Deformation of an axisymmetric viscoplastic drop in extensional/compressional flow

Abstract

The dynamic and stationary deformations of a viscoplastic drop in an axisymmetric linear viscous flow is addressed through numerical analyses for a variety of governing parameters. A variation of the integral equation method used by Toose et al. (1996, 1999) is employed. It is demonstrated that a spherical drop embedded in compressional or extensional flow, which provides viscous stresses at the interface strong enough to yield the drop medium, deforms into oblate or prolate shapes, respectively. With the passage of time, the drops attain elongated (in extensional flow) or flattened (in compressional flow) forms. For moderate shear intensity, stable stationary states are established, with either entirely yielded or partially un-yielded flow inside the drop. When the velocity gradients exceed critical values the drop loses its stable shape and continues to deform indefinitely.