Hydrodynamic and colloidal interactions effects on the rejection of a particle larger than a pore in microfiltration and ultrafiltration membranes

Abstract

The application of membrane separation processes, such as microfiltration and ultrafiltration, is one of the most important developments in chemical engineering in recent years. Membrane fouling is the most important problem which restricts application of membrane processes. Recently, it has been demonstrated that colloidal and hydrodynamic interactions govern membrane fouling and they can be manipulated by choice of processing conditions, for example, pH, ionic strength and applied pressure. The paper presents a quantification of both colloidal (electrostatic and van der Waals) and hydrodynamic effects to identify conditions for the operation of such processes with much greater efficiency. In particular, the hydrodynamic and colloidal forces on a charged spherical particle slightly larger than a pore at various distances from a charged cylindrical pore in a charged planar surface have been calculated. In the absence of electrostatic interactions, filtration of such particles can result in a catastrophic loss in flux as they can plug pores highly effectively. The rejection of the particle at a membrane pore is described in terms of a balance between the hydrodynamic force which is driving the particle towards the membrane and the colloidal forces between the charged particle and the charged membrane surface. A Galerkin finite element scheme combined with automatic mesh refinement and error estimation strategy has been used to provide numerical solutions of the non-linear Poisson–Boltzmann equation for electrostatic interactions and of the Navier–Stokes equation for hydrodynamic interactions. 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 of such a particle to a pore. The calculations have a number of 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, a demonstration that the manufacture of membranes with a high surface potential would be very beneficial to the efficient operation of such processes.