The limiting flux in the crossflow microfiltration of particle suspensions was calculated by numerically solving the convective-diffusion equation governing concentration polarisation. It was assumed that a cake layer is formed at the membrane surface, and that particles are transported towards the membrane by convection, and transported away From the membrane by Brownian diffusion or shear-induced diffusion, or a combination of both these mechanisms. The numerical results for Brownian diffusion and for shear-induced diffusion could be summarised by approximate equations which related the predicted flux to parameters such as wall shear stress, bulk concentration, and membrane length. Both the approximate equations and the exact numerical results compared well with fluxes measured in crossflow microfiltration of non-interacting spherical silica particles. It was shown theoretically that turbulent diffusion contributes only marginally to particle transport in the concentration polarisation layer. Microfiltration fluxes for turbulent flow conditions were therefore predicted accurately by the numerical calculations, although turbulent diffusion was neglected.