 Finite mass-transfer boundary in drug release

A finite mass-transfer boundary in drug release represents a release surface whose receiving medium removes drug at a finite rate. The surface concentration can therefore exceed the bulk concentration. This is an alternative to imposing a perfect sink condition in drug release directly at the matrix surface.

Write the outward mass flux aswhere $h$ is a transfer coefficient, $c_s$ is surface concentration and $c_b$ is bulk concentration on the same concentration scale. Combined with a diffusion equation inside the matrix, this is a Robin boundary condition: surface value and concentration gradient are coupled. If the two phases use different concentration scales, an appropriate partition relation is also needed rather than silently equating them.

A steady planar example makes the resistances explicit. Suppose a matrix layer of thickness $L$ has a maintained concentration $c_i$ at its inner face and constant diffusion coefficient $D$. ThenThe matrix resistance $L/D$ and external resistance $1/h$ add. This calculation assumes a maintained inner reservoir; it is not a complete transient solution for a depleting dosage form.

The mass-transfer Biot number for drug release compares those resistances:For $D=10^{-12}{\mathrm{m}}^2/s$, $L=10^{-4}\mathrm{m}$ and $h=10^{-7}m/s$, ${\mathrm{Bi}}_m=10$ and the flux is about $90.9\%$ of the negligible-external-resistance value. Doubling $h$ raises this to about $95.2\%$; it does not double the flux because matrix resistance remains.

The distinction is experimentally important. Increasing stirring, flow or membrane permeability tests whether receiving-side transport limits an observed release curve, although other experimental conditions must be controlled. The FDA’s primary adaptive-perfusion description specifically identifies passive dialysis-membrane transport as potentially rate-limiting and describes pressure-driven tangential filtration as an alternative.^[ref] Small bulk concentration alone cannot establish negligible surface resistance.