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fiber when it is withdrawn from a bath of Newtonian fluid sufficiently rapidly.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predictions of the film thickness that coats a substrate when it is withdrawn from a bath of viscoelastic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