Model of Selectivity of Membrane Processes and Dissolution of Impurities in a Membrane Pore in a Medium with Surface-Active Micelles

It is shown that concentration polarization affects the size of the Knudsen layer and the mechanism of mass transfer in the Knudsen layer is established. Based on the analysis of the selectivity patterns of ultrafiltration membranes, an equation was obtained for calculating the total probability of particle drift through the boundary diffusion layer and penetration into the Knudsen layer region and an equation for calculating the diffusion coefficient determined by the value of the derivative of the chemical potential in concentration. An equation is derived for determining the flow of particles to the membrane surface in the Knudsen layer by its thickness using the free path length of particles, the average velocity of thermal motion of molecules, the average residence time of particles in the Knudsen layer. The probability of particles passing through the pore is estimated, taking into account the influence of the activation energy for the passage of the solvent and the ratio of the interparticle distance in the pore to the free path length, and the selectivity of the membrane is estimated. An equation is obtained for calculating the length of the dissolution front in a micellar solution inside a membrane pore. An equation is obtained for calculating the kinetic factor in a micellar solution inside a membrane pore, taking into account the mass transfer coefficient along the interface, the diffusion coefficient, as well as the concentration of micelles in the medium and the solubilization rate constant. An effective design of a membrane apparatus for water purification is proposed.