Radial Diffusion in a Sphere with Subsequent Change in Dimension. Desorption with a Finite Surface Coefficient of Mass Transfer in an Infinite Volume

Abstract

The liquid located in a polymer evaporates by following a process controlled by diffusion-evaporation. The general case when the desorption is followed by subsequent shrinkage is studied by considering a spherical polymer with a radial diffusion and a finite rate of evaporation. The volume of the surrounding is so large that it can be considered as infinite. The mathematical treatment is achieved, leading to general equations of radial diffusion and evaporation with a following change in dimension of the polymer. These general equations reduce to the Fick's equation when the amount of substance transferred is small enough. These general equations have no analytical solution, and the problem is resolved by using a numerical method with finite differences. The following parameters are of interest: the diffusivity, the coefficient of mass transfer on the surface, the radius of the empty bead, the relative volume expansion of the polymer due to the presence of the diffusing substance.

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