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

• Published in: Physics of fluids (1994) Vol. 18; no. 7; pp. 072106 - 072106-10
• Main Authors: Zhang, J., Miksis, M. J., Bankoff, S. G.
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.07.2006
• Subjects: Condensed matter: structure, mechanical and thermal properties; Drops and bubbles; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Physics; Solid-fluid interfaces; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Wetting; Parallel plane channel; Geometrical shape; Wetting; Shear flow; Digital simulation; Moving contact; Drops; Modelling; Viscous fluids
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2222336

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.