Membrane dialysis is one of the membrane contactors applied to wastewater treatment. The dialysis rate of a traditional dialyzer module is restricted because the solutes transport through the membrane only by diffusion, in which the mass-transfer driving force across the membrane is the concentration gradient between the retentate and dialysate phases. A two-dimensional mathematical model of the concentric tubular dialysis-and-ultrafiltration module was developed theoretically in this study. The simulated results show that the dialysis rate improvement was significantly improved through implementing the ultrafiltration effect by introducing a trans-membrane pressure during the membrane dialysis process. The velocity profiles of the retentate and dialysate phases in the dialysis-and-ultrafiltration system were derived and expressed in terms of the stream function, which was solved numerically by the Crank-Nicolson method. A maximum dialysis rate improvement of up to twice that of the pure dialysis system (Vw=0) was obtained by employing a dialysis system with an ultrafiltration rate of Vw=2 mL/min and a constant membrane sieving coefficient of θ=1. The influences of the concentric tubular radius, ultrafiltration fluxes and membrane sieve factor on the outlet retentate concentration and mass transfer rate are also illustrated.
Keywords: dialysis; mass transfer; separation efficiency; tubular dialyzer; ultrafiltration.