DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Shawn Walker, LSU

**Title: ***
A New Mixed Formulation For a Sharp Interface Model of Stokes Flow and Moving Contact Lines
*

**Abstract:**
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 (see
Falk & Walker in the context of Hele-Shaw flow) 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. 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.

**Time:** Friday, October 25, 2013, 1:30-2:30 p.m.

**Place:** Exploratory Hall (formerly S & T II), Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491