Find in Library

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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>) was obtained by employing a dialysis system with an ultrafiltration rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>=</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">L</mi><mo>/</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></semantics></math></inline-formula> and a constant membrane sieving coefficient of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. 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.