(v
n(c
Spatially
Inhomogeneous
,x,y,z,t)
,v,x,y,z,t)
Multicomponent
,v,z,t) n"(c... ,C_ ,v,x,y,z,t)
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13R
There are two alternative forms of dynamic urban air pollution models:
(1) models based on the solution of the conservation equations on a fixed
grid and (2) those based on the solution of the conservation equations with
respect to a moving coordinate frame that follows a surface wind trajectory
(see, for example, Seinfeld et al., 1972). As normally applied, trajectory
models are based on the solution of the governing conservation equations in
a vertical column of air, having a fixed area and a variable height (to accom-
modate inversion base height changes), that moves through the airshed at the
local mean surface wind velocity. Horizontal turbulent mixing across the
boundaries of the parcel is neglected, as are the effects of the variations
of wind speed and direction with height on the pollutant concentrations in
the parcel. Liu and Seinfeld (1974) have delineated the conditions under
which such a model is valid. The most serious assumption limiting the validity
of the model is the lack of consideration of the changes of wind speed and
direction with height, although it appears that for typical conditions in the
Los Angeles airshed this assumption may not be seriously in error.
Grid models generally require more computer storage than trajectory
models. However, the two model types cannot be compared with respect to
computing time because grid models predict the variables of interest at all
locations as a function of time, whereas trajectory models predict the varia-
ble only along a given wind path.
The entries in Table 29, based on spatial distribution, correspond,
respectively, to a trajectory model with no vertical gradients, a trajectory
model with vertical gradients, and a full three-dimensional grid model. One
possibility not shown is that of a two-dimensional, vertically homogeneous
grid model, for example, rf(v,x,y,t) in the chemically homogeneous case.
' " f-- ,'=^"-c "
•-".„ ^ * ''"'*- "'•-•''
The most important process in governing the size and composition distri-
bution of photochemical aerosols is heterogeneous condensation. As. discussed
in Chapter III, the principal secondary species in a "typical" photochemical
aerosol are sulfate, nitrate, organic carbon, and water. The key problem in
developing a mathematical model of urban aerosol dynamics is the representation
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139
of the condensation growth process. The degree of detail required in this
representation depends on the degree of detail in the functiona} dependence
of the density function computed in the model. We have already discussed
the type of growth relation needed for a model based on n~Q(v,r,t), for
example. Because only a few studies have been carried out to determine con-
densation growth relations for photochemical aerosols, validated expressions
for use in urban models do not now exist. Although we derived a complete
growth relation for a spherical droplet consisting of K species in Chapter II,
insufficient knowledge of the initial composition and of the composition of
the condensing species have prevented the application of this relationship
to atmospheric photochemical aerosols. Such calculations will need to be
carried out in developing appropriate growth relations. For initial model
development, certain simplifications of the treatment of particle growth may
be possible by reducing the number of variables on which the growth rate
depends.
The rate of condensation depends, in general, on both the aerosol and
gas phase compositions. Let us consider first how the gaseous condensing
species can be treated in an aerosol model. First, the potential condensing
species must be identified, for example, ^SCty, HN03, NH3, and organic
species. For the aerosol model, these species, say K of them, are the only
ones of interest in the calculation. Therefore, it would be necessary in
a gas phase model to predict the concentrations of these species as a function
of location and time. If the amount of the gaseous species that transfers to
the particulate phase is small compared with that which remains in the gas
phase, then the gas phase model calculation can be done independently of the
aerosol calculation. For the intermediate case in which roughly comparable
amounts of the condensible species are in the gas and aerosol phases, it
is necessary to account for the condensation loss in the gas phase model, thus
coupling the two models.
Let us now consider how the condensation process is treated. The major
distinction in describing the condensation process rests on whether the
chemical composition of the particle is accounted for. As we have demonstrated
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140
in Chapter II, if the composition of the particle is explicitly included in
the condensation growth law, then it is possible, in principle, for the par-
ticle to reach an equilibrium size at a particular gas phase concentration.
In addition, if the growth is rapid in comparison to the rate of change of
the gas phase concentrations, then the particle size and composition will
attain a pseudo-steady state at any time when the particle size and composi-
tion are in equilibrium with the local gas phase concentration. The "steady
state" size and composition can be determined by solving the following
equations:
dt
dc.
dt
1 = 0
i = 1, 2, ..., K-l
Applying the steady-state concept, Chu and Seinfeld (1975) found that the
time required for particles to attain an equilibrium size and composition
was on the order of minutes.
Growth relations based on the assumption that the concentrations of
species in the aerosol are independent of time predict that a continuous
volume increases as long as the particle is exposed to the gas. Relation-
ships of this type are required if the particle chemical composition is not
included in the model.
