Approximation for modelling electro-osmotic mixing in the boundary layer of membrane systems

• Numerical simulation of electro-osmotic flow disruptions in membrane channels.
• Comparison of Helmholtz–Smoluchowski approximation against charge density solution.
• Better agreement between these two methods at higher solute concentration.
• The effect of the electric field normal to the membrane surface is negligible.
• HS approximation is valid for modelling electro-osmotic flows in typical RO systems.

A Computational Fluid Dynamics (CFD) model is used to compare the reliability and accuracy of the Helmholtz–Smoluchowski (HS) approximation against a one-dimensional charge density distribution (CD) solution of an electro-osmotic perturbation in a 2D membrane channel for reverse osmosis (RO). Electro-osmotic flow within the boundary layer is induced via the placement of a pair of electrodes parallel to the membrane surface and perpendicular to the bulk flow. Although this electrode configuration results in a two-dimensional electric field, the HS approximation considers only the electric field in the direction tangential to the membrane and not the normal component. The effect of the normal component of the electric field (Ey) on the flow field in the CD solution is compared against the solution using the HS approximation and it is found that the effect of Ey is minimal. Greater agreement between the CD solution and the HS approximation is found at higher bulk solute mass fractions, such as typically found on the membrane surface in RO systems. The relationships between cross-flow velocity, perturbation velocity and mixing are explored.