Bifurcation study for a surface-acoustic-wave driven meniscus

TL;DR

This study analyzes a thin-film model driven by surface acoustic waves, revealing complex bifurcation structures and shedding behaviors relevant to wetting and film dynamics.

Contribution

It introduces a detailed bifurcation analysis of a SAW-driven meniscus model, combining hydrodynamics with surface effects, and explores the emergence of time-periodic states.

Findings

Identification of bifurcation points and regimes of steady and periodic states

Analysis of Hopf bifurcations leading to liquid ridge shedding

Insights applicable to general dragged-film problems

Abstract

A thin-film model for a meniscus driven by Rayleigh surface acoustic waves (SAW) is analysed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath. We consider a mesoscopic hydrodynamic model for a partially wetting liquid, were wettability is incorporated via a Derjaguin (or disjoining) pressure and combine SAW driving with the elements known from the dragged-film problem. For a one-dimensional substrate, i.e., neglecting transverse perturbations, we employ numerical path continuation to investigate in detail how the various occurring steady and time-periodic states depend on relevant control parameters like the Weber number and SAW strength. The bifurcation structure related to qualitative transitions caused by the SAW is analysed with particular attention on the {appearance and interplay of Hopf bifurcations where branches of time-periodic states emerge. The latter correspond to the regular shedding of liquid ridges from the meniscus. The obtained information is relevant to the entire class of dragged-film problems.