CENTER FOR COMPUTATION & TECHNOLOGY

Two phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines.  We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate.  The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis through a variational inequality.  We prove the well-posedness of the time semi-discrete and fully discrete (finite element) model and discuss error estimates (ongoing).  Simulation movies will be presented to illustrate the method.  We conclude with some discussion of a 3-D version of the problem as well as future work on optimal control of these types of flows.

Shawn Walker is an assistant professor in mathematics at LSU. He received his Ph.D. from the University of Maryland, College Park.  He held a postdoctoral position at the Courant Institute (New York University), and joined the LSU faculty in 2010 in the computational mathematics group.  His research interests include: PDEs and finite element methods for moving domain problems, PDE-constrained (shape) optimization, and mesh generation.