Stabilization of purely elastic instabilities in cross-slot geometries

Davoodi, Mahdi and Houston, Gemma and Downie, Jenna and Oliveira, Mónica S.N. and Poole, Robert J. (2021) Stabilization of purely elastic instabilities in cross-slot geometries. Journal of Fluid Mechanics, 922. A12. ISSN 0022-1120 (https://doi.org/10.1017/jfm.2021.473)

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Abstract

In this work, two-phase flows of Newtonian and/or viscoelastic fluids in a 'cross-slot' geometry are investigated both experimentally and numerically in the creeping-flow limit. A series of microfluidic experiments-using Newtonian fluids-have been carried out in different cross-section aspect ratios to support our numerical simulations. The numerical simulations rely on a volume of fluid method and make use of a log-conformation formulation in conjunction with the simplified viscoelastic Phan-Thien and Tanner model. Downstream from the central cross, once the flow has become fully developed, we also estimate analytically the thickness of each fluid layer for both two-and three-dimensional cases. In addition to providing a benchmark test for our numerical solver, these analytical results also provide insight into the role of the viscosity ratio. Injecting two fluids with different elastic properties from each inlet arm is shown to be an effective approach to stabilize the purely elastic instability observed in the cross-slot geometry based on the properties of the fluid with the larger relaxation time. Our results show that interfacial tension can also play an important role in the shape of the interface of the two fluids near the free-stagnation point (i.e. in the central cross). By reducing the interfacial tension force, the interface of the two fluids becomes curved and this can consequently change the curvature of streamlines in this region which, in turn, can modify the purely elastic flow transitions. Thus, increasing interfacial tension is shown to have a stabilizing effect on the associated steady symmetry-breaking purely elastic instability. However, at high values of the viscosity ratio, a new time-dependent purely elastic instability arises most likely due to the change in streamline curvature observed under these conditions. Even when both fluids are Newtonian, outside of the two-dimensional limit, a weak instability arises such that the fluid interface in the depth (neutral) direction no longer remains flat.

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