Related papers: Stationary liquid drops in Lorentz-Minkowski space
We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for…
We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a…
We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…
Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as it is observed for water drops on a heated plate, kept aloft by a stream of water vapor. We investigate the limit of small flow rates,…
We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…
A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show theoretically…
In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space $\l^3$ which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support…
This paper describes the techniques and physical parameters used to produce stable centimetric water drops in microgravity, and to study single cavitation bubbles inside such drops (Parabolic Flight Campaigns, European Space Agency ESA).…
In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. This type of drops is a consequence of the breakup processes occurring in thin films when anisotropic contact line…
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…
Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop…
We study the equilibrium shape of a liquid drop resting on top of a liquid surface, i.e., a floating lens. We consider the surface tension forces in non--wetting situations (negative spreading factor), as well as the effects of gravity. We…
Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffusive, as…
Phase field theory is widely used to model multi-phase flows. A drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy. In this paper, the spontaneous behaviour of a drop…
The wetting behavior of drops on natural and industrial surfaces is determined by the advancing and receding contact angles. They are commonly measured by the sessile drop technique, also called goniometry, which doses liquid through a…
We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration…
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…
We study the equilibrium solutions of a sessile drop on top of a horizontal substrate when it is partially covered by another inmiscible liquid, so that part of the drop is in contact with a third fluid (typically, air). The shapes of the…
We simulate the impact of a viscous liquid drop onto a smooth dry solid surface. As in experiments, when ambient air effects are negligible, impact flattens the falling drop without producing a splash. The no-slip boundary condition at the…
Beyond a threshold, electric or magnetic fields cause a dielectric or ferromagnetic fluid drop respectively to develop conical tips. We analyze the appearance of the conical tips and the associated shape transition of the drop using a local…