The deformation of a Newtonian drop in the uniaxial extensional flow of a viscoelastic liquid

Abstract

The deformation of a Newtonian drop in uniaxial flow of a viscoelastic fluid is studied via numerical computations. The viscoelastic fluid is modeled using the FENE-CR constitutive theory. The computations are performed for two values of the Chilcott–Rallison extensibility parameter L 2 = 144 and L 2 = 600, for Deborah numbers between 0 and 2, and for several values of the concentration parameter c in the range appropriate for dilute (Boger) solutions. It is found that the deformation is always increased for the viscoelastic fluid compared to the shape in a Newtonian fluid, and that there is a viscoelastic mechanism (an `instability' of shape) that tends to produce a high curvature at the tips of the drop. The magnitude of stress gradients immediately downstream from the tip of the drop are reduced as the viscosity ratio (interior/exterior) is reduced, though the viscoelastic contribution to the drop deformation is actually increased for small viscosity ratios.