Advice on Analyzing Chloride Ion Penetration Profile Data
(Assumption of a semi-infinite media)
If at a fixed time, t, the free chloride concentration, C, as a
function of depth, x, is available, one can estimate the diffusion
coefficient, D, by fitting the following equation to the available
data (based on a solution of Fick's 2nd law for a semi-infinite media):
This assumes that C(external) is constant, such as exposure in
- C(x,t)/C(external) = erfc (x/(2.*sqrt(D*t)))
- Crank, J., The Mathematics of Diffusion,
Oxford University, 1975.
- Carslaw, J.S., and Jaeger, J.C., Conduction of Heat in Solids,
Oxford Press, 1978.
In practice, C(external) may vary with time and D may vary with
distance and time. The model available as part of this
distributed knowledge system computes C(x,t) for the case
where C(external) varies as a square-wave function and D is
a function of distance.
For the case of a two-layer composite, Carslaw and Jaeger
have developed a solution for the analogous heat conduction
problem. Transformed to mass transfer variables (as performed
by Andrade et al), the solution for a
semi-infinite media with a constant value of C(external) is given by:
where b is the thickness of the first layer and D1 and D2 are the diffusion
coefficients for the first (surface) and second (bulk) layers.
- Andrade, C., Diez, J.M., and Alonso, C., Mathematical Modelling
of a Concrete Surface "Skin Effect" on Diffusion in Chloride Contaminated Media,
Advances in Cement-Based Materials, 6, 39-44, 1997.