The influence of polymer concentration and chain architecture on free surface displacement flows of polymeric fluids

Abstract

We examine the effect of polymer concentration and chain architecture on the steady state displacement of polymeric fluids by air in between two infinitely long closely spaced parallel plates, i.e., Hele-Shaw flow. A stabilized finite element method coupled with a pseudosolid domain mapping technique is used for carrying out the computations. The constitutive equations employed in this study are the Finitely Extensible Nonlinear Elastic–Chilcott Rallison (FENE-CR) and the Finitely Extensible Nonlinear Elastic–Peterlin (FENE-P) models for dilute solutions, the Giesekus constitutive equation for dilute, semidilute and concentrated solutions, and the Extended Pom-Pom (XPP) constitutive equation for linear and branched polymeric melts. Our study indicates the presence of a recirculation flow at low Ca and a bypass flow at high Ca irrespective of polymer concentration and chain architecture. We show that the interfacial dynamics in both the recirculation and the by-pass flow depend on extensional hardening and shear thinning characteristics of the fluids. In the recirculation flow, we observe the formation of normal elastic stress boundary layers in the capillary transition region, an accompanying increase in the film thickness and a compression of the bubble in the capillary transition region, at moderate Wi. In the bypass flow, in addition to the elastic stress boundary layer in the capillary transition region, an additional stress boundary layer is observed at the tip of the bubble. The amount of film thickening, the magnitude of the stress in the stress boundary layer and the amount of bubble compression are largest for the most extensional hardening fluids and reduce with decreasing extensional hardening and increasing shear thinning. We show that the film thickness is determined by two competing forces, i.e., normal stress gradients in the flow direction, in the capillary transition region (recirculation flow) and the tip region (bypass flow) and shear stress gradientsin the gap direction. For both the recirculation and the bypass flow, we show how the film thickness scales with fluid normal stresses and shear viscosities, and develop correlations for the film thickness as a function of Ca and Wi.