Related papers: Equilibrium solutions of a sessile drop partially …
In this work, we develop a novel model describing the equilibrium shape of sessile droplets on a wetted horizontal surface in a gravitational field. The model takes into account the intermolecular Lenard-Jones forces between solid and the…
Interfaces with a liquid are governing several phenomena. For instance, these interfaces are giving the shape of sessile droplets and rule the spread of liquids on surfaces. Here we analyze the shape of sessile axisymmetric drops and how it…
The interface shape of a fluid in rigid body rotation about its axis and partially filling the container is often the subject of a homework problem in the first graduate fluids class. In that problem, surface tension is neglected, the…
It is well-known that liquid and saturated vapor, separated by a flat interface in an unbounded space, are in equilibrium. One would similarly expect a liquid drop, sitting on a flat substrate, to be in equilibrium with the vapor…
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…
This paper investigates the properties of a three dimensional shear flow overpassing a hemispherical droplet resting on a plane wall. The exact solution is computed as a function of the viscosity ratio between the droplet and the…
We construct a novel model for the steady-state contact angles of liquid droplets at the wetted substrate. The non-removable, thin liquid film covering the substrate is governed by the intermolecular forces between molecules of liquid and…
An analytical solution is obtained for the problem of the slow movement of a small drop of a fluid in another immiscible fluid in an infinitely large reservoir with the boundary condition of the normal slip and/or tangential partial slip at…
Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width $L$ separated by distances $D_1$ and $D_2$. The stripes interact with…
We present a solvable model inspired by dimensional analysis for the time-dependent spreading of droplets that partially wet a substrate, where the spreading eventually stops and the contact angle reaches a nonzero equilibrium value. We…
We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume constrained minimizer of the total interfacial energy. The large-scale shape of such a drop strongly depends on the micro-structure of the solid surface.…
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by two equal point charges. The support of the equilibrium measure is known as the droplet. Brauchart et al. showed that the…
Using an identity, directly derived from the Young-Laplace equation, the problem of the equilibrium shape of an axisymmetric sessile drop is reduced to a one-parameter shooting method problem. Based on the method the numerical solutions for…
Inviscid flow within an evaporating sessile drop is analyzed. The field equation, E^2(Psi)=0, is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux…
We investigate numerically quasi-steady internal flows in an axially symmetrical evaporating sessile droplet depending on the ratio of substrate to fluid thermal conductivities, fluid volatility, contact angle and droplet size. Temperature…
When two immiscible liquids that coexist inside a porous medium are drained through an opening, a complex flow takes place in which the interface between the liquids moves, tilts and bends. The interface profiles depend on the physical…
We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid.…
It is well known that, at a macroscopic level, the boundary condition for a viscous fluid at a solid wall is one of "no-slip". The liquid velocity field vanishes at a fixed solid boundary. In this paper, we consider the special case of a…
Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes…
Superhydrophobicity relies on the stability of drops's interfaces pinned on sharp edges to sustain non-wetting (Cassie-Baxter) equilibrium states. Gibbs already pointed out that equilibrium is possible as long as the pinning angle at the…