Friedman M H
Biophys J. 1970 Nov;10(11):1013-28. doi: 10.1016/S0006-3495(70)86350-0.
The formalisms of irreversible thermodynamics are used to describe multi-ionic nonconvective flow through an arbitrarily charged membrane. Interactions between oppositely charged ions are included and are measured by a single phenomenological coefficient. The consequent generalized Nernst-Planck flux equations are integrated to yield a relation between the species fluxes and the composition of the solutions bounding the membrane. It is assumed in the derivation that activity coefficient gradients within the membrane and direct interactions between ions of like charge are negligible. Some special cases are examined. To illustrate the use of the final equations, a single membrane separating solutions of differing composition is modeled, and the effect of ion-ion interactions on the membrane potential and the ion fluxes is demonstrated for several values of diffusion current density and membrane charge density.
不可逆热力学的形式体系被用于描述通过任意带电膜的多离子非对流流动。包含了相反电荷离子之间的相互作用，并通过一个单一的唯象系数来度量。由此得到的广义能斯特-普朗克通量方程被积分，以得出物种通量与界定膜的溶液组成之间的关系。在推导过程中假设膜内的活度系数梯度以及同电荷离子之间的直接相互作用可忽略不计。研究了一些特殊情况。为说明最终方程的应用，对分隔不同组成溶液的单个膜进行了建模，并针对几个扩散电流密度和膜电荷密度值，展示了离子-离子相互作用对膜电位和离子通量的影响。
