Theory of diffusion in gels

Abstract

It has been shown that when concentration of solute is expressed as amount per unit volume of gel-solvent-solute system, Fick's laws for diffusion in a gel take the same form as for diffusion in solvent alone, except that the usual coefficient must be replaced by a new coefficient, D', equal to D(1 - alphaphi)/(1 - phi), where phi is the effective volume fraction of the gel substance and alpha is a coefficient of obstruction equal to 5/3 if the gel substance can be considered to be made up of randomly oriented rods. An equation was derived for the total amount of solute entering the gel, which is analogous to but not identical with the equation for the total amount of solute crossing the initial boundary in free diffusion. The effect of slice thickness was investigated by a mathematical procedure involving the solutions of approximate differential equations. It was shown that even for slices so thick that 95 per cent of the solute in the gel is contained in the first two, a correction factor equal to the square of the slice thickness divided by 48D't permits one to obtain accurate measurement of D' from the mean concentration and the position of the midplane of the slice.