Duke Applied Mathematics

Publications [#320453] of Thomas P. Witelski

Papers Published

1. Ji, H; Witelski, TP, Finite-time thin film rupture driven by modified evaporative loss, Physica D Nonlinear Phenomena, vol. 342 (March, 2017), pp. 1-15, Elsevier BV [doi]
   (last updated on 2026/01/19)

   Abstract:
   Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with modified evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term. Several different types of finite-time singularities are observed due to balances between conservative and non-conservative terms. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.