Effective hydraulic resistance of the first cake layers at the membrane surface in microfiltration

The usual procedure for predicting the filtration flux in microfiltration processes is to assume that the total hydraulic resistance to filtration flow can be calculated as the mere addition of the membrane resistance and the intrinsic cake layer resistance. It is shown that this assumption is acceptable when the cake layer is sufficiently thick but questionable when the cake layer is thin, i.e. at the beginning of the microfiltration process when the filtration flux decreases drastically. In fact, the simple additive model underestimates the total hydraulic resistance in the early stages of the cake formation. This problem is studied using two dimensional boundary element methods to solve the coupled problem of Darcy flow in the cake layer and Stokes flow in the upper fluid region. For a given cake layer thickness, the numerical results show that the effective resistance of the cake layer increases as the membrane surface porosity decreases.