Papers Published

1. Thomas P. Witelski and A. J. Bernoff, Three-dimensional van der Waals driven thin film rupture, Physica D, 147 (1-2), pp. 155--176, (2000). [science] .
   (last updated on 2003/02/05)

   Abstract:
   We consider the problem of thin film rupture driven by van der Waals forces. A fourth-order nonlinear PDE governs the low Reynolds number lubrication model for a viscous liquid on a solid substrate. Finite-time singularities in this equation model rupture which lead to formation of dry spots in the film. Our study addresses the problem of rupture in the full three-dimensional geometry. We focus on stability and selection of the dynamics from the initial conditions in planar and axisymmetric geometries as well as the final stages of self-similar dynamics for point, line, and ring rupture. We will demonstrate that line and ring rupture are unstable and will generically destabilize to produce axisymmetric rupture at isolated points.