- Thomas P. Witelski and Andrew J. Bernoff, Stability of self-similar solutions for van der Waals driven thin film rupture,
Physics of Fluids, 11,9, (1999), pp. 2443-2445
(last updated on 1999/11/09)
Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang & Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular ``ring rupture.''