(187a) On Modification of Sieving Coefficient On Account of Formation of Concentration Polarization Layer

Authors: 
Sharma, K. R., Prairie View A & M University


The relation between the flow of fluid across the capillary wall or porous membrane is given by Starling's Law (1). The combined effect of osmotic pressure and hydrostatic pressure is taken into account. The hydraulic conductance can be calculated either from flow rate vs. pressure drop data or from membrane architecture properties. Alongwith the solvent some solute is brought along across the membrane. The filtration effect is accounted for by use of a 'sieve coefficient'. The sieving coefficient is defined as the ratio of solute concentration in teh filtrate (Se) to the solute concentration of the feed solution. Theoretical expressions based on the motion of a spherical solute miving through a cylindrical pore have been developed in order to estimate the value of sieving coefficient (2). The model developed by Deen can be expressed as a 7th degree polynomial expression for the sieving coefficient in terms of the solute radius to the capillary pore radius. With a RMS error of 0.04% the 6th degree term can be dropped from the expression. Concentration polarization layer refers to the formation of a coat of retained solute on the feed side of the membrane. At high filtration rates the formation of concentraiton polarization layer has been found in practice. This can cause an unpredictable change in protein transport. The sieving coefficient can be modified to correct for the concentration polarization layer. The sieving coefficient that includes the concentration polarization layer effects can be given by the ratio of solute concentration in the filtrate to that of the solute concentration in the bulk blood (Sc). Sc is given as a function of filtration flux, surface renewal mass transfer coefficient. Sherwood number is related to Sharma number, Maxwell number and Peclect number (mass), length of capillary and diamter and diffusion coefficient.