United States
Environmental Protection
Agency
Atmospheric Sciences
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S3-88/027 Sept. 1988
x>EPA Project Summary
Theoretical Damage
Function for the Effects of
Acid Deposition on Galvanized
Steel Structures
J. W. Spence and F. H. Haynie
A theoretical damage function for pre-
dicting the corrosion of galvanized steel
structures by wet and dry deposition has
been developed from thermodynamics
and kinetics of atmospheric corrosion
chemistry. The function mathematical-
ly expresses the competing reactions for
the build up and dissolution of the basic
zinc carbonate corrosion film with ex-
posure time. Major findings as expressed
by the theoretical function are as follows:
• During periods of surface wetness,
SO2 reaching the surface reacts
stoichiometrically with the zinc.
• Rain acidity reacts stoichiometrical-
ly with the zinc.
• The corrosion film of basic zinc car-
bonate is soluble in clean rain. The
dissolution depends on the
residence time of rain on the
galvanized steel surface.
• Deposition velocity controls the rate
of corrosion of galvanized steel
structures by gaseous S02 during
periods of wetness.
Chamber and field exposures of
galvanized steel were conducted to
enhance the development of wet and dry
deposition components of the
theoretical damage function.
This Project Summary was developed
by EPA's Atmospheric Sciences Research
Laboratory, Research Triangle Park, NC,
to announce key findings of the research
project that is fully documented in a
separate report of the same title (see Pro-
ject Report ordering information at
back).
Introduction
The Atmospheric Sciences Research
Laboratory (ASRL) within the Environmen-
tal Protection Agency is conducting an ex-
posure research program on various
materials of construction. A goal of this
research is to develop damage functions for
construction materials sensitive to wet and
dry deposition. Wet deposition involves an-
thropogenic acidity within rain, snow, and
fog, whereas gaseous pollutants are
associated with dry deposition. A damage
function is a mathematical expression that
relates the rate of degradation of particular
material to the environmental factors that
contribute to the degradation.
Galvanized steel is one construction
material that ASRL is investigating because
it is widely used as roofing, siding, fencing,
automotive bodies, etc., and is exposed to
wet and dry deposition. Zinc is galvanical-
ly more active than iron and serves as an
anode when the two metals are coupled,
thereby protecting steel structures. The ser-
vice life of galvanized steel structures
depends on maintaining the zinc coating
during exposure.
The use of an empirically-derived
damage function from test panels to predict
corrosion rates of galvanized steel products
on real structures with environmental data
of unknown accuracy and precision, raises
considerable concern. Galvanized steel
structures are not standard test specimens.
Moreover it is not possible to determine the
environmental parameters surrounding
each structure with the same accuracy and
precision as measured at test sites. It would
produce not only biased errors, moreover
-------
the calculated confidence limits would be
misleading.
To address this problem, the following
steps are being taken to develop a damage
function for galvanized steel that can be us-
ed to assess damage to real structures.
1. Use fundamental principles of ther-
modynamics and kinetics to derive a
theoretical damage function,
2. Establish the applicability and con-
sistency of the theoretical function us-
ing laboratory and field experiments,
3. Confirm applicability to changing real
world environments using standard-
ized exposure procedures at test sites
where the accuracy and precision of
environmental parameters are known,
and
4. Check how well the function can
predict corrosion rates on real struc-
tures with environmental parameters
of unknown accuracy and precision.
This paper describes a damage function
for galvanized steel structures that was
developed using princples of ther-
modynamics and kinetics. The function
which predicts the effects of wet and dry
deposition is consistent with existing
laboratory and field exposure data of
galvanized steel and zinc specimens.
Theoretical Considerations
Galvanized steel exposed to the at-
mosphere soon forms a protective coating
of basic zinc carbonate 2ZnC03«3Zn(OH)2.
Recent studies suggest that this coating
consists of two layers, in which ZnO or
Zn(OH)2 is the adherent layer at the zinc
surface, and the outer layer is basic zinc
carbonate. The basic zinc carbonate film
retards corrosion, and if its composition
does not change or is not removed, corro-
sion would be parabolic with time. The film
is soluble, however, in acidic solutions. Ac-
cordingly, it can be expected that (1) wet
deposition will dissolve this protective film
and (2) dry deposition, e.g., SO2, will
chemically change its composition into
more soluble salts of zinc.
