PHYSICAL MATHEMATICS SEMINAR TITLE: NEWTONIAN AND NON-NEWTONIAN COATING FLOWS AUTHOR: JACQUELINE ASHMORE Division of Engineering and Applied Sciences Harvard University ABSTRACT: One type of fluid flow common in industrial processes involves the deposition of a thin film on a moving substrate. The mathematical description of the free surface shape in such coating problems involves a nonlinear third-order differential equation. In the Early 1940s, Landau, Levich and Derjaguin used matched asymptotics to solve the equation and determine the thickness of the uniform film which coats a plate or cylindrical fiber when it is withdrawn from a bath of Newtonian fluid sufficiently rapidly. Since then, matched asymptotics have been used to derive theoretical descriptions of the film thickness for Newtonian and generalized Newtonian fluids in a variety of geometries. We consider the interface shape of fluid inside a horizontal cylinder rotating about its axis with a small fraction of its volume filled with viscous Newtonian fluid. This problem has been studied extensively, although analytical work has mainly focused on axially uniform shapes and the limit that surface tension effects are negligible everywhere. Since the surface tension term contains the highest derivatives in the equation, it represents a singular perturbation and solutions may differ qualitatively when it is included. By accounting for surface tension effects we find a new solution in a region of parameter space in which, when surface tension effects are neglected, no axially uniform steady solution can be found. Analytical arguments for the scalings are based on the analysis of Landau, Levich and Derjaguin, and are confirmed numerically. Finally, theoretical predictions of the film thickness that coats a substrate when it is withdrawn from a bath of viscoelastic fluid will be presented, for a number of substrate geometries. TUESDAY, APRIL 8, 2003 2:30 pm 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