Numerical simulations of lift force and drag force on a particle in cross-flow microfiltration of colloidal suspensions to understand limiting flux

Abstract The aim of this study was to understand the limiting flux in cross-flow microfiltration of a colloidal suspension in terms of the balance of hydrodynamic forces on a particle. Numerical simulations were carried out to estimate the lift force resulting from the cross-flow, drag force resulting from the convective flux, and net force. Assuming that the limiting flux is the flux when the net force on a particle is zero, we analyzed the simulation data to determine the correlation of two particle Reynolds numbers: R e p _ J l i m i t , calculated from the limiting flux, and R e p _ u δ , calculated from the cross-flow rate. The results indicate that R e p _ J l i m i t is proportional to the square of R e p _ u δ when a particle is at a dimensionless distance (distance divided by diameter) of less than 6.7 from the cake layer, in spite of the experimental fact that R e p _ J l i m i t is proportional to the 1.5th power of R e p _ u δ . In contrast, R e p _ J l i m i t is proportional to the 1.5th power of R e p _ u δ when a particle is at a dimensionless distance of 48–60. This means that the force balance of a particle at such a position, not at the membrane surface, determines the limiting flux in cross-flow microfiltration of a colloidal suspension.