The net metal corroded (C) at any time
can be accounted for as the sum.of metal
ion dissolved from the film (Btw) and the
metal ion contained in the film (F).
The rate of corrosion film thickness growth
in term of metal corroded is
Btw
(D
where C = corrosion
tw = time of wetness (yrs)
B = solution rate of the pro-
tective corrosion film, a
function of pollutant flux
to the film (;tm/yr)
= A/F - B
dtw
(2)
where A = function of diffusivity
of corrosive species
through film (/jm2/yr)
Diffusivity (A) may also be affected by
pollutants. Integrating equation 2 under
constant condition, Haynie derived the
following transcendental equation:
C = Btw + A[1-exp(-BC/A)]/B
(3)
After long exposures, the term -BC/A is
large and the term exp(-BC/A) approaches
zero and equation 3 becomes a linear
function:
C = Btw + A/B,
(4)
i.e., when the long term steady state is
reached, the rate of formation of the corro-
sion product film is equal to the rate of
dissolution.
Corrosion should be controlled by the dif-
fusion of ions through the corrosion product
film, a function of diffusivity and film
thickness. Dissolution removal of the film
will increase the corrosion rate. When ex-
posed in a polluted environment, the cor-
rosion product film would be thin hence
linear corrosion would occur early in the ex-
posure. In a nonpolluted environment, the
film would continue to grow and curvature
of the corrosion-time curve would be
observed. The corrosion function becomes
linear with respect to the solubility term
(Btw and the amount of corrosion in the in-
soluble film (F=A/B) remains constant with
respect to a given set of solubility condi-
tions (B). The solubility term (Btw) can be
separated into environmental components
involving wet and dry deposition. These wet
and dry delivery mechanisms serve as a
convenient means of describing the corro-
sion rate-controlling factors. We attempt to
express corrosion as a sum of contributions
from wet and dry deposition.
Wet Deposition
Rain contributes not only to the time of
wetness but also delivers reactive species
(SCv2, H + , HCCv, etc.) to the surface.
The rate of delivery is the amount of rain
per unit time multiplied by the ion
concentration.
Acid Reaction with Metal
The acidity in rain, pH or (H+), can in-
crease the corrosion rate by increasing the
solubility of the corrosion product film.
These ions also are consumed and replac-
ed electrochemically in solution by zinc
ions, 2H+ = Zn++. The reaction is pro-
bably fast enough so that the rain residence
time on the surface is not a factor. The up-
per limit of acid zinc corrosion simply is a
function of the amount of rainfall and its pH.
Hydrogen ion concentration [H + ],
equivalents per liter, is 10-PH. Hence,
hydrogen ion equivalents delivered per cm2
of horizontal surface is the amount of rain
(R), cm, times 10-3-PH. One equivalent of
H + per cm2 of zinc will consume 4.6 cm of
zinc (the ratio of equivalent weight to den-
sity). Thus zinc corrosion caused by rain
acidity is
Cra = 46 R10-PH.
(5)
where R = total rainfall during ex-
posure (cm)
Cra = corrosion due to acidic
rain
With rain assumed to fall vertically, the
average loss on both sides of a specimen
exposed at 30° from the horizontal will be
less by a factor of 0.5 cos 30°.
Dissolution of Zinc Carbonate
Clean rain solubility is associated with
acidity caused by dissolved carbon dioxide
from the atmosphere. This produces the
HCO3- ion that contributes to the solubili-
ty of the basic zinc carbonate. The solubility
of zinc carbonate varies with the concen-
tration of CO2 in aqueous solutions which
depends on the atmospheric concentration
of C02 and temperature; as temperature in-
creases, the solubility decreases. If it is
assumed that rain water equilibrates with
both atmospheric CO2 and the galvanized
steel surface, then "clean rain" corrosion
can be calculated from the solubility of zinc
carbonate.
The solubility of a metal carbonate
(MeCO3) in water containing dissolved car-
bon dioxide can be treated as an
equilibrium problem between two con-
densed phases and a reactive gas. The en-
thalpy, entropy and heat capacity are
used to calculate the equilibrium constants
for the relationship.
