Gradient-dynamics model for liquid drops on elastic substrates
arXiv:2107.08397 · doi:10.1039/D1SM01032H
Abstract
The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.
References in corpus (37)
- Elastocapillarity: Surface Tension and the Mechanics of Soft Solids
- The Deformation of an Elastic Substrate by a Three-Phase Contact Line
- Static wetting on deformable substrates, from liquids to soft solids
- Patterning droplets with durotaxis
- Droplets move over viscoelastic substrates by surfing a ridge
- Morphology changes in the evolution of liquid two-layer films
- Soft lubrication
- Coalescence of sessile drops
- Direct Measurement of Strain-dependent Solid Surface Stress
- Capillary Pressure and Contact Line Force on a Soft Solid
- Drops on soft solids: Free energy and double transition of contact angles
- Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation
- Soft wetting and the Shuttleworth effect, at the crossroads between thermodynamics and mechanics
- Straight contact lines on a soft, incompressible solid
- Surface energy of strained amorphous solids
- Role of uncrosslinked chains in droplets dynamics on silicone elastomers
- Elastic deformation due to tangential capillary forces
- Gradient dynamics models for liquid films with soluble surfactant
- Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall
- Breath figures under electrowetting: electrically controlled evolution of drop condensation patterns
- Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting
- Dynamic solid surface tension causes droplet pinning and depinning
- How ice grows from premelting films and water droplets
- Regimes of Soft Lubrication
- Validity of Winkler's mattress model for thin elastomeric layers: Beyond Poisson's ratio
- Morphological transitions of sliding drops: Dynamics and bifurcations
- Persistent vs. arrested spreading of biofilms at solid-gas interfaces - the role of surface forces
- A liquid contact line receding on a soft gel surface : dip-coating geometry investigation
- Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets
- Continuous and discontinuous dynamic unbinding transitions in drawn film flow
- Droplets sit and slide anisotropically on soft, stretched substrates
- Thin-Film Modelling of Resting and Moving Active Droplets
- Gradient dynamics model for drops spreading on polymer brushes
- Sliding drops - ensemble statistics from single drop bifurcations
- How many ways a cell can move: the modes of self-propulsion of an active drop
- Coarsening rates for the dynamics of slipping droplets
- The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates
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- Wetting on Silicone Surfaces
- Sessile drop evaporation in a gap -- crossover between diffusion-limited and phase transition-limited regime
- Soft wetting with (a)symmetric Shuttleworth effect
- Drops on polymer brushes -- advances in thin-film modelling of adaptive substrates
- Stick-slip Dynamics in the Forced Wetting of Polymer Brushes
- Stick-Slip Contact Line Motion on Kelvin-Voigt Model Substrates
- The role of substrate mechanics in osmotic biofilm spreading
- Dynamics of particle aggregation in dewetting films of complex liquids
- Gradient dynamics approach to reactive thin-film hydrodynamics
- Drops of volatile binary mixtures on brush-covered substrates
- Mesoscopic hydrodynamic model for spreading, sliding and coarsening compound drops
- Gradient dynamics model for chemically driven running drops
- Confinement-induced drift in Marangoni-driven transport of surfactant: a Lagrangian perspective
- Liquid film rupture beyond the thin-film equation: a multi-component lattice Boltzmann study