Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery

TL;DR

This paper develops an analytical model for mass diffusion in multi-layer spheres immersed in semi-infinite media, with applications to drug delivery, providing explicit solutions for concentration profiles and mass transfer.

Contribution

It introduces a general analytical solution for multi-layer sphere diffusion problems with boundary resistance, specifically applied to drug kinetics in microcapsules.

Findings

Explicit concentration profiles in multi-layer spheres

Dependence of drug release on surface mass transfer coefficient

Analytical solutions avoiding finite domain truncation

Abstract

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.