Finite-time thin film rupture driven by modified evaporative loss

Highlights: • A fourth-order thin film equation with modified non-conservative flux is analyzed. • Non-conservative loss can overcome disjoining pressure and cause finite-time singularities. • The generalized PDE yields various forms of rupture dynamics. • A bifurcation diagram for rupture regimes is obtained from the model. • Analytical predictions are supported by high-precision PDE simulations. 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.