Asymptotic analysis of drug dissolution in two layers having widely differing diffusion coefficients

TL;DR

This paper uses asymptotic methods to analyze drug dissolution across two layers with vastly different diffusion coefficients, revealing that only one numerical calculation is needed regardless of the second layer's diffusion rate.

Contribution

It introduces an asymptotic approach to understand the moving boundary problem in drug dissolution with highly contrasting diffusion coefficients, simplifying the computational process.

Findings

Asymptotic analysis clarifies behavior in the second layer.

Only one numerical computation is needed regardless of the second layer's diffusion coefficient.

The similarity solution applies in the first layer but breaks down in the second, requiring new analysis.

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.