Control study on mixing enhancement in boundary layers of membrane systems

• An activation scheme for improving mixing in the boundary layer of pressure driven membrane systems is presented.
• Electroosmotic flow is introduced and controlled to reduce the concentration polarization on the membrane surface.
• An optimal control problem is formulated and solved to determine the waveform of the control action required.

This paper proposes an activation scheme for improving the mixing in the boundary layer of pressure-driven membrane systems such as reverse osmosis and ultrafiltration. Through the application of an external electric field, a flow of ions in the vicinity of the membrane surface is generated, creating an electro-osmotic flow that should reduce the extent of concentration polarization. An optimal control problem is formulated and solved to determine the waveform of the control action required to produce an electric field that can effectively increase mixing in the vicinity of the membrane surface with improved energy efficiency. This paper uses a mixing index in terms of a measure of spatial gradients of the perturbation velocities, which describes the mixing caused by both length stretching and vortices. The efficacy of the proposed control is validated by Computational Fluid Dynamics (CFD) simulations.