Bounded Film Evolution with Nonlinear Surface Properties
Author(s) | Debisschop, C.A. | |
Author(s) | Braun, Richard J. | |
Author(s) | Snow, S.A. | |
Date Accessioned | 2005-02-18T16:11:53Z | |
Date Available | 2005-02-18T16:11:53Z | |
Publication Date | 2001-09-12 | |
Abstract | We study the evolution of a Newtonian free surface of a thin film above a solid wall. We consider the case in which the horizontal solid is covered by a non-wetting fluid and an insoluble monolayer of surfactant is present on the fluid-air interface. We pose a model that incorporates a variety of interfacial effects: van der Waals forces, variable surface tension and surface viscosity. The surface tension and surface viscosity depend nonlinearly on the surfactant concentration. Using lubrication theory we obtain a leading order description of the shape and velocity of the fluid-air interface, and the surfactant concentration, in the form of coupled nonlinear partial differential equations. A linear stability analysis reveals that the wavenumber that characterizes the marginal state is independent of the presence of the surfactant and the nonlinearity of the surface properties. We solve the 1+1-dimensional system numerically to obtain the spatio-temporal evolution of the free surface in the nonlinear regime, and observe the progression to rupture. | en |
Sponsor | Supported by NSF Grant DMS-9631287 and also supported by NSF Grant DMS-9631287 and Dow Corning Corporation Grant. | en |
Extent | 834188 bytes | |
MIME type | application/pdf | |
URL | http://udspace.udel.edu/handle/19716/353 | |
Language | en_US | |
Publisher | Department of Mathematical Sciences | en |
Part of Series | Technical Report: 2001-10 | |
Title | Bounded Film Evolution with Nonlinear Surface Properties | en |
Type | Technical Report | en |