Practical Kedem-Katchalsky equations and their modification

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 . 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.