DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Burt Tilley, Worcester Polytechnic Institute

**Title: ***
Thermocapillary Control of Thin Fluid Sheets
*

**Abstract:**
We consider the evolution and rupture dynamics of a thin
viscous planar sheet subject to a symmetric initial long-wave
disturbances in the thermal and velocity fields. We apply a long-wave
analysis in the limit where deviations from the mean sheet velocity are
small, but thermocapillary stresses, fluid inertia, van der Waals
effects, capillarity, and heat transfer to the environment can be
significant. From a linear stability analysis, we find that a stable
thermal mode couples the velocity and interfacial dynamics. The phase
difference between the initial temperature and velocity distributions is
a key parameter in determining the time to rupture. Using phase
modulation in the initial temperature along with amplitude modulation in
the initial velocity allows the potential for control of the rupture
patterns along the sheet. Self-similar rupture dynamics in the limit of
zero van der Waals forces are also presented.

**Time:** Friday, Nov. 18, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

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