Mechanism of Cake Buildup in Cross-Flow Filtration of Colloidal Suspensions

Experimental results are presented for the crossflow filtration of concentrated bentonite suspensions. It is proposed that the hydrodynamic forces acting on the suspended colloids determine the rate of cake buildup and, therefore, the fluid loss rate. A simple model is proposed that predicts a power law relationship between the filtration rate and the shear stress at the cake surface (q γ τ^1/n_w). This is found to be consistent with experimental data at different filtration times at various suspension flow rates using three different suspensions. The model shows that the cake formed will be inhomogeneous with smaller and smaller particles being deposited as filtration proceeds. An equilibrium cake thickness is achieved when no particles small enough to be deposited are available in the suspension. The cake thickness as a function of time can be computed from the model. It is also shown that for a given suspension rheology and flow rate there exists a critical permeability of the filter below which no cake will be formed. This critical permeability has been computed for our experiments. The model suggests that the equilibrium cake thickness can be precisely controlled by an appropriate choice of suspension flow rate and filter permeability. These observations have important implications in cross-flow filtration and in slip-casting of inorganic membranes.