The effects of viscoelasticity and shear thinning on the inertial instability and mixing performance in a T-channel geometry

The T-channel, in which two opposing square inlet streams join and turn through 90° into a rectangular outlet of equal cross-sectional area, exhibits a steady symmetry-breaking bifurcation above a critical Reynolds number. For Newtonian fluids it is well-established that this transition produces engulfment flow and consequent enhanced mixing. However, the transition behaviour and mixing of viscoelastic and shear thinning fluids in the T-channel is less well studied or understood. In this work, finite-volume flow simulations are used to investigate how non-Newtonian rheology influences both the onset of instability and the resulting mixing performance. For constant-viscosity viscoelastic models, the Oldroyd-B fluid destabilises the flow, leading to transition at lower Reynolds numbers than in the Newtonian case, while the Oldroyd-A fluid stabilises the flow, delaying the onset of the engulfment regime. This contrast highlights the influence of normal stress differences on critical conditions. For shear-thinning Giesekus and Carreau models, the critical Reynolds number depends strongly on how the Reynolds number is defined; using the zero-shear viscosity both predict destabilisation relative to the Newtonian baseline. Analysis of the outlet channel shows that the instability mechanism is governed by the strength of secondary Dean-type vortices generated by the 90° turn, which are amplified or suppressed depending on the balance between inertia, curvature and rheology. Finally, the quantification of the mixing index reveals that, despite shifting the onset of instability, all non-Newtonian models studied reduce mixing efficiency of the mixer relative to the Newtonian case. • Inertial symmetry-breaking transition in a T-channel for constant-viscosity models shown to occur at constant value of the maximum secondary flow velocity. • Oldroyd-B model slightly destabilizing in that critical Re is smaller than Newtonian value in qualitative agreement with dilute polymer solution experiments. • Oldroyd-A model more strongly stabilizing in that critical Re can become much larger than Newtonian value. • Enhanced mixing is still observed beyond the symmetry-breaking transition for all fluids.