View graph of relations

This paper concerns mathematical modeling and computational fluid dynamics of back-shocking during hollow fibre ultrafiltration of dextran T500. In this paper we present a mathematical model based on first Principles, i.e., solving the Navier-Stokes equation along with the continuity equation for both the solute and the solvent.We investigate the validity of the estimate On the optimal back-shock time, i.e., the back-shock time needed to achieve the highest permeate flux, published in a previous paper by the authors (Vinther et al., Predicting optimal back-shock times in ultrafiltration hollow fibre membranes, J. Membr. Sci. 470 (2014) 275-293 [33]).Furthermore, the simulations have been performed with two different inlet velocities, i.e., crossflow velocities and are clone with and without a concentration dependent viscosity. This enables us, for the first time, to investigate the effect of different inlet velocities and the effect of a concentration polarization on the observed rejection and the permeate flux, as a function of different back-shock times.In all cases the average permeate flux and the observed rejection during one period of back-shocking were found to be higher than the steady-state values - representing the long time behavior of a similar separation process performed without back-shocking - when using the optimal back-shock time.It is concluded that the estimate of the optimal back-shock time is in good agreement with the optimal time found in the simulations performed in this paper.Furthermore, it is found that the optimal back-shock time increases when the viscosity is allowed to depend on the concentration It is found that this can be explained by a decrease in the velocity tangential to the membrane due to the increase in viscosity where the concentration is high - resulting in a longer time for the concentration polarization to be convected tangentially along the membrane surface.The ratio between the average flux over a back-shock cycle and the steady-state flux is found to increase with increasing inlet velocity. Furthermore, this ratio increases when the viscosity depends on the concentration. This is clue to the relatively lower steady-state value when the viscosity depends on the concentration.Moreover, an increase in observed rejection is found when using back-shocking. The increase in observed rejection is found to be largest when the inlet velocity is high and the viscosity depends on the concentration. (C) 2015 Elsevier B.V. All rights reserved.
Original languageEnglish
JournalJournal of Membrane Science
Pages (from-to)486-495
StatePublished - 2015
CitationsWeb of Science® Times Cited: 1


  • Back-shocking, Membrane separation, CFD, Mathematical modeling, Dextran, Ultrafiltration
Download as:
Download as PDF
Select render style:
Download as HTML
Select render style:
Download as Word
Select render style:

ID: 117327060