Fouling layer growth and distribution at the interface of pressure-driven membranes

Abstract

A model of the flow of a dilute particle-laden fluid in the channel with porous walls and the deposition of the particles as a fouling layer on the walls is developed. The equations governing the flow and the rate of change for the fouling layer thickness are non-dimensionalized. As a result, two parameters characterizing the effects of the inertia terms and the fouling layer are obtained. A perturbation solution with variable suction velocity is presented for small wall Reynolds number and thin fouling layer ( Re w ⪡ 1 and S ⪡ 0). The equations governing the flow and the rate of change for the fouling layer thickness in a channel are also solved by an integral method. The method is based on assuming a profile for the axial velocity and satisfying the partial differential equations in an integral sense. From the perturbation analysis, it is found that for relatively large values of the dimensionless parameter E (which correspond to microporous systems with high permeability) the pressure, the suction velocity and the fouling layer thickness decay exponentially along the channel. This is in contrast to the solution with constant suction velocity (Berman, 1953, J. appl. Phys. 24, 1232–1234), where the pressure gradient remains nearly constant. For small values of E (which correspond to microporous systems with low permeability) the exponential decay is approximately linear, with the wall suction velocity nearly constant. Also, it is noticed that the build-up of the fouling layer tends to decrease the driving pressure force. In other words, the pressure difference required to move the fluid through the channel is less than that which is needed for the undisturbed problem (no fouling layer and inertia terms). The inertia terms lead to a larger pressure difference. The integral method is not restricted by the smallness of the Reynolds number and the fouling layer. The results compare well with those obtained by the perturbation method for small Reynolds number and thin fouling layer. As the fouling layer thickens, the integral method predicts flow reversal.