Mathematics Colloquia and Seminars
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Models for a Vertical Draining Film with an Insoluble SurfactantColloquium
|Speaker: ||Richard Braun, Unversity of Delaware|
|Location: ||693 Kerr|
|Start time: ||Mon, Oct 22 2001, 4:00PM|
The drainage of the thin fluids layers, or lamellae, in a foam may
be modeled by a vertical draining thin liquid film.
A sequence of mathematical models is described that attempts to
explain some aspects of the drainage of the film. Lubrication theory is
used to derive the nonlinear PDEs that describe the film;
all models assume an insoluble surfactant.
The models include effects from gravity,
viscosity, surface tension and its dependence on surface concentration
(the Marangoni effect), and surface viscosity; they may also include nonlinear
equations of state. The models are able to predict very well the fast
and slow limits of the drainage observed experimentally; a limited range of intermediate drainage
rates has been described by these models to date. The limitations
of the models and possible extensions will be discussed.
Coffee and cookies will be served at 3:30.