$$H^{*}$$ H ∗ Peusner’s Form of the Kedem–Katchalsky Equations for Non-homogenous Non-electrolyte Binary Solutions

Abstract

The paper presents a hybrid matrix form of Kedem–Katchalsky equations that contains Peusner’s coefficients $$H_{ij}^{*}\;(i, j = 1, 2)$$ for the conditions of concentration polarization and $$H_{ij}$$ for homogeneous solutions. The aqueous glucose solutions were analyzed in Nephrophan membrane system with membrane in horizontal plane. The calculations of coefficients $$H_{ij}^{*}$$ were made for the A and B configurations of the membrane system. In the A configuration glucose solution with higher concentration was located below and the solution with lower concentration above the membrane. In configuration B locations of the solutions were reversed. Non-diagonal coefficients of matrix $$[H^{*}]$$ (concentration polarization conditions) were shown to be linearly dependent on average concentration of glucose solution in the membrane. $$H_{12}^{*}$$ in A configuration was lower than in B configuration. Non-diagonal coefficients of matrix $$[H^{*}]$$ were lower than appropriate coefficients of matrix [H] (homogeneous solutions). For diagonal coefficients of matrix $$[H^{*}]$$ coefficient $$H_{11}^{*}$$ is constant and equal to $$H_{11}$$ , whereas $$H_{22}^{*}$$ and $$H_{22}$$ are nonlinearly dependent on average concentration of glucose solution in the membrane. Value of $$H_{22}^{*}$$ in A was lower than in B configuration of the membrane system. Additionally, $$H_{22}^{*}$$ were lower than $$H_{22}$$ . For both A and B configurations and concentration polarization conditions, the coefficients $$H_{12}^{*}$$ and $$H_{22}^{*}$$ of matrix $$[H^{*}]$$ are different for average solution concentrations $${>}5.41\,\hbox {mol}\,\hbox {m}^{-3}$$ due to convective mixing of solutions in B configuration.