Nonlinear dynamics of a two-dimensional viscous drop under shear flow

The dynamics of a viscous drop moving along a substrate under the influence of shear flow in a parallel-walled channel is investigated. A front tracking numerical method is used to simulate a drop with moving contact lines. A Navier slip boundary condition is applied to relax the contact line singularity. Steady state solutions are observed for small Reynolds and capillary number. Unsteady solutions are obtained with increasing Reynolds or capillary number. For large values of the parameters, the interface appears to rupture, but for intermediate parameter values, time periodic drop interface oscillations are possible as the drop is moving along the bottom channel wall. These different states are identified in the Reynolds number-capillary number plane for a specific range of physical parameters. The effects of density and viscosity ratio are also illustrated. (c) 2006 American Institute of Physics.