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 microfiltration and ultrafiltration, is one of the most important developments in chemical engineering in recent years. The separation characteristics of such membranes are usually interpreted sterically in terms of the relative size of membrane pores and solutes. However, electrostatic effects are also important, though often neglected. The paper presents a quantification of both electrostatic and hydrodynamic effects to identify conditions for the operation of such proceses with much greater efficiency. 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 been calculated. A Galerkin finite-element scheme has been used to provide numerical solutions of the nonlinear Poisson-Boltzmann equation for electrostatic interactions and of the Navier-Stokes equation for hydrodynamic interactions, with the Newton sequence technique being used to solve the Poisson-Boltzmann equation. The results show that under the conditions covered by the calculations, which correspond to those occurring in practice, the electrostatic interactions can play a crucial role in controlling the approach and entry of such a particle to a pore. The calculations have several important consequences for membrane separation processes. Firstly, the quantification of the operating conditions which allow separation without the particles coming into intimate contact with the membrane-potentially non-fouling conditions. Secondly, the quantification of the operating conditions allowing fractionation of particles of identical size but differing surface potential. Thirdly, a demonstration that the manufacture of membranes with a high surface potential would be very beneficial to the efficient operation of such processes.