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Kedem-Katchalsky (K-K) equations, commonly used to describe the volume and solute flows of nonelectrolyte solutions across membranes, assume that the solutions on both sides are mixed. This paper presents a new contribution to the description of solute and solvent transfer through a membrane within the Kedem-Katchalsky formalism. The modified K-K equation obtained here, which expresses the volume flow (J v ), includes the effect of boundary layers of varied concentrations that form in the vicinity of the membrane in the case of poorly-mixed solutions. This equation is dependent on the following: membrane parameters (σ, L p , ω), complex h/M/l parameters ( σ s − reflection, L ps −hydraulic permeability, ω s −solute permeability coefficients, δ h , δ l − thicknesses of concentration boundary layers), and solution parameters (c−concentration, ρ -density, ν -kinematic viscosity, D -diffusion coefficient). In order to verify the elaborated equation concerning J v , we calculated the following functions:

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The following paper includes a derivation of practical Kedem-Katchalsky (K-K) equations for the volume flow Jν and the solute flow Js for non-electrolytes. This derivation makes the equations clearer and consequently their interpretation also becomes easier. The equations have been derived on the basis of the analysis of the membrane transport generated by simultaneous action of two thermodynamic stimuli: the hydrostatic

On the basis of Kedem-Katchalsky equations a mathematical analysis of volume flow (Jv) of a binary solution through a membrane (M) is presented. Two cases of transport generators have been considered: hydrostatic (Δp) as well as osmotic (Δπ) pressure difference. Based on the Poiseuille's law we derive the formula for the membrane filtration coefficient (Lp) which takes into account the membrane properties, kinetic viscosity and density of a solution flowing across the membrane. With use of this formula we have made model calculations of the filtration coefficient Lp and volume flow Jv for a polymer membrane in the case when the solutions on both sides of the membrane are mixed