K = 4(Me + 2)3pco2 or (6)
ME+2 = [KPco2/4]1/3
and expressed as a function of temperature
using appropriate thermodynamic data for
zinc
K = exp[-126.6 + 9583H" + 13.59lnT]. (7)
-------
WJien the mean value for atmospheric
concentration of carbon dioxide of approx-
imately 345 ppm, or 0.000345 atmospheres
pressure as reported in Chemical &
Engineering News is substituted above, the
equilibrium concentration of zinc ion
dissolved from zinc carbonate by air-
saturated water is 4.42x10-2K1'3 moles/liter.
Thus R cm of rain will dissolve
4.42x10-4RK1/3 moles of zinc carbonate. If
it is assumed that each mole of zinc car-
bonate is replaced by corrosion of an
equivalent amount of zinc metal, then,
multiplying by the ratio of zinc atomic
weight to density gives the amount of cor-
rosion by "clean" rain (Crc) as
Similarly for air flowing perpendicular to
cylinders, such as fencing, where diameter
replaces length in the Reynolds number the
friction factor is:
Crc = 4.05
(8)
where a residence time factor (r) has been
included to allow for the fact that rainwater
may not remain in contact with the surface
long enough to reach equilibrium.
Dry Deposition
Both gaseous and paniculate pollutants
are deposited to surfaces, but the deposi-
tion mechanism differs. The rate of delivery
of gases to a surface is determined by air
flow, whereas particulate matter is
deposited by gravitational settlement and
wind-blown impaction.
Deposition Gases
The ambient concentration of a gaseous
pollutant is related to pollutant flux to a sur-
face by defining deposition velocity (Vd) as
the ratio of the flux to the ambient concen-
tration measured at some point away from
the surface. From analogy with momentum
transport, gases with a Schmidt number of
approximately one that readily absorb on
a surface have a deposition velocity of:
Vd = V*2/V = Vf/2
0)
where V* = friction velocity,
V = average windspeed
near the surface, but
not within the bound-
ary layer.
The friction velocity (V*) is equal to V Vf/2
where f is the friction factor. From boundary
layer theory for smooth flat plates, the equa-
tion for the friction factor is:
f = 0.03/(REL)1'7 (10)
where RE[_ = Length Reynolds
number, LV/v,
L = length of surface over
which air flows, and
= kinematic viscosity of
air (0.15 cm2/s at
20°C).
f = 0.6/(RE)i/2
(11)
Another factor to consider is that wind-
speeds are normally measured at the top
of a tower while corrosion panels as well
as fencing and siding are usually closer to
the ground. Windspeed varies with height
from the ground and can be approximated
by the following relationship:
V+ = 8.5 + 2.5 ln(Z/e) (12)
where V+ = a dimensionless
velocity (V/V*),
V* = friction velocity for the
ground surface veloci-
ty profile,
Zi = the measured height
above ground, and
e = the surface roughness
height.
The ratio of the velocity at exposure height
(Z2) to the velocity at measured height (Z^
with a surface roughness of 0.1 m will be
[1 + 0.175ln(Z2)]/[1 + 0.175ln(Z1)].
From the above relationships it can be
seen that wind velocity, and shape and size
of a surface affect deposition velocity. It is
informative to compare deposition
velocities calculated for 10.2 x 15.2 cm2 cor-
rosion specimens, with those for a three
meter length of sheet and nine gauge
(3.76mm diameter) galvanized fence wire.
With deposition velocity (Vd) in cm/sec and
windspeed (V) in m/sec, the results are:
Corrosion Specimen: Vd = 0.414V6'7 (13a)
Large Sheet: Vd = 0.259V6/7(13b)
Fencing: Vd = 1.89V1/2 (13c)
For an average windspeed at the surface
of 3 m/s, the respective deposition
velocities are 1.06 cm/s, 0.66 cm/s, and 3.27
cm/s. Thus, fencing is expected to corrode
faster than roofing and siding when ex-
posed to the same gaseous pollutants.
