Viscoelastic effects on drop deformation in a converging pipe flow

Abstract

This paper reports finite-element simulations of drop deformation in converging flows in an axisymmetric conical geometry. The moving interface is captured using a diffuse-interface model and accurate interfacial resolution is ensured by adaptive refinement of the grid. We have explored the effects of viscoelasticity on drop deformation when either the drop or the matrix is a Giesekus fluid. Contrary to the popular belief that viscoelasticity in the drop hinders deformation and that in the matrix enhances deformation, we predict a more complex picture in which viscoelasticity in either component may suppress or promote drop deformation depending on the capillary number Ca and the drop-to-matrix viscosity ratio ␤. Smaller Ca and ␤ are conducive to the behavior mentioned above, while large Ca and ␤ may produce the opposite effect. Both trends are explained by the reaction of the polymer stress to the inhomogeneous and transient deformation in the converging flow field. Finally, this understanding reconciles contradictory results in the literature as opposite limits in the parameter space.

A particle-based model for the transport of erythrocytes in capillaries

“…G can be likened to the capillary number in drop dynamics (e.g., Zhou et al, 2008). We can also define two ratios between the moduli:…”

Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear

“…As with previous studies ( [14], [35], [15,36], [18]) Oldroyd B model is chosen as a simple constitutive model despite its shortcomings. Recent numerical simulations [8,37] have incorporated a small Giessekus parameter to the Oldroyd B model used by the same investigators previously, but the results were found not to be affected by it. In view of this we prefer not to incorporate any additional parameter; the simulation results seem to be free of the numerical difficulties within the range of Deborah numbers studied.…”

Deformation and breakup of viscoelastic droplets in confined shear flow

“…They report a non-monotonic change in deformation for a viscoelastic droplet in a viscous matrix while the reversed case was seen to increase droplet deformation. Yue et al [39][40][41][42][43][44] performed various numerical calculations based on a diffuse-interface formulation and the Oldroyd-B constitutive equation for the non-Newtonian phase [40]. Such analysis was then extended by Aggarwal & Sarkar [21,22] using a 3D front-tracking finite difference numerical method.…”