Asymptotic theory for a moving droplet driven by a wettability gradient
arXiv:physics/0509260 · doi:10.1063/1.2191015
Abstract
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.
8 figs
References in corpus (6)
- Hydrodynamic theory of de-wetting
- Dynamical Model for Chemically Driven Running Droplets
- Self-propelled running droplets on solid substrates driven by chemical reactions
- Toward a description of contact line motion at higher capillary numbers
- Contact line motion for partially wetting fluids
- Droplet motion driven by surface freezing or melting: A mesoscopic hydrodynamic approach
Cited by in corpus (22)
- Numerical Study of Drop Motion on a Surface with Wettability Gradient and Contact Angle Hysteresis
- Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates
- Non-coalescence of sessile drops from different but miscible liquids: Hydrodynamic analysis of the twin drop contour as self stabilizing, traveling wave
- 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
- Continuation for thin film hydrodynamics and related scalar problems
- Numerical Bifurcation Analysis of Marine Ice Sheet Models
- Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
- Persistent vs. arrested spreading of biofilms at solid-gas interfaces - the role of surface forces
- Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
- On the depinning of a drop of partially wetting liquid on a rotating cylinder
- Directional spreading of a viscous droplet on a conical fibre
- From a thin film model for passive suspensions towards the description of osmotic biofilm spreading
- Dynamics of nanodroplets on topographically structured substrates
- Perturbation Theory for Traveling Droplets
- Comparing kinetic Monte Carlo and Thin-Film Modeling of Transversal Instabilities of Ridges on Patterned Substrates
- Rugotaxis: Droplet motion without external energy supply
- Unidirectional Droplet Propulsion onto Gradient Brushes without External Energy Supply
- Antidurotaxis Droplet Motion onto Gradient Brush Substrates
- Durotaxis and antidurotaxis droplet motion onto gradient gel-substrates
- Equilibrium Contact Angle at the Wetted Substrate
- Directed droplet motion -- Its versatile nature and anticipated applications