A Novel Microfluidic Mixing Element for Viscoelastic Fluids

Abstract. The flow visualizations of viscoelastic flows in the mixing-separating geometry of Cochrane et al. [1] showed provocative flow features that inspired the current numerical research using the upper-convected Maxwell (UCM) model. The effects of Deborah (De) and Reynolds (Re) numbers and gap size were analyzed in depth in this two-dimensional flow investigation. The normalized gap size was varied between 0 and 5, Re varied between 0 and 50 and De was varied between 0 and the maximum attainable value. The creeping flow of Newtonian fluids is always anti-symmetric, due to the anti-symmetry of the inlet conditions and the symmetry of the flow geometry. The increase in the gap size leads to an increase in the reversed flow rate ratio (i? ̂), here defined as the ratio between the reversed and total flow rates, an effect enhanced only fori?e> 5. The creeping flow of UCM fluids however, showed two distinct flow patterns. For normalized gap sizes below a critical value the reversed flow is slightly enhanced by viscoelasticity, followed by a strong decrease in Rr towards zero as De further increase, whereas for a supercritical gap size viscoelasticity is responsible for a continuous increase in Rr. For near-critical flow geometries it was possible to observe a sudden jump between the two flow conditions at slightly different Deborah numbers, thus suggesting the possibility to use such geometry as a micro-mixer for viscoelastic fluids if the imposed flow rates are made time periodic to enhance an oscillation between flow patterns. At low Reynolds numbers the dependence of flow pattern on gap size and Deborah number still exhibits the described double behavior, but inertia naturally enhances the straight flow case and at Re = 5, Rr always decreases with Debora