Viscoelastic Low-Reynolds-Number Flows in Mixing-Separating Cells

Abstract

In this work we investigate the flow of Newtonian and viscoelastic fluids in a mixing-separating geometry consisting of two opposed channel flows interacting through a gap in the common separating wall. This type of flow was experimentally investigated by Cochrane et al. [1] using Newtonian and viscoelastic fluids at low Reynolds number flows (Re < 40). In the present numerical study we assess the effects of Deborah and Reynolds numbers and gap size on the two-dimensional flow dynamics. The normalized gap size was varied between 0 and 5, Re varied between 0 and 50 and De varied between 0 and the maximum attainable value. For Newtonian fluids the creeping flow is anti-symmetric, due to the anti-symmetry of the fully-developed inlet conditions and the symmetry of the flow geometry. Increasing the gap size increased the reversed flow rate ratio (Rr), here defined as the ratio between the reversed and total flow rates. In this investigation we also investigate in detail the creeping flow of viscoelastic fluids obeying the upper-convected Maxwell model for which two distinct flow patterns are found. For normalized gap sizes below a critical value the reversed flow is slightly enhanced by viscoelasticity, followed by a decrease in Rr towards zero as De further increases. For a supercritical gap size viscoelasticity is responsible for a continuous increase in Rr. This flow type transition can be exploited to promote mixing, and this application will also be addressed in this work.