Title: Numerical simulations of drop deformation for viscoelastic
liquid-liquid systems. 

Abstract: We implement a volume-of-fluid
algorithm with a parabolic re-construction of the interface for the
calculation of the surface tension force (VOF-PROST). This achieves
higher accuracy for drop deformation simulations in comparison with
existing VOF methods based on a piecewise linear interface
re-construction.  The algorithm is formulated for the Giesekus
constitutive law. The evolution of a drop suspended in a second liquid
and undergoing simple shear is simulated. Numerical results are first
checked against two cases in the literature: the small deformation
theory for second-order liquids, and an Oldroyd-B extensional flow
simulation. We then address the experimental data of Guido, Simeone
and Greco (Deformation of a Newtonian drop in a viscoelastic matrix
under steady shear flow. Experimental validation of slow flow theory.
J. Non-Newtonian Fluid Mech., 114:65--82, 2003) The data deviate from
existing theories as the capillary number increases, and reasons for
this are explored with numerical simulations.