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Hong S.H.,Pohang University of Science and Technology | Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Hwang H.J.,Pohang University of Science and Technology
Journal of Fluid Mechanics

We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick-slip motion. © 2016 Cambridge University Press. Source

Eggers J.,University of Bristol | Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Josserand C.,CNRS Jean Le Rond dAlembert Institute | Zaleski S.,CNRS Jean Le Rond dAlembert Institute
Physics of Fluids

We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier-Stokes equation. © 2010 American Institute of Physics. Source

Fontelos M.A.,Institute Ciencias Matematicas ICMAT | De La Hoz F.,University of the Basque Country
Journal of Fluid Mechanics

We describe, by means of asymptotic methods and direct numerical simulation, the structure of singularities developing at the interface between two perfect, inviscid and irrotational fluids of different densities 1 and 2 and under the action of gravity. When the lighter fluid is on top of the heavier fluid, one encounters the water-wave problem for fluids of different densities. In the limit when the density of the lighter fluid is zero, one encounters the classical water-wave problem. Analogously, when the heavier fluid is on top of the lighter fluid, one encounters the Rayleigh-Taylor problem for fluids of different densities, with this being the case when one of the densities is zero for the classical Rayleigh-Taylor problem. We will show that both water-wave and Rayleigh-Taylor problems develop singularities of the Moore-type (singularities in the curvature) when both fluid densities are non-zero. For the classical water-wave problem, we propose and provide evidence of the development of a singularity in the form of a logarithmic spiral, and for the classical Rayleigh-Taylor problem no singularities were found. The regularizing effects of surface tension are also discussed, and estimates of the size and wavelength of the capillary waves, bubbles or blobs that are produced are provided. © 2010 Cambridge University Press. Source

Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Grun G.,Friedrich - Alexander - University, Erlangen - Nuremberg
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

We prove regularity results and, as a consequence, uniqueness for a system of partial differential equations arising in the study of dynamic electrowetting phenomena and more general electrokinetic processes in three space dimensions. The system consists of Stokes equations coupled with equations for the motion of electric charges, Poisson equation for computing the electric field generated by such charges and a Cahn-Hilliard equation for a phase field describing two fluids with different material parameters. The deduction and existence of weak solutions for this system was established in an earlier paper (Christof Eck et al., On a phase-field model for electrowetting, Interfaces Free Bound. 11 (2), 259-290, (2009)). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source

Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Kindelan U.,Technical University of Madrid
IOP Conference Series: Materials Science and Engineering

In this work we study the static shape of charged drops of a conducting fluid placed over a solid substrate, surrounded by a gas, and in absence of gravitational forces. The problem can be posed, since Gauss, in a variational setting consisting of obtaining the configurations of a given mass of fluid that minimize (or in general make extremal) a certain energy involving the areas of the solid-liquid interface and of the liquid-gas interface, as well as the electric capacity of the drop. In [6] we have found, as a function of two parameters, Young's angle θYand the potential at the drop's surface V0, the axisymmetric minimizers of the energy. In the same article we have also described their shape and showed the existence of symmetry-breaking bifurcations such that, for given values of θYand V0, configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We have proved the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. In this work we study all other cases numerically. When dealing with radially perturbed equilibrium shapes we lose the axially symmetric properties and need to do a full three-dimensional approximation in order to compute area and capacity and hence the energy. We use a boundary element method that we have already implemented in [3] to compute the surface charge density. From the surface charge density we can obtain the capacity of the body. One conclusion of this study is that axisymmetric drops cannot spread indefinitely by introducing sufficient amount of electric charges, but can reach only a limiting (saturation) size, after which the axial symmetry would be lost and finger-like shapes energetically preferred. © 2010 IOP Publishing Ltd. Source

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