Determination of Concentration Dependent Diffusion Coefficient from Drying Rates

Abstract

When the diffusion coefficient decreases with decreasing concentration, an isothermal drying process(desorption process), in which the surface concentration holds its equilibrium value, can be divided into two stages. In the first stage, where the process can be considered as diffusion in a semi-infinite medium, the initial desorption rate is usually approximated to an integral average diffusion coefficient. However, this is not a good approximation when the concentration dependence of the diffusion coefficient is strong. In the second stage, the effect of the initial concentration is negligible and the desorption rate is governed by the average concentration only as shown by Schoeber. A method for the determination of the concentration dependent diffusion coefficient from the drying rates of both stages is proposed. The desorption curves were numerically calculated with various types of the concentration dependence of the diffusion coefficient. Then, the desorption rates were correlated with a weighted mean diffusion coefficient. It was found that in the first stage the desorption rates were closely related to a single type of weighted mean diffusion coefficient proposed by Crank. In the second stage, another single type of weighted mean diffusion coefficient was found to represent the desorption rates. An approximate calculation procedure for the whole desorption curve is presented, in which the above two weighted mean diffusion coefficients are used. The calculated results by this method were in good agreement with those by the finite-difference method.