PHYSICAL MATHEMATICS SEMINAR


TOPIC:		GRAVITATIONALLY-DRIVEN DRAINAGE
		OF THIN FILMS

SPEAKER:	SHAILESH NAIRE
		Department of Mathematical Sciences
		Worcester Polytechnic Institute

ABSTRACT:

A 1+1- and 2+1- dimensional mathematical model is constructed to
study the evolution of a vertically-oriented thin liquid film draining
under gravity when there is an insoluble surfactant with finite surface
viscosity on its free surface.

Lubrication theory for the 1+1-D free film results in three coupled
nonlinear partial differential equations (PDEs)  describing the free
surface shape, the surface velocity and the surfactant transport at
leading order.  A large surface viscosity limit recovers the
tangentially-immobile model; for small surface viscosity, the film is
mobile.  Transition from a mobile to an immobile film is observed for
intermediate values of surface viscosity and Marangoni number.  This model
reproduces a number of features observed in experiments, these include
film shapes and thinning rates which can be correlated to experiment.

The 2+1-D model for simplified surface properties has also been studied.
Numerical experiments are performed to understand the stability of the
system to perturbations across the film.  An instability is seen in the
mobile film case; this is caused by a competition between gravity and the
Marangoni effect.  The behavior observed from this model qualitatively
matches the structures observed in Dow Corning experiments; more work is
needed to compare our numerics with experiment quantitatively.

DATE:		TUESDAY, FEBRUARY 13, 2001

TIME:		2:30 PM

LOCATION:	Building 2, Room 338

Refreshments will be served at 3:30 PM in Room 2-349



Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA  02139