Analysis of vibration impact on stability of dewetting thin liquid film

TL;DR

This paper investigates how moderate-frequency, large-amplitude vertical vibrations can stabilize thin liquid films against dewetting by analyzing the fluid dynamics and deriving an amplitude equation, revealing conditions for stability.

Contribution

It introduces a nonlinear amplitude equation for the averaged film thickness under vibration and identifies a stability window in the frequency-amplitude domain.

Findings

Vibration can suppress dewetting and rupture of thin films.

A stability window exists where flow instabilities are absent.

Numerical and analytical results confirm stabilization effects.

Abstract

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.