Modification of the Kedem — Katchalsky — Zelman Model-Equations of the Transmembrane Transport

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“…The CBL are regions in the external solutions, adjacent to the membrane interfaces where concentration gradients are maintained under steady-state conditions and act as pseudo-membranes in series with the physical membrane [19][20][21][22]. Consequently, they can produce substantial reductions in transmembrane flows [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The paper by Barry and Diamond [19] reviews the effects of boundary layers on membrane phenomena.…”

“…Of especial interest is the case of formation of CBL on both sides of horizontally mounted membranes. The gravitational field has a varied influence on the thickness of these layers and decreases value and change distributions of solution concentrations, which occur in them [24][25][26][27][28][29][30][31][32][33][34][35][36][37].Ślȩzak et al [24] showed that the osmotic flux was significantly higher when the denser liquid was below the membrane in a horizontally mounted osmotic-diffusion cell. They explained this observation in terms of natural convection instability that reduced boundary layer thickness.…”

“…Gravitational effects on transmembrane volume and solute flows of the nonelectrolyte and electrolyte solutions in single-membrane system were reported in previous papers [24][25][26][27][28][29][30][31][32][33][34][35][36][37]. From these papers, the conclusion was drawn that the influence of the gravitational field on transmembrane transport manifests itself in Rayleigh-Taylor instability [24], rectyfying and amplifying properties of osmotic and solute fluxes [25,26] and gravielectric effect [27].…”

“…From these papers, the conclusion was drawn that the influence of the gravitational field on transmembrane transport manifests itself in Rayleigh-Taylor instability [24], rectyfying and amplifying properties of osmotic and solute fluxes [25,26] and gravielectric effect [27]. In paper [36] the Kedem-Katchalsky-Zelman model equations (KKZ-model) of the volume and solute flows across an isotropic membrane were modified for cases in which the membrane separated two multicomponent, non-ionic and heterogeneous solutions at different concentrations. The ik factor, which determines the influence of concentration boundary layers on transmembrane transport, was introduced.…”

“…The ik factor, which determines the influence of concentration boundary layers on transmembrane transport, was introduced. For vertically [36] and horizontally [25] mounted membrane and for binary and ternary solutions the modified KKZ-model was verified. These findings were interpreted in terms of a convective gravitational instability that reduces boundary layer dimensions and increases the permeability coefficient of the complex system: boundary layer/membrane/boundary layer.…”