Abstract
Antipolarization dialysis (APD) has previously been proposed (Nitsche, L.C.Q. Appl. Math. 1994, 52, 83-102) as a concept for fractionation that combines countercurrent dialysis with longitudinal polarization of macrosolutes at the downstream end of each flow channel. The paper applies singular perturbation theory to the practically important (but numerically problematical) limit of large aspect ratio, subject only to very general assumptions about the flow field. At leading order, APD is shown to yield the same basic functional form of the membrane selectivity curve as does conventional countercurrent dialysis - but without the requirement of additional clean solvent (dialysate) for selective removal of macrosolutes. Changing the second species-selective parameter, Peclet number, shifts the curve horizontally without changing its shape. This means that the macrosolute-macrosolute selectivity of one membrane could be optimized for different regimes of conductivity simply by adjusting the flow rate. Asymptotic concentration profiles and/or selectivity curves compare favorably with previous numerical results for (1) a simplified plug-flow model (Ibid.) and (2) a more realistic flow field associated with a practical plate-spacer design (Nitsche, L.C.; Zhuge, S. Chem. Eng. Sci. 1995, 50, 2731-2746)
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