Deformation of a two-dimensional viscoelastic drop at non-zero Reynolds number in time-periodic extensional flows
The authors investigate the behavior of a non-Newtonian drop, characterized by an upper-convected Maxwell model, suspended in an incompressible Newtonian fluid. The following three related cases are considered: (a) a potential vortex modelled by an extensional flow near the drop with rotating axes of stretching; (b) a rotating extensional flow in which the frequency of revolution of the flow is varied independently of the shear rate; (c) oscillating extensional flow. The above problems are solved at small Reynolds numbers using an ADI front-tracking/finite difference method. The authors develop an analytical elastic viscous stress splitting and utilize it to treat the non-Newtonian constitutive equation. Finally, the authors investigate the effects of periodicity, Reynolds number and relaxation time on drop dynamics. A number of interesting results have been obtained. For example, the authors show that for the potential vortex the drop reaches a steady state of deformation -- a similar result is also obtained for the rotating extensional flow.
ADI front-tracking/finite difference method
scientific article; zbMATH DE number 1556248