Thin Films Seminar
Wednesday, February 26, 2003, 12:00pm, 054 Physics
Sandra Wieland (Duke University)
A degenerate parabolic system modelling the surfactant spreading on thin films
Abstract:- In general we study the evolution of a thin film, the surface tension
of which is reduced by a surface active agent (surfactant) spreading
on it. The situation occurs e.g. in biological applications, where
the surface tension in lung alveols is reduced in the presence of a
monolayer of surfactant molecules. The concentration dependent surface
tension generates a Marangoni force which is a tangential force on the
free surfae of the film.
Starting from a Navier-Stokes equation for the incompressible fluid and
an evolution equation for the density of surfactant molecules a parabolic
system for the film height and the surfactant concentration is derived by
means of lubrication theory. Making use of the energy functional on the
level of the N-S equation we obtain a priori estimates which are used to
establish an existence result for a weak solution of the parabolic system.
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