  One of the promising frontiers of bioengineering is the controlled release of
a therapeuticdrug from a vehicle across the skin (transdermal drug delivery).
In order to study the complete process, a two-phase mathematical model
describing the dynamics of a substance between two coupled media of different
properties and dimensions is presented. A system of partial differential
equations describes the diffusion and the binding/unbinding processes in both
layers. Additional flux continuity at the interface and clearance conditions
into systemic circulation are imposed. An eigenvalue problem with discontinuous
coefficients is solved and an analytical solution is given in the form of an
infinite series expansion. The model points out the role of the diffusion and
reaction parameters, which control the complex transfer mechanism and the drug
kinetics across the two layers. Drug masses are given and their dependence on
the physical parameters is discussed.
