A theoretical study of permeability enhancement for ultrafiltration ceramic membranes with conical pores and slippage

Abstract

Ceramic membranes are currently favourable in membrane filtration applications due to their excellent mechanical strength, thermal and chemical resistance, backflush capability, and thus a long-service cycle. Coated on top of a mesoporous support, the selective top layer of ultrafiltration ceramic membranes has pore size not exceeding a few tens of nanometers and thickness in the order of O10 μm. In fact, the permeability of an ultrafiltration ceramic membrane can be estimated by the permeability of the top layer due to its smallest pore size. Without impairing the filtration function but still improving the permeability, a gradient conical pore shape is proposed. Two formulae for the filtrate flow rate versus pressure drop relationship through a conical pore exhibiting surface slippage are established here by extending the Hagen-Poiseuille law and an analytical solution for the axisymmetric creeping flow. It is analytically proved that the surface slip length in a conical flow is proportional to a local pore radius by a slip coefficient that is unique for a given pore configuration at a prescribed flow rate. The permeability of a conical-pore membrane is enhanced for radius ratio not exceeding 6.5. The optimum configuration, achieved at a ratio of 2.3, produces an enhancement factor for a membrane permeability of 1.5 for a no-slip surface; this enhancement increases linearly with the slip coefficient if a surface slippage exists.