Scale-up of the vortex wave microfilter using the power ratio

The vortex wave technique enhances microfiltration performance by combining the mixing characteristics of oscillatory flow and flow deflectors. The ability to reproduce these highly convective mixing patterns on a scale applicable to pilot plant studies has been investigated in this paper. The scale-up of a single channel membrane unit (18200 mm²) to a double channel element (106080 mm²) has been investigated in terms of geometric, kinematic and dynamic similarity. A non-dimensional approach has been adopted, wherever possible, to characterise the performance of both microfilters. The kinetics of each system are dominated by the Reynolds number, and the dynamics have been classified in terms of a new non-dimensional number — the power ratio. The power ratio has been employed to predict accurately the performance of the scaled-up filter, and also to provide an indication of transitional flow patterns. The inhibition of a gel-layer within the vortex wave modules has been demonstrated by the non-linear relationship between flux and transmembrane pressure. Experimental results and a theory which includes the effects of osmotic-pressure show that the flux is directly proportional to the cube root of the transmembrane pressure. Non-dimensional analysis of the experimental results indicates a similar trend, whereby the flux is directly proportional to the cube root of power dissipation under two-dimensional, laminar flow conditions.