  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.
