= Sink-boundary approximation error in drug release
<Sink-boundary approximation error in drug release> is the difference between a release prediction using an ideal receiving boundary and one that accounts for the actual boundary. The reference prediction and the error denominator must be specified. Finite external resistance and nonzero bulk drug concentration are separate departures from a <perfect sink condition in drug release>.
For the maintained-reservoir steady planar model, let the internal concentration be $c_i>0$, receiving bulk concentration $c_b$, matrix thickness $L$, internal <diffusion coefficient> $D$ and external transfer coefficient $h$. With compatible concentration scales,
$$
J=\frac{c_i-c_b}{L/D+1/h}.
$$
The ideal zero-bulk, negligible-external-resistance prediction is $J_0=Dc_i/L$. Defining $\beta=c_b/c_i$ and the <mass-transfer Biot number for drug release> $B=hL/D$ gives
$$
\frac{J}{J_0}=(1-\beta)\frac{B}{1+B},\qquad
\frac{J_0-J}{J_0}=\beta+\frac{1-\beta}{1+B}.
$$
This is the <combined boundary-resistance and bulk-concentration error in drug release> for the stipulated model. It is not an exact transient error formula for every dosage form.
An original example with $B=20$ and $\beta=0.10$ gives $J/J_0=6/7$. The ideal flux overpredicts by about $14.3\%$ relative to $J_0$, or $16.7\%$ relative to $J$. Making external transport arbitrarily fast still leaves the concentration-related error floor $\beta$ in the first error convention.
The model also supplies a transparent tolerance rule. For $0\le\beta<\varepsilon<1$, requiring $(J_0-J)/J_0\le\varepsilon$ gives
$$
B\ge\frac{1-\varepsilon}{\varepsilon-\beta}.
$$
At $\varepsilon=0.05$ and $\beta=0.01$, the threshold is $23.75$. If bulk accumulation already exceeds the tolerance, increasing $h$ alone cannot meet it.
Experimentally, changing receiving volume tests accumulation, while changing flow or membrane transport tests external resistance; <sampling correction in drug release testing> is needed when material is removed. The FDA’s primary adaptive-perfusion account specifically identifies passive membrane transport as potentially rate-limiting.<Adaptive Perfusion: A Novel In Vitro Drug Release Testing Method for Complex Drug Products by the FDA>[Technology Summary, dialysis limitations and pressure-driven filtration]{ref} Separating the two effects prevents a large receiving volume from being mistaken for proof of an ideal surface boundary.
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