Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids

The effect of viscoelasticity on the deformation of a circular drop suspended in a second liquid in shear is investigated with direct numerical simulations. A numerical algorithm based on the volume-of-fluid method for interface tracking is implemented in two dimensions with the Oldroyd-B constitutive model for viscoelastic liquids. The code is verified against a normal mode analysis for the stability of two-layer flow in a channel; theoretical growth rates are reproduced for the interface height, velocity and stress components. Drop simulations are performed for drop and matrix liquids of different viscosities and elasticities. A new feature is found for the case of equal viscosity, when the matrix liquid is highly elastic and surface tension is low; hook-like structures form at the drop tips. This is due to the growth of first normal stress differences that occur slightly above the front tip and below the back tip as the matrix elasticity increases above a threshold value.