A computational study of the effects of viscoelasticity on drop deformation and macroscopic rheology in a steady shear flow, is undertaken using a three dimensional front-tracking algorithm adapted for non-Newtonian flow computations. An Oldroyd-B constitutive equation is used to model the non-Newtonian phase.

We first investigate the drop response of an Oldroyd-B drop suspended in a Newtonian matrix. Drop deformation is seen to decrease from its Newtonian value with increasing viscoelasticity. Its time evolution is non-monotonic displaying an overshoot before settling down to a lower value of deformation. The overshoot increases with increasing polymeric contributions to the total drop viscosity. Drop breakup is inhibited by viscoelasticity with the critical Capillary number increasing linearly with Deborah number. A simple ordinary differential equation model is developed to explain the various behaviors and the scalings observed numerically.

For the inverse problem of a Newtonian drop in a viscoelastic fluid, the change in drop deformation and orientation with increasing Deborah number is established. Drop response is explained by examining the stresses at the interface, the polymer orientation and the elastic and viscous forces in the domain. Orientation of the drop with the flow direction increases with increasing viscoelasticity. Non-monotonic change in steady state deformation is observed with increasing Deborah number. This is explained in terms of the competition between increased deformation due to localized polymer stretching at drop tips and decreased deformation due to change in drop orientation. For fully elastic systems, the drop deformation is found to decrease monotonically with increasing drop to matrix elasticity ratio. Numerical results are validated against existing experimental and theoretical results.

Finally, the macroscopic rheological behavior for the viscoelastic drop in a Newtonian matrix is studied. Drop deformation gives rise to shear thinning and normal stress differences in the emulsion. The interfacial contribution to the normal stress increases linearly with the Capillary number and decreases with increasing viscoelasticity due to decrease in the drop deformation. Viscoelasticity does not change the effective viscosity of the emulsion significantly. However, it gives rise to an extra normal stress which increases linearly with the Capillary and Deborah number, for small parameter values.