The paper presents the Rr matrix form of Kedem–Katchalsky–Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner’s coefficients Rijr and det [Rr] (i, j ∈ {1, 2, 3}, r = A, B) occurring in these equations, were calculated for Nephrophan biomembrane, glucose in aqueous ethanol solutions and two different settings of the solutions relative to the horizontally oriented membrane for concentration polarization conditions or homogeneity of solutions. Kedem–Katchalsky coefficients, measured for homogeneous and non-homogeneous solutions, were used for the calculations. The calculated Peusner’s coefficients for homogeneous solutions depend linearly, and for non-homogeneous solutions non-linearly on the concentrations of solutes. The concentration dependences of the coefficients Rijr and det [Rr] indicate a characteristic glucose concentration of 9.24 mol/m3 (at a fixed ethanol concentration) in which the obtained curves for Configurations A and B intersect. At this point, the density of solutions in the upper and lower membrane chamber are the same. Peusner’s coefficients were used to assess the effect of concentration polarization and free convection on membrane transport (the ξij coefficient), determine the degree of coupling (the rijr coefficient) and coupling parameter (the QRr coefficient) and energy conversion efficiency (the (eijr)r coefficient).

中文翻译：

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描述浓度极化条件下膜传输的 Kedem-Katchalsky-Peusner 模型方程的 Rr 形式

本文提出了非均质三元非电解质溶液膜传输的 Kedem-Katchalsky-Peusner 方程的 Rr 矩阵形式。这些方程中出现的 Peusner 系数 Rijr 和 det [Rr] (i, j ∈ {1, 2, 3}, r = A, B) 是针对 Nephrophan 生物膜、乙醇水溶液中的葡萄糖以及两种不同的溶液设置进行计算的相对于水平定向膜的浓差极化条件或溶液的均匀性。对均匀和非均匀溶液测量的 Kedem-Katchalsky 系数用于计算。对于均质溶液，计算出的 Peusner 系数与溶质浓度呈线性关系，对于非均质溶液，则与溶质浓度呈非线性关系。系数 Rijr 和 det [Rr] 的浓度依赖性表明特征葡萄糖浓度为 9.24 mol/m3（在固定乙醇浓度下），其中配置 A 和 B 获得的曲线相交。此时，上下膜室中溶液的密度相同。Peusner系数用于评估浓差极化和自由对流对膜传输的影响（xiij系数），确定耦合程度（rijr系数）和耦合参数（QRr系数）和能量转换效率（（eijr） r系数）。