= 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> as
$$
J=h(c_s-c_b),
$$
where $h$ 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> $D$. Then
$$
J=\frac{D(c_i-c_s)}{L}=h(c_s-c_b),\qquad
J=\frac{c_i-c_b}{L/D+1/h}.
$$
The 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:
$$
\mathrm{Bi}_m=\frac{hL}{D},\qquad
\frac{J}{J_{h\to\infty}}=\frac{\mathrm{Bi}_m}{1+\mathrm{Bi}_m}.
$$
For $D=10^{-12}\,\mathrm{m^2/s}$, $L=10^{-4}\,\mathrm m$ and $h=10^{-7}\,\mathrm{m/s}$, $\mathrm{Bi}_m=10$ 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.<Adaptive Perfusion: A Novel In Vitro Drug Release Testing Method for Complex Drug Products by the FDA>[Technology Summary, transport limitation and pressure-driven filtration]{ref} Small bulk concentration alone cannot establish negligible surface resistance.
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