Mikulecky D C
Biophys J. 1972 Dec;12(12):1642-60. doi: 10.1016/S0006-3495(72)86187-3.
A concept is presented for modeling flows through membranes using continuum mechanics. Viscous interactions (due to velocity gradients) are explicitly incorporated and position-dependent local water-membrane interactions are taken into account before obtaining slab averages. This is in distinction to other treatments where strictly one-dimensional force balance equations are written using slab average friction coefficients which are really composite functions of local interactions. It is shown that the viscous and other frictional interactions do not simply form linear combinations in the solutions to the equations of motion. Flow profiles for pressure-driven flows ranging from Poiseuille's flow to "diffusion" flow are obtained depending on the strength and extent of the water-membrane interaction. The model is also applied to self-diffusion flows and the measurement of "equivalent pore size." It is shown that for a fixed pore size the ratio of filtration flow to self-diffusion flow for equal driving forces is able to vary over a wide range depending on the water-membrane interaction.
提出了一种使用连续介质力学对通过膜的流动进行建模的概念。明确纳入了粘性相互作用（由于速度梯度），并在获得平板平均值之前考虑了位置相关的局部水 - 膜相互作用。这与其他处理方法不同，在其他方法中，使用实际上是局部相互作用的复合函数的平板平均摩擦系数来编写严格的一维力平衡方程。结果表明，粘性和其他摩擦相互作用在运动方程的解中并非简单地形成线性组合。根据水 - 膜相互作用的强度和程度，获得了从泊肃叶流到“扩散”流的压力驱动流的流动剖面。该模型还应用于自扩散流和“等效孔径”的测量。结果表明，对于固定孔径，在相等驱动力下过滤流与自扩散流的比率能够根据水 - 膜相互作用在很宽的范围内变化。