E. SUMMARY
In this chapter, we have discussed the modeling of photochemical aerosols
and the simplifications that can be made in a model. In general, the specifi-
cation of the spatial and species dependence of the number density distribu-
tion function exhibit trade-offs in the description of the aerosol properties
and the computational complexity of the model. Modeling the condensational
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141
growth of the aerosol particles represents the major problem in developing
the urban aerosol model. If the growth relationship includes the time-dependent
composition of the particle, a key simplification in the model can be made if
one assumes that the particles reach equilibrium with the gas phase concentra-
tion on a time scale that is short compared with the time scale for changes
in the gas phase composition. Another assumption that we have used to obtain
empirical growth relations is that of the independence of the composition of
the aerosol with respect to time. The determination of the utility of each
of these approximations awaits development and testing.
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142
V RECOMMENDATIONS FOR FUTURE RESEARCH
In the preceding chapters, we have delineated the current state of
understanding of the evolution of photochemical aerosols and have cited
areas in which further research is needed. In this chapter, we briefly
summarize those areas of research that will provide additional information
about the nature of photochemical aerosols and the physical and chemical
processes that are responsible for the evolution of the aerosol size distri
bution. Such information—particularly classification of the important
processes involved in gas-to-particle conversion—is essential to the dev-
elopment of dynamic models. We recommend that the following research be
undertaken to delineate the form of the growth relationship in the aerosol
model:
> Determination of the dependence of the rate of volume growth
on particle diameter. In Chapter II, we showed that the rate
at which the volume of an aerosol particle increases would be
proportional (1) to DD if the process were diffusion limited,
2
(2) to Dp if the growth were limited by surface-catalyzed
K o
reactions, or (3) to Dp if the growth were limited by volume-
catalyzed heterogeneous reactions. The rate constants measured
for heterogeneous reactions involving S02 and NOX indicate
diffusion-limited particle growth. However, further studies,
similar to those reported by Heisler and Friedlander (1974),
should be undertaken to provide experimental evidence for
diffusion-limited or heterogeneous-reaction-limited growth.
> Consideration of the use of growth relationships that treat
the composition of the aerosol particles as independent of
time. One of the most important questions that must be
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143
addressed in aerosol modeling is whether a growth relation-
ship that predicts unlimited growth of a particle (concen-
tration independent of time) can replace the rigorous theo-
retical expression that predicts an equilibrium size de-
pending on the gas phase concentration of the species being
converted. If the empirically derived growth relationships
can be employed in the modeling of urban aerosols, then a
significant simplification can be achieved by separating
the chemistry from the dynamics of the aerosol growth.
> Investigation of the behavior of the peak in the submicron
volume distribution in photochemical aerosols. Evidence
from the ACHEX study indicates that the mode in the sub-
micron volume distribution is not consistently centered about
0.25 pm as was previously thought. Since the growth of this
mode is apparently a result of gas-to-particle conversion,
an investigation of the development of this mode with time
can provide information about the process by which mass is
converted from the gas phase to the particulate phase. The
spatial variation of the mode may reflect the variation of
the chemical composition of the aerosol and the atmosphere.
> Examination of the distribution of chemical species in
individual aerosol particles. A closer examination of aero-
sol particles present in photochemical smog should be made
to determine whether particles are composed of an agglomera-
tion of chemical species or whether each particles consists
of only a limited number of species. ,
- .&
> Investigation of the thermodynamic state of aerosol particles.
It is generally assumed that the aerosol particles of interest
are droplets rather than solid particles. Further studies
should be made to determine the validity of this assumption.
-------
> Examination of the relation of the distribution of sulfate,
nitrate, and hydrocarbons to that of the gaseous pollutants.
In particular, the distribution of 03, NH3, and H20 gases,
which are known to play an important role in the stabiliza-
tion or transformation of sulfur-, nitrogen-, and carbon-
containing compounds should be compared with the distribu-
tion of the aerosol species. The availability of the ACHEX
data, the data from the Three-Dimensional Gradient Study
sponsored by the State of California Air Resources Board,
and the improvement of ammonia emissions inventories pro-
vide an excellent opportunity to investigate the role of
ozone, ammonia, and water vapor in aerosol chemistry.
> Further investigation of the role of liquid water in the
evolution of aerosols. During the 1972 ACHEX study, the
measurements of water content in aerosols indicated larger
quantities of liquid water present than would be expected
from the water vapor present in the air. The paths by
which water is adsorbed into aerosol particles must be
studied, since water represents a substantial fraction of
the aerosol mass. In particular, many of the constituents
of photochemical aerosols are hygroscopic or deliquescent,
and the size of the aerosol particles may be very sensitive
to the water vapor concentration in the surrounding air.
