Influence of viscoelasticity on the interfacial dynamics of air displacing fluid flows—a computational study

Abstract

A pseudo-solid domain mapping technique, based on a finite strain model, coupled with a DEVSS finite element formulation is applied to study the effects of viscoelasticity on free surface displacement flows. The flow type analyzed is the displacement of a dilute polymeric solution, modeled by a FENE-CR constitutive equation, in a Hele Shaw Cell. Our study indicates the presence of two distinct flow regimes. In the absence of gravity, a recirculation flow at low Ca ( Ca < 1.0) and a bypass flow at high Ca ( Ca > 1.0), are observed. In the recirculation flow we observe the formation of elastic stress boundary layers in the capillary transition region (the thickness of which decrease with increasing elasticity), an increase in the hydrodynamic film thickness with increasing elasticity and a meniscus invasion when the stresses in the elastic boundary layer become very large. We have also qualitatively studied the effect of channel wall divergence on the flow dynamics and ascertained that the elastic stress boundary layer formation is a purely local phenomenon and largely independent of geometric considerations. For the bypass flow, in addition to the elastic stress boundary layer in the capillary transition region, an additional elastic stress boundary layer near the bubble tip is observed. As the Wi is increased, film thickening is observed but no meniscus invasion occurs. We have also studied the effect of gravity on both flows. Addition of gravity in recirculation flow results in a film thinning effect and an increase in the normal stresses in the capillary transition regime. For the bypass flow, even a small amount of gravity introduces recirculation. Finally, we discuss how both flows are elastically unstable and plausible mechanisms for the onset of instability are suggested.