Efficient CFD-based method for designing cross-flow nanofiltration small devices

Small devices of cross-flow nanofiltration (NF) may become a tool to concentrate small samples of valuable substances, if the concentration polarization can be minimized by designing new feed channels with bas-reliefs similar to the ones that have been developed for efficient passive micromixers. These bas-reliefs may have a complex 3D shape and the recourse to intensive CFD simulations is necessary to optimize the geometry. To speed up the simulations, a hybrid, semi empirical approach is used where the average and local mass transfer coefficients are first computed by CFD, using a dissolving wall instead of a semi-permeable membrane boundary condition. The computed mass transfer coefficients are then used to predict the local and average concentration polarization, using a mass transfer correction factor correlation. This computational approach was validated using detailed CFD simulations and experimental concentration distributions obtained by holographic interferometry. A NF ribbed-wall rectangular channel with 2 mm height was used, with potassium sulfate solutions, transmembrane pressures lower than 8 bar and Reynolds numbers between 1 and 125. Using this computational approach, local and average concentration polarization and permeate flux were predicted with an error less than 15%. With these findings, it is possible to speed up the simulation and design of small nanofiltration cross-flow devices.