Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

Abstract

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusion coefficient is many orders of magnitude smaller. It has been shown in an earlier paper that a similarity solution exists while the front is passing through the first layer, but that this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusion coefficient is for the second layer.

Theoretical model for diffusion-reaction based drug delivery from a multilayer spherical capsule

“…A recent paper presented analysis of diffusion-reaction in a multilayer Li-ion cell [9]. Some work also exists in the context of drug diffusion in a two-layer or three-layer structure [20][21][22][23][24], but these studies are focused on specific problems, do not present generalized multilayer analysis and often rely on numerical analysis. On the other hand, analytical solutions may be desirable compared to numerical solutions because of the fundamental insights that analytical solutions provide, as well as the potential improvement in computational cost and complexity.…”