A computational study of the effects of viscoelasticity on the interfacial dynamics of free surface displacement flows

We have implemented a finite strain pseudo-solid domain mapping technique, coupled with a stabilized finite element formulation, to study the effects of viscoelasticity on free surface displacement flows. We start by analyzing the displacement of a viscoelastic fluid by a bubble of air confined between two infinitely long parallel plates, separated by a small distance (Hele-Shaw cell type of flow), using the Finitely Extensible Non-Linear Elastic Chilcott Rallison (FENE-CR) model for extensional hardening, non-shear thinning dilute solutions. We extend the computations to incorporate the effects of shear thinning, normal stress thinning and concentration by employing the Finitely Extensible Non-Linear Elastic Peterlin (FENE-P) model for extensional hardening, shear thinning dilute solutions, the Giesekus model for semi-dilute and concentrated solutions, and the Extended Pom-Pom (XPP) model for linear and branched polymeric melts. We have developed a very robust and efficient code that works well for a wide range of processing conditions and geometries. For each of these models, we inspect the flow streamlines, the flow stresses and the film thickness. We compare and contrast the relative film thickening observed with each of these models and correlate the film thickness to the predicted extensional viscosity. Furthermore, we extend the prototypical flow type analyzed to a dip coating flow. We compare our numerical simulations qualitatively with existing experimental data for both the Hele-Shaw cell and the dip coating flow. In addition to these base flow computations, we also illustrate how elasticity destabilizes the flow by altering the normal stress balance at the interface. By conducting a linear stability study of a model planar stagnation viscoelastic free surface displacement flow, utilizing the Oldroyd-B and FENE-P models, we show that elastic destabilization of the flow occurs due to the alteration of the isotropic pressure distribution at the free surface by the elastic normal stress boundary layer localized near the stagnation point.