In this paper, the Kedem–Katchalsky equations in matrix form for nonhomogeneous ternary nonelectrolyte solutions were applied for interpretation of transport through the membrane mounted in horizontal plane. Coefficients , , and (for nonhomogeneous solutions), H_ij and (for homogeneous solutions) (i, j ∈ {1, 2, 3}, r = A, B), , and were calculated on the basis of experimentally determined coefficients (L_p, σ₁, σ₂ω₁₁, ω₂₂, ω₂₁, ω₁₂, , and ) for glucose in aqueous ethanol solutions and two configurations of the membrane system. From the calculations, it results that the values of coefficients , , , , , , and depend nonlinearly on solution concentration as well as on a configuration of membrane system. Besides, the values of coefficients , , , , , and depend linearly on solution concentration. The value of coefficients H₁₃, H₂₃, and H₃₃ do not depend on solution concentration. The coefficients ψ₁₂, ψ₁₃, ψ₂₂ = ψ₂₃, ψ₃₂ = ψ₃₃, and ψ_det depend nonlinearly on solution concentration and for  ≈ 9.24 mol m⁻³ are equal to zero. For  < 9.24 mol m⁻³, the values of coefficients ψ₁₂ and ψ₁₃ are negative and for  > 9.23 mol m⁻³, positive. In contrast, the values of coefficients ψ₂₂ = ψ₂₃, ψ₃₂ = ψ₃₃, and ψ_det for  < 9.24 mol m⁻³ are positive and for  > 9.24 mol m⁻³, negative. For  = 0, we can observe nonconvective state, in which concentration Rayleigh number reaches the critical value R_C = 1691.09, for is convective state with convection directed straight down and for is convective state with convection directed straight up.

中文翻译：

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浓差极化条件下非电解质溶液的膜迁移：Kedem–Katchalsky–Peusner方程的形式

在本文中，非均质三元非电解质溶液的矩阵形式的Kedem–Katchalsky方程用于解释通过安装在水平面中的膜的传输。系数，，和（对于非均质溶液），ħ _IJ和（均相溶液）（我，Ĵ  ∈{1，2，3}，- [R  = A，B）， ，和分别计算实验确定的系数的基础上（大号_p，σ ₁，σ ₂ ω ₁₁，ω ₂₂，ω ₂₁，ω ₁₂，，和）在含水乙醇溶液中的葡萄糖与膜系统的两个配置。从计算，其导致该系数的值，，，，，，和对溶液中的浓度以及对膜系统的结构非线性依赖。此外，系数的值，，，，，和对溶液浓度线性依赖。系数H ₁₃，H ₂₃和H _33的值 不依赖于溶液浓度。系数ψ ₁₂，ψ ₁₃，ψ ₂₂  =  ψ ₂₃，ψ ₃₂  =  ψ ₃₃，和ψ _DET非线性取决于溶液浓度和 ≈9.24摩尔米^-3都等于零。对于 <9.24摩尔米^-3，系数的值ψ ₁₂和ψ ₁₃为负，而为 > 9.23摩尔米^-3，正。与此相反，系数的值ψ ₂₂ =  ψ ₂₃，ψ ₃₂  =  ψ ₃₃，和ψ _DET为 <9.24摩尔米^-3为正和为 > 9.24摩尔米^-3，负极。对于 = 0，我们可以观察到非对流状态，其中浓度瑞利数达到临界值R _C  = 1691.09，对于对流状态为对流垂直向下，对于对流状态为对流垂直向上。