Hydrodynamic analysis of vibrating hollow fibre membranes

Abstract

Dynamic shear-enhanced filtration through vibration can be an effective method to reduce concentration polarization and membrane fouling in high solids suspension loaded membrane applications such as membrane bioreactors (MBRs). In this approach, the wall shear rate on the membrane surface is one of the most important parameters which can control the fouling in vibrating membrane systems. In the present study, the effects of vibration parameters (i.e., frequency and amplitude) and geometrical parameters (i.e., fibre radius and distance between the fibres in a bundle of fibres) on the wall shear rate at the membrane surface have been studied both analytically and numerically. The analytical solution uses the cylindrical coordinate for the analysis of a vibrating single fibre. The former Cartesian solution for a flat sheet membrane used also for fibres by others, was compared to the new solution. It was found that a relative error of up to 75% can arise comparing the two solutions within a realistic range of hollow fibre diameters. The results also showed that fibres with smaller radii are more effective for the vibrating system. Computational Fluid Dynamics simulations were also performed to examine the optimal configuration and distance between fibres for different configurations. The computational results with two remote fibres were first obtained and compared with the analytical results of a single vibrating fibre. The comparison was satisfactory and shows the compatibility of the modeling and analytical results. Subsequently, the CFD analysis was conducted for a fibre bundle with both staggered and in-line arrangements, and the former was found to be marginally more responsive to vibrations.