Membrane transport of the non-homogeneous non-electrolyte solutions: mathematical model based on the Kedem-Katchalsky and Rayleigh equations.

Mathematical model of the volume and solute flows through artificial polymeric membrane under occurrence of the concentration boundary layers on both sides of this membrane is presented. This nonlinear model, based on the Kedem-Katchalsky and Rayleigh equations, describes the volume flux generated by osmotic and hydrostatic forces, thicknesses of the concentration boundary layers, concentrations and hydrostatic pressures on the membrane-concentrations boundary layers' borders. Besides, this model shows that the volume flows and individual forces causes the flows influences on the thickness of concentration boundary layers. The nonlinear equations for volume flux, concentration and thickness of concentration boundary layers can be used to numerical calculation in linear regime of the hydrodynamical stability.