Computer simulations of mass transfer in the concentration boundary layer over ultrafiltration membranes

The phenomenon studied in this article is high-Schmidt-number mass transfer in the concentration polarization boundary layer during ultrafiltration (UF). The equations governing the transport of momentum, mass and concentration of a chemical species are solved throughout the boundary layer by a simulation program based on a control volume formulation. This formulation has the important quality that concentration-dependent physical properties can be calculated throughout the concentration boundary layer at spatially resolved points. To obtain a closeable set of momentum equations the turbulent transport of momentum is calculated using a slightly modified version of a low-Reynolds-number k-ϵ turbulence model formulated by Chien [1980]. The turbulent momentum transport is related to the turbulent transport of species concentration by a turbulent Schmidt number expression. The ability of the program to predict high-Schmidt-number mass transfer to a surface with suction is verified by comparison with experimental results. Thereafter the calculation procedure is used to predict mass transfer in UF, both for steady state and for a developing concentration polarization boundary layer. The simulation results are also compared with results obtained with the film theory equation, commonly used in membrane technology.