A comparison of viscoelastic stress wakes for two-dimensional and three-dimensional Newtonian drop deformations in a viscoelastic matrix under shear

A recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in drop deformation which is qualitatively similar to two-dimensional (2D) numerical simulation results. Despite the similarity, an interpretation in light of the 2D result is misleading because the overshoot is absent in the fully three-dimensional (3D) simulation. This motivates a study of regimes where qualitatively different and interesting features such as overshoots in deformation occur for a 2D drop but not for a 3D drop. The influence of viscoelastic "wakes" that emanate from the drop tips is reported. The viscoelastic wakes are larger and of higher magnitude in 3D than in 2D, and lead to more deformation in 3D. During drop evolution, the less deformed drop is found to be aligned more with the flow direction. As the drop-to-matrix viscosity ratio increases from 1 to past 3, drop rotation is promoted, with accompanying retraction when the capillary number is sufficiently high. Thus, a 3D overshoot in deformation is promoted with increasing viscosity ratio.