Symmetry-breaking Bifurcations in T-channel Flows: Effects of Fluid Viscoelasticity

Abstract

It is well known that, beyond a critical aspect-ratio-dependent Reynolds number, the flow in a three-dimensional T-channel junction, i.e. two-opposing planar channel streams joining and turning through 90 degrees, can break symmetry. For the case of two square cross-section inlets and an outlet arm of equal area (i.e. aspect ratio of two) this bifurcation is to a steady asymmetric flow. This flow bifurcation has been proposed as a method of enhancing mixing in microfluidic channels where significant increases in mixing quality are observed beyond the bifurcation. In the current work we investigate numerically the effects of viscoelasticity on this supercritical pitchfork bifurcation using a numerical finite-volume method. Results from both the upper-convected Maxwell and Oldroyd-B models show that the instability occurs at lower Reynolds numbers for viscoelastic fluids in comparison to the Newtonian base case. At higher Deborah numbers the transition leads directly to an unsteady flow.