Session Cd - Interfacial & Thin-Film Instabilities.
ORAL session, Sunday, November 23
304, Moscone Center
We construct scaling theories for the rupture of thin bodies of fluid in three geometries: (i) a 2D layer with planar symmetry, (ii) with central symmetry, and (iii) a cylindrical thread. The model equations contain the effects of surface tension, viscosity, and van der Waals forces, as originally derived by Enreux and Davis~(T. Erneux and S. H. Davis, Nonlinear rupture of free films, Physics of Fluids A, 5 (1993) 1117--1122.). \underlineAt high Reynolds numbers, there is (in each geometry) a countable set of solutions with the same scaling exponents. In 2D, the solutions are symmetric, whereas for the thread the solutions are 0. For each geometry, only one solution is dynamically selected for generic initial conditions. In all geometries, at high Reynolds number the solutions violate the long wavelength assumption, under which the equations were derived. \underlineAt low Reynolds number, the situation is very different: There is a continuous family of similarity solutions with different scaling exponents. The dynamics picks special members of this family. These special solutions all obey the long wavelength assumption and, therefore, should be physically realizable. The selection mechanism determining which solution occurs will be remarked upon.