KAGAKU KOGAKU RONBUNSHU, Vol.30, No.4, 522-531, 2004
Calculation of concentration-dependent diffusivity in desorption processes in which the diffusivity may have a maximum value, based on the integral form of diffusion equation with the dissolved solid-based coordinate
The solid-based coordinate, which is useful for auto-matic treatment of shrinkage due to evaporation of solvent, may include a maximum value of diffusivity in a desorption (isothermal drying) process with a high initial solvent concentration. Here, a method for calculation of (integral diffusivity)/(desorption rate x efficiency) in such cases is presented, based on the integral form of the diffusion equation with the solid-based coordinate, using two empirical correration equations: 1) the relation between the 1st moment and the zero moment of concentration distribution, 2) the estimation equation for the ratio of average to center concentration from desorption rate master curves. Both (integral diffusivity) and (desorption rate x efficiency) are constant in the penetration period. The ratio of the two decreases monotonously with center concentration to a constant value of 0.65 in the last stage of the regular regime. The ratios at the end-point of the penetration period and in the regular regime are presented by empirical equations and in figures as functions of the ratio of average to center concentration. The diffusivity and the mutual diffusion coefficient can be calculated as a function of concentration, by differentiation of plots of (integral diffusivity) vs. (center concentration), obtained from desorption data of various initial concentrations with a constant surface concentration. The numerical solutions of the diffusion equation were used for derivation and confirmation of the above calculation method, using various actual systems besides power and exponential models. As actual systems with empirical concentration-dependent diffusivities that have a maximum diffusivity, a food aqueous solution of sucrose and polymer-solvent solutions such as PVA-water, polystyrene-ethylbenzene, polyimide-parachlorophenol were used.