Three-dimensional structures and symmetry breaking in viscoelastic cross-channel flow

Rheological effects on purely-elastic flow asymmetries in the cross-slot geometry

Viscoelastic flows in the cross-slot geometry can undergo a transition from a steady symmetric to a steady asymmetric flow state, ostensibly due to purely-elastic effects arising beyond a critical flow rate, or Weissenberg number Wi. However, some reports suggest that shear thinning of the fluid's viscosity may also play an important role in this transition. We employ a series of polymer solutions of varying rheological properties to investigate in detail how the interplay between fluid elasticity and shear thinning affects the onset and development of asymmetric flows in the cross-slot. Flow velocimetry is performed on each of the polymer solutions, and is used to assess the degree of flow asymmetry I in the cross-slot as a function of both Wi and a dimensionless parameter S quantifying the flow-rate-dependent extent of shear thinning. Typically, the flow field breaks symmetry as Wi is increased beyond a critical value, but the magnitude of I is found to also be dependent on S. For a few specific polymer solutions, the flow field recovers symmetry above a second, higher critical Wi as S becomes small. The experimental results are summarized in a flow state diagram in Wi-S space, showing the relationship between flow asymmetry and fluid rheology. Finally, to gain a deeper understanding of the effects of shear thinning, numerical simulations are performed using the linear simplified Phan-Thien-Tanner model. We demonstrate that the degree of both shear thinning and elasticity of the fluid, and their interplay, are important factors controlling elastic instabilities in the cross-slot geometry.

Electrokinetics of polymeric fluids in narrow rectangular confinements

The flow of polymeric liquids in narrow confinements with a rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many of the previous studies on the flow of complex fluids tend to focus on highly idealized parallel plate channels, which are markedly different from the rectangular ducts, used in many experiments and devices. We consider the combined electroosmotic and pressure driven flows as well as the streaming potential resulting from a mechanically driven flow. We use two distinct constitutive relations to model the polymeric liquids, namely the simplified exponential Phan-Thien-Tanner (sePTT) model and the Giesekus model, both of which are non-linear viscoelastic models, capable of capturing the shear thinning behavior. We establish that the applied electric field may have a strong influence on the overall flow rate, which rapidly increases with the field strength as well as the extent of viscoelasticity of the fluid. Viscoelasticity and shear thinning behavior also enhance the streaming potential by several fold as compared to a Newtonian medium. We demonstrate that the aspect ratio of a channel has a bigger influence on the net throughput and the streaming potential, when the extent of viscoelasticity is relatively large. We illustrate that for sePTT fluids, the flow is strictly unidirectional, while for Giesekus fluids, secondary flows are inevitably present on account of their non-zero second normal stress coefficient. Although the electric field does not change the overall patterns of these secondary flows, their magnitude does depend on the imposed field strength for combined flows.