Actuation of spatially-varying boundary conditions for reduction of concentration polarisation in reverse osmosis channels

Reduction of concentration polarisation is of great value in reverse osmosis membrane systems. Concentration polarisation leads to a reduction in flux, which corresponds to a reduction in separation efficiency. This paper studies an approach by which to reduce concentration polarisation in reverse osmosis channels using a steady, spatially variant slip velocity profile. A method is developed to identify the most effective wall slip velocity profile for increasing the diffusive driving force away from the wall, which in turn increases mass transfer away from the membrane and reduces concentration polarisation. The nonlinear partial differential equations (PDEs) that govern fluid and mass transport behaviours are difficult to solve. In this work, an approximate solution to the nonlinear system is developed using systems of linearised ordinary differential equations (ODEs) to approximate the behaviour of the PDEs and determine the steady-state actuation profile that most effectively increases mass transfer at the wall. This leads to a systematic method for determination of a spatially-varying actuation profile (the most effective slip velocity profile) that decreases concentration polarisation in reverse osmosis membrane channels.