While gases may be delivered to the sur-
face at calculated deposition velocities, the
net flux of a gas is not necessarily propor-
tional to the deposition velocity. For exam-
ple, sulfur dioxide is readily absorbed and
then reacts with a wet zinc surface whereas
nitrogen dioxide does not. A dry zinc sur-
face is soon saturated with a monolayer of
sulfur dioxide, hence the net flux is zero,
i.e., the amount delivered is equal to that
removed. This monolayer can be consum-
ed later when the surface becomes wet. A
monolayer of S02 is equivalent to 1.29 x
10-* micrometers loss of a clean zinc sur-
face. Unless the SO2 concentration is ex-
tremely low a monolayer will form between
periods of wetness (usually daily).
Sulfur dioxide, which has a solubility of
1.24 mole/latm in liquid water at 25 °C, not
only readily dissolves in water but also
reacts with zinc. Therefore when a zinc sur-
face is wet, the rate of reaction of SO2 will
be controlled by the calculated deposition
velocity.
A metal surface will be wet by rain or dew.
The presence.of hygroscopic salts, e.g.,
ZnSO4, increases the effective dew point,
or equivalently lowers the critical relative
humidity as:
RHC = 96.3 - 0.313DP (14a)
where DP = ambient dew point
Therefore, time-of-wetness (tw) can be
defined as the amount of time that it is rain-
ing plus when the relative humidity exceeds
96.3 - 0.313DP and the dew point is greater
than O°C (not freezing). A relationship for
relative humidity as a function of
temperature (T) and dew point (DP) above
°C is
RH = 100 exp [-.07222 + (14b)
0.00025(T + DP)(T-DP)]
where T and DP = temperature and
dew point, °C respectively
The total zinc corrosion (Cd) due to
deposition of gaseous sulfur dioxide dur-
ing periods of surface dryness (Cm) and
wetness can be calculated as follows:
Cd = Cm + 0.045 Vd(S02M15)
where Cm = 1.29.10-4ArN
Ar = actual to apparent surface
area ratio,
N = number of dryness
periods, and
Vd = deposition velocity (cm/s).
During a year with daily periods of dryness
and Ar equals two, the corrosion due to the
monolayer(Cm) of SO2 equals 0.094
micrometers for a year. This contribution
should not be very significant unless SO2
concentrations during period of wetness
are relatively low.
Theoretical Damage Function
Combining all of the theoretical com-
ponents contributing to the corrosion of zinc
and galvanized steel the following damage
function is obtained:
-------
; = F + Cra + Crc + Ca, or (16)
= F + 46R10-PH + 3.9rRK1/3 +
.29.10-4ArN + 0.045Vd(SO2)tw
For this function, F represents the zinc
corrosion remaining in the corrosion film,
the components Cra + Crc represent the
effects of acidic rain and clean rain for wet
deposition, and the last two components
represent the effect of dry deposition of
gaseous SO2 that occurs during periods of
surface dryness and wetness.
A listing of all the terms, the appropriate
units, and definition of these terms for the
components of the theoretical damage
function is shown in Table 1. There are
twenty-two terms not counting temperature,
dewpoint, length and diameter.
Experimental Procedure
Laboratory and field exposure ex-
periments were conducted to enhance the
development of the theoretical damage
function. The galvanized steel panels for
these experiments were prepared from
sheet stock of 20-gauge zinc-coated (hot-
dipped) steel. The average thickness of the
coating was 20 ^m. The panels were
cleaned prior to exposure by two minute im-
mersion in 10% aqueous solution of am-
monium chloride (NH4CI) at 60 to 80°C. The
panels then were rinsed with deionized
Vd
SO,
F
R
pH
K
r
Ar
N
V
V
B
f
RE
Table 1. Definition of terms for the theoretical damage function
Terms Units Definition of Terms
C /im Total zinc corrosion
Cra /"" Corrosion caused by rain acidity = 46R x 10-"H
Crc prn Clean rain effect = 3.9rRK'/3
Cm fim SO2 monolayer absorption effect = 1.29 x
cm/s Deposition velocity = V2/V = Vf/2
fig/m3 Sulfur Dioxide concentration
years Time-of-wetness = when raining plus when critical relative humidity (RHc) is ex-
ceeded and dew point (DP) exceeds 0°C
/
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