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

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