THE HYDRODYNAMIC AND ELECTROSTATIC INTERACTIONS ON THE APPROACH AND ENTRY OF A CHARGED SPHERICAL-PARTICLE TO A CHARGED CYLINDRICAL PORE IN A CHARGED PLANAR SURFACE WITH IMPLICATIONS FOR MEMBRANE SEPARATION PROCESSES

The application of membrane separation processes, such as microfiltrat ion and ultrafiltration, is one of the most important developments in chemical engineering in recent years. The separation characteristics o f such membranes are usually interpreted sterically in terms of the re lative size of membrane pores and solutes. However, electrostatic effe cts are also important, though often neglected. The paper presents a q uantification of both electrostatic and hydrodynamic effects to identi fy conditions for the operation of such proceses with much greater eff iciency. In particular, the hydrodynamic and electrostatic forces on a charged spherical particle as a function of distance of approach and entry to a charged cylindrical pore in a charged planar surface have b een calculated. A Galerkin finite-element scheme has been used to prov ide numerical solutions of the nonlinear Poisson-Boltzmann equation fo r electrostatic interactions and of the Navier-Stokes equation for hyd rodynamic interactions, with the Newton sequence technique being used to solve the Poisson-Boltzmann equation. The results show that under t he conditions covered by the calculations, which correspond to those o ccurring in practice, the electrostatic interactions can play a crucia l role in controlling the approach and entry of such a particle to a p ore. The calculations have several important consequences for membrane separation processes. Firstly, the quantification of the operating co nditions which allow separation without the particles coming into inti mate contact with the membrane-potentially non-fouling conditions. Sec ondly, the quantification of the operating conditions allowing fractio nation of particles of identical size but differing surface potential. Thirdly, a demonstration that the manufacture of membranes with a hig h surface potential would be very beneficial to the efficient operatio n of such processes.