> Determination of the important reactions in the homogeneous
oxidation of SO? and the rate constants of these reactions.
> Determination of the route by which sulfate is incorporated
Into aerosols. It is possible that H2S04 or (NH^SC^ can
form homogeneously after the diffusion of S02 or SOs to the
particle. The importance of each of these routes and the
contribution of catalytic conversion should be determined.
-------
> Determination of the routes by which nitrate is formed in
aerosols.
> Determination of the organic compounds present in aerosols
Although organic compounds comprise the largest fraction of
photochemical aerosols and although most of these substances
are known to result from gas-to-particle conversion, knowledge
of the organic compounds present in aerosols and of their
spatial and temporal distributions is inadequate. In particu-
lar, to determine the paths by which organic compounds are
converted to the particulate phase, one must elucidate the
distribution of these compounds with respect to size and the
chemical species that are present with them.
> Measurement of the vapor pressures of these organic compounds
at room temperature.
> Improvement and extension of aerosol emissions inventories
to include both primary and secondary emissions. Existing
primary particulate emissions inventories specify tailpipe
emissions and locally measured size distributions. However,
these sources do not represent the sources that will be used
as input to the model. Because of the limited spatial reso-
lution of the model (for example, the SAI airshed model uses
two mile by two mile grid squares), the size distribution
of the primary aerosol emissions defined on the basis of the
grid size of the model will differ from that measured at the
sources because coagulation, sedimentation, and other physical
processes modify the size distribution and number density.
The emissions inventory for gaseous pollutants should be ex-
tended to include emissions of NH3 and to differentiate the
emissions of individual hydrocarbons, particularly olefins.
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146
> Investigation of the spatial distribution of aerosols and
water vapor In the Los Angeles basin. The three-dimensional
data obtained by the California Air Resources Board should
be studied to establish initial conditions on the vertical
distribution of pollutants in the Los Angeles basin. Fur-
thermore, the spatial and temporal distributions of water
vapor in the basin can be obtained from these data; they
should permit parameterization of the distribution of water
vapor in the aerosol model.
> Formulation of a dynamic aerosol model and its integration
into the airshed model. Clearly, much information is re-
quired before the process by which the distribution of aero-
sols in the urban atmosphere changes can be fully understood.
However, the information required to initialize and verify
simple models is now available, and an effort should be made
to develop such models, as discussed in Chapter IV.
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147
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156
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/4-76-016 d
2.
3. RECIPIENT'S ACCESSI ON-NO.
.TITLE AND SUBTITLE „
CONTINUED RESEARCH IN MESOSCALE AIR
POLLUTION SIMULATION MODELING. VOLUME IV- Examination
of the Feasibility of Modeling Photochemical Aerosol
Dynamics
5. REPORT DATE
May 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
T. N. JERSKEY AND J. H. SEINFELD
8. PERFORMING ORGANIZATION REPORT NO.
EF75-26
9. PERFORMING ORG \NIZATION NAME AND ADDRESS
SYSTEMS APPLICATIONS, INC.
950 NORTHGATE DRIVE
SAN RAFAEL, CALIFORNIA 94903
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
68-02-1237
12. SPONSORING AGENCY NAME AND ADDRESS
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
FINAL REPORT 6/74-6/75
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A mathematical model of the dynamics of photochemical aerosols should include
emissions of primary particulates and gaseous precursors of secondary aerosols, homo-
geneous nucleation, heterogeneous condensation, heterogeneous chemical reaction,
coagulation, advection, diffusion, settling, and deposition on surfaces. This report
discusses the tbaory of each of these processes and assesses the relative importance
of each in shaping the volume distribution of photochemical aerosols. The authors
conclude that in Los Angeles photochemical smog heterogeneous condensation is the
principal mechanism for changes of the volume distribution in the accumulation size
range, though homogeneous nucleation can be important under certain conditions for
forming very small particles (less than 100 A diameter). Coagulation must be con-
sidered in reshaping the size distribution- of emissions and in reducing the number of
particles formed by homogeneous nucleation. An in-depth assessment is also presented
of the pathways for the formation of aerosol material from the gas phase via homogen-
eous and heterogeneous chemistry. Finally, the equations governing the evolution of
the photochemical aerosol are derived and simplified on the basis of order-of-magnitud
calculations of the individual terms, and various equations for different properties
of the aerosol are derived and discussed.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
*Air Pollution
^Mathematical Models
*Photochemical Reactions
^Aerosols
13B
12A
07E
07D
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
156
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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