Vinther, Frank1; Pinelo, Manuel2; Brøns, Morten1; Jonsson, Gunnar Eigil2; Meyer, Anne S.2
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Department of Chemical and Biochemical Engineering, Technical University of Denmark3 Center for BioProcess Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark4 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark
This paper presents a two dimensional mathematical model of back-shocking in ultrafiltration. The model investigates the effect of back-shocking on concentration polarization. The model shows a positive effect on both the volumetric flux and the observed rejection when back-shocking is applied as compared to the steady-state solution. Furthermore, the effect of changing different parameters such as inlet velocity, forward and backwards pressure on the back-shock time, the increase in volumetric flux and observed rejection, is presented. Moreover, two analytical estimates for the optimal back-shock time derived from calculating the path-lines during a back-shock cycle are presented. Both of these expressions are in good agreement with the results obtained from the mathematical model and data collected from the literature. Based on this, a simple expression for an optimal back-shock time in a multi-parameter problem is provided.
Journal of Membrane Science, 2014, Vol 470, p. 275-293