Viscoelastic flows in mixing-separating cells

Abstract

The flow of Newtonian and viscoelastic fluids in a mixing-separating geometry that consists of two opposed channel flows interacting through a gap in the common separating wall is investigated. The flow in this type of geometry was studied experimentally by Cochrane et al. (Philos Trans R Soc Lond A301:163-181, 1981) using Newtonian and viscoelastic fluids at low Reynolds numbers (Re < 50). In this numerical study, by use of a finite-volume method, the effects of Deborah (De) and Reynolds numbers and gap size on the two-dimensionalflow dynamics are assessed. The normalized gap size varies between 0 and 5, Re varies between 0 and 50 and De varies between 0 and the maximum attainable value. Due to the anti-symmetry of the fully developed inlet conditions and the symmetry of the flow geometry, the Newtonian creeping flow is anti-symmetric. Increasing the gap size of the separating walls leads to an increase of the reversed flow-rate ratio (Rr), which is defined as the ratio of the reversed and the total flow rate. For creeping flow of viscoelastic fluids, here described by the upper-convected Maxwell model, two distinct flow patterns are observed. Below a critical gap size, the reversed flow is slightly enhanced when the Deborah number increases. Further increase of De leads to a subsequent decrease in Rr towards zero. For a supercritical gap size, increasing the Deborah number leads to a monotonic increase in Rr.