Enhancement of filtration by hydrodynamic instabilities in a Taylor-Couette cell with semi-permeable cylinders.*

This study addresses the interplay between hydrodynamic instabilities and a transmembrane flow, under the coupling by the osmotic pressure driven by a concentration boundary layer building up at the membrane. The configuration consists of a Taylor-Couette cell filled with solvent carrying a passive scalar. Whereas the concentric inner and outer cylinders are permeable to the solvent, they totally reject the scalar. As a radial flow of solvent is superimposed across the cell, a concentration boundary layer builds up at one of the cylinders. Besides, the rotation of the inner cylinder drives centrifugal instabilities stirring the concentration boundary layer.

By mean of the osmotic pressure, the concentration boundary layer promotes the instabilities. In return, the instabilities increase the mean radial flow across the cell. The impact of the different physical parameters on these two mechanisms is then addressed.

These results obtained by analytical stability analyses are in agreement with dedicated Direct Numerical Simulations. They quantitatively assess the roll of hydrodynamic instabilities to improve the performances of filtration devices.