Related papers: Equilibrium solutions of a sessile drop partially …
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.
The contact angle of a liquid drop on a rigid surface is determined by the classical theory of Young-Laplace. For chemically homogeneous surfaces, this angle is a constant. We study the minimal-energy configurations of liquid drops on rough…
Deformed droplets are ubiquitous in various industrial applications, such as inkjet printing, lab-on-a-chip devices, and spray cooling, and can fundamentally affect the involved applications both favorably and unfavorably. Here, we employ…
Second order perturbation solutions of profiles of bubbles suspended in liquid and liquid gas interfaces when liquid all sinks in the bottom under different accelerations are derived. Six procedures are developed based on these solutions,…
We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. Thereby, the drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow…
In the present study, the axisymmetric natural oscillations of a liquid drop supported by a flat surface is investigated by direct numerical simulation. The liquid-gas interface is captured using a geometric volume-of-fluid (VOF) method. A…
Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque…
The rich structures arising from the impingement dynamics of water drops onto solid substrates at high velocities are investigated numerically. Current methodologies in the aircraft industry estimating water collection on aircraft surfaces…
We examine the classical problem of the height of a static liquid interface that forms on the outside of a solid vertical cylinder in an unbounded stagnant pool exposed to air. Gravitational and surface tension effects compete to affect the…
We consider a coexistence of two axisymmetric liquid bridges LB_i and LB_m of two immiscible liquids i and m which are immersed in a third liquid (or gas) e and trapped between two smooth solid bodies with axisymmetric surfaces S_1,S_2 and…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…
We investigate the collision of a continuous liquid jet with a regular stream of immiscible droplets. The immiscible liquids, namely silicon oil for the continuous jet and an aqueous glycerol solution for the drop stream, are selected to…
We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi:…
This paper analyzes the configurations of shapes that shows a spacelike liquid drop in Minkowski space deposited over a spacelike plane $\Pi$. We assume the presence of a uniform gravity field directed toward $\Pi$ and that the volume of…
An analytical description of the interface motion of a collapsing nanometer-sized spherical cavity in water is presented by a modification of the Rayleigh-Plesset equation in conjunction with explicit solvent molecular dynamics simulations.…
The morphological paths towards equilibrium droplets during the late stages of the dewetting process of a liquid film from a liquid substrate is investigated experimentally and theoretically. As liquids, short chained polystyrene (PS) and…
We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which…
The shape of drop on a flat horizontal plane is obtained by including the first order of correction by the weight. The sphere solution of the weightless drop is used to introduce a new polar coordinate by which the perturbative expression…
The theory of solute transfer and deposit growth in evaporating sessile drops on a plane substrate is presented. The main ideas and the principal equations are formulated. The problem is solved analytically for two important geometries:…