Numerical simulation of solute removal from a cross-flow past a row of parallel hollow-fiber membranes

A multi-parametric simulation of the 2-D steady transverse flow of viscous incompressible fluid and diffusion transport of a dissolved solute past a model fibrous medium - a row of parallel sorbent fibers or hollow-fiber membranes is performed in a wide range of Schmidt (Sc) and Peclet (Pe) numbers for fiber Reynolds numbers up to Re = 100. The Navier-Stokes and convection-diffusion equations are solved numerically and the fiber capture efficiency for solute molecules is calculated as a function of Re, Sc and inter-fiber distance. The field of solute concentration and the fiber capture efficiency are found with zero concentration-fixed and diffusion flux boundary conditions set at the streamlined fiber surface, and the difference between the results of simulations with the two boundary conditions is shown for high Peclet numbers. It is also shown that the fiber capture efficiencies estimated with both boundary conditions tend to a constant maximum value for low Peclet numbers. The results of simulations for the fiber capture efficiency are validated by comparison with existing analytical asymptotic solutions for low and high Peclet numbers, and the agreement is shown.