Effect of particle-size and pore-size distributions in cross-flow filtration

Abstract

This paper presents the results of a finite-element model of cross-flow filtration that examines both radial and axial variations in velocity and concentration for different particle-size and pore-size distributions modeled using a lognormal distribution function. Also examined was the roll of particle diffusion. Assuming that the properties of the fluid were independent of the particle concentration allowed the Navier–Stokes equations to be solved independently from the mass transport problem. Flow at an inlet Reynolds number of 2000 was examined at constant inlet pressure and pressure outside the membrane. Once the velocity profiles had been determined, concentration profiles and permeate concentration were calculated for monodisperse particles as a function of pore-size distribution. The permeate concentrations were then numerically integrated to determine the permeate concentration of polydisperse particles. These results demonstrate that a six-order-of-magnitude reduction in the particulate concentration in the permeate can only be achieved when both the pore-size and particle-size distributions are narrow. Furthermore, they provide guidance for the average pore size necessary to achieve a specified level of purity in the permeate depending on the particle-size distribution and operating conditions of the filtration unit.