Anderson J L, Malone D M
Biophys J. 1974 Dec;14(12):957-82. doi: 10.1016/S0006-3495(74)85962-X.
A model for osmotic flow in porous membranes is developed from classical transport and thermodynamic relations. Mathematical expressions for the reflection coefficient as a function of solute dimension and shape, and more generally pore/bulk distribution coefficient, are derived for long cylindrical pores of circular cross section. For a rigid, spherical macromolecule the osmotic reflection coefficient equals (1 - Phi)(2), where Phi is the solute distribution coefficient; this result differs significantly from expressions found in the literature. The effect of weak solute adsorption to (or repulsion from) the pore wall can also be accounted for in the derivation. The driving force for osmotic flow arises from solute-pore wall interactions which cause radial variations in concentration and concomitant gradients in pressure normal to the wall. Implications of this three-dimensionality of osmotic phenomena are discussed with particular reference to the adequacy of one-dimensional treatments in relating reflection coefficient to membrane and solute properties.
基于经典的输运和热力学关系，建立了一种多孔膜中渗透流的模型。对于圆形横截面的长圆柱形孔，推导了反射系数作为溶质尺寸和形状函数的数学表达式，更一般地说，推导了孔/本体分配系数的数学表达式。对于刚性球形大分子，渗透反射系数等于(1 - Φ)²，其中Φ是溶质分配系数；这一结果与文献中的表达式有显著差异。在推导过程中，也可以考虑溶质对孔壁的弱吸附（或排斥）效应。渗透流的驱动力源于溶质与孔壁的相互作用，这种相互作用导致浓度的径向变化以及垂直于壁的伴随压力梯度。特别参考了一维处理在将反射系数与膜和溶质性质联系起来方面的充分性，讨论了渗透现象这种三维特性的影响。
