Bifurcation study for a surface-acoustic-wave driven meniscus
arXiv:2006.12113 · doi:10.1103/PhysRevFluids.6.094002
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(SAW) is analysed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath.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.
References in corpus (21)
- Patterned deposition at moving contact lines
- Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation
- Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
- Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting
- Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
- Morphological transitions of sliding drops: Dynamics and bifurcations
- Continuous and discontinuous dynamic unbinding transitions in drawn film flow
- Modelling Pattern Formation in Dip-Coating Experiments
- A partially wetting film of water and surfactant under the influence of a propagating MHz surface acoustic wave
- First order phase transitions and the thermodynamic limit
- Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
- Thin-Film Modelling of Resting and Moving Active Droplets
- Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems
- Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model
- Connecting monotonic and oscillatory motions of the meniscus of a volatile polymer solution to the transport of polymer coils and deposit morphology
- Hopf bifurcation from fronts in the Cahn-Hilliard equation
- Self-organised dip-coating patterns of simple, partially wetting, nonvolatile liquids
- Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer
- Two-dimensional patterns in dip coating -- first steps on the continuation path
- Dip-coating with prestructured substrates: transfer of simple liquids and Langmuir-Blodgett monolayers
- The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates