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

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 diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but 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 diffusivity is for the second laye

A Singular-Perturbed Two-Phase Stefan Problem Due to Slow Diffusion

The asymptotic behaviour of a singular-perturbed two-phase Stefan problem due to slow diffusion in one of the two phases is investigated. In the limit the model equations reduce to a one-phase Stefan problem. A boundary layer at the moving interface makes it necessary to use a corrected interface condition obtained from matched asymptotic expansions. The approach is validated by numerical experiments using a front-tracking method

A Singular-Perturbed Two-Phase Stefan Problem Due to Slow Diffusion

this paper to give even a rough overview of the existing literature. Instead we refer the interested reader to [9] for an excellent review. In the sequel we shall make extensive use of the fact that our model problem (1.1), (1.2) has a unique solution. This existence and uniqueness result is well--known and a special case of much more general results [2, 3, 4]. We are interested in the case, where the diffusion equations degenerate to a singularly perturbed problem due to slow diffusion in one of the two phases, e.g. k 1 = " ø k 2 = 1. 2 J. Struckmeier and A. Unterreite

A Singular-Perturbed Two-Phase Stefan Problem Due to Slow Diffusion

this paper to give even a rough overview of the existing literature. Instead we refer the interested reader to [9] for an excellent review. In the sequel we shall make extensive use of the fact that our model problem (1.1), (1.2) has a unique solution. This existence- and uniqueness result is well-known and a special case of much more general results [2, 3, 4]. We are interested in the case where the diffusion equations degenerate to a singularly perturbed problem due to slow diffusion in one of the two phases [7], e.g. k 1 = " ø k 2 = 1. 2 J. Struckmeier and A. Unterreite