Finite-time self-similar rupture in a generalized elastohydrodynamic lubrication model

TL;DR

This paper analyzes finite-time rupture in a generalized elastohydrodynamic lubrication model, revealing self-similar solutions and the effects of elastic and surface forces on rupture dynamics.

Contribution

It introduces a sixth-order nonlinear PDE model for thin film rupture, analyzing self-similar solutions and the influence of elasticity and surface tension.

Findings

Identification of sixth-order self-similar rupture solutions

Discovery of transient fourth-order self-similar dynamics in weak elasticity limit

Insights into the interplay between disjoining pressure and elastic bending

Abstract

Thin film rupture is a type of nonlinear instability that causes the solution to touch down to zero at finite time. We investigate the finite-time rupture behavior of a generalized elastohydrodynamic lubrication model. This model features the interplay between destabilizing disjoining pressure and stabilizing elastic bending pressure and surface tension. The governing equation is a sixth-order nonlinear degenerate parabolic partial differential equation parameterized by exponents in the mobility function and the disjoining pressure, respectively. Asymptotic self-similar finite-time rupture solutions governed by a sixth-order leading-order equation are analyzed. In the weak elasticity limit, transient self-similar dynamics governed by a fourth-order similarity equation are also identified.