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Practical Kedem-Katchalsky equations and their modification

100%

Jarzyńska M.

Open Physics

2007

vol. 5

issue 4

586-598

The research problem presented in this work concerns modification of the Kedem-Katchalsky (K-K) equation for volume flow (J v) through system (h|M|l), consisting of a membrane M and boundary layers h and l. Such boundary layers appear in the vicinity of the membrane on both sides due to the lack of mixing of solutions. This paper also includes the derivation of the equation for volume flow (J vr) dissipated on concentration boundary layers h and l. The derivation of these equations concerns the case in which the substance transport through the membrane is generated by the osmotic pressure gradient $$\Delta \dot \prod $$ . On the basis of the equations for the volume flows (J v) and (J vr), some calculations for a nephrophane membrane, used in medicine, and for aqueous glucose solutions have been carried out. In order to test the equations for (J v) and (J vr), we have also carried out calculations for the volume flow (J′ v) that is transferred through the membrane in the case of mixed solutions on both sides of the membrane. This volume flux has been calculated on the basis of the original (K-K) equation. The results are presented in Fig. 2.

The application of practical Kedem-Katchalsky equations in membrane transport

86%

Jarzyńska M.

Open Physics

2006

vol. 4

issue 4

429-438

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, v-kinematic viscosity, D-diffusion coefficient). In order to verify the elaborated equation concerning J v, we calculated the following functions: $$J_v = f(\Delta c)_{\Delta p,R_C = const} $$ , $$J_v = f(R_C )_{\Delta p,\Delta c = const} $$ , and $$J_v = f(\Delta p)_{\Delta c,R_C = const} $$ . The J v equation was derived by means of two methods.

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Practical Kedem-Katchalsky equations and their modification

The application of practical Kedem-Katchalsky equations in membrane transport