Direct Numerical Simulations of Unsteady Mixing and Concentration Polarization in Reverse Osmosis Systems

Concentration polarization in reverse osmosis (RO) systems increases the transmembrane osmotic pressure and formation of mineral scale. These impede filtration, reduce membrane life, and increase maintenance costs. Polarization in RO is difficult to simulate numerically due to the coupling between the transmembrane filtrate flow, pressure, and osmotic pressure. This coupling is further complicated in systems with feed spacers. Spacers induce a complicated mixing that plays an important role in polarization by creating regions of low shear stress that promote solute accumulation. However, because spacers are themselves challenging to simulate, simulations of polarization tend to neglect spacers, while simulations of spacers often neglect polarization. Simulations of spacers also often assume steady flow, which neglects that such flows can be unsteady due to hydrodynamic instabilities. In fact, the promotion of such instabilities can enhance mixing and reduce polarization. In this presentation, we summarize our progress developing numerical methods to efficiently simulate unsteady fluid mixing and concentration polarization in RO systems with spacers. Specifically, we simulate a 2D plate-and-frame RO system with idealized cylindrical spacers. Though this geometry has been considered previously for steady simulations, we demonstrate that operating conditions and spacer geometry can promote unsteady flow regimes in which vortices are periodically shed from the spacer. These in turn interact with the membrane surface to create regions of low and high polarization, with corresponding variations in permeate flow. Conversely, we also show that though the transmembrane permeate flow is small compared to the bulk feed flow, it can nevertheless affect vortex shedding, and have a very strong influence on the bulk feed flow far from the membrane surface.