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 upperconvected 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.

Inertioelastic Flow Instability at a Stagnation Point

“…10 and the reduction in critical Reynolds number with increasing polymer concentration reported for the onset of EIT by Samanta et al [4], although the onset Reynolds number for vortex formation in the cross slot is around 2 orders of magnitude smaller than that for EIT. The critical Reynolds number for the onset of inertioelastic flow instabilities in T-shaped intersecting channels with two inlets of aspect ratio α ¼ 1 and one outlet of α ¼ 2 has also been found to be dependent on El [80]. In the Newtonian case, flow in such channels becomes unstable, resulting in the formation of vortices extending along the outlet channel when the Reynolds number exceeds a critical value Re c ≈ 100 [53,54,81].…”

“…In the Newtonian case, flow in such channels becomes unstable, resulting in the formation of vortices extending along the outlet channel when the Reynolds number exceeds a critical value Re c ≈ 100 [53,54,81]. There are rather few numerical or experimental studies of non-Newtonian flows in T channels [80,[82][83][84]. However, using the upperconvected Maxwell model, Poole et al showed numerically that low levels of fluid elasticity could cause a reduction in Re c [80].…”

“…There are rather few numerical or experimental studies of non-Newtonian flows in T channels [80,[82][83][84]. However, using the upperconvected Maxwell model, Poole et al showed numerically that low levels of fluid elasticity could cause a reduction in Re c [80]. With highly elastic fluids (El ¼ 861), Soulages et al [83] reported flow asymmetries in microfluidic T channels that appear closely related to the purely elastic asymmetries seen in cross-slot devices [31,32].…”

Numerical Investigation of T-Shaped Microfluidic Oscillator with Viscoelastic Fluid

“…They reported that in the range of similar Re and Wi numbers where forward bifurcation usually occurs, forward Hopf bifurcation was observed instead, and the existence of the long recirculating cavity played a decisive role. Poole et al numerically investigated the effects of aspect ratio and shear-thinning properties for generalized Newtonian fluid [ 48 ] and viscoelasticity [ 49 ] on the symmetry-breaking bifurcations in T-channel flows. A common feature of the above studies is that two streams collided head-on from two opposite entrances and then evacuated through 90 degrees.…”

Numerical modelling of steady and unsteady flows of generalized Newtonian fluids

“…Branching of pipes occurs in many technical or biological applications. In [13] the effects of viscoelasticity on the pitchfork bifurcation using a numerical finite volume method was investigated. 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.…”