Article

The shape of charged drops over a solid surface and symmetry-breaking instabilities

SIAM Journal on Applied Mathematics (Impact Factor: 1.41). 01/2008; 69(1). DOI: 10.1137/080713707
Source: DBLP

ABSTRACT 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 question can be formulated as a variational problem where 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, has to be minimized. As a function of two parameters, Young’s angle µY and the potential at the drop’s surface V0, we find the axisymmetric minimizers of the energy and describe their shape. We also discuss the existence of symmetry-breaking bifurcations such that, for given values of µY and V0, configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We prove the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. All other cases are studied numerically with a boundary integral method. 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.

0 Followers
 · 
86 Views
  • Source
    • "In this paper we shall describe the numerical method we have used in [6] to determine for what values of V 0 such instabilities do develop as a function of θ Y . "
    [Show abstract] [Hide abstract]
    ABSTRACT: 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 θY and 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 θY and 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.
    IOP Conference Series Materials Science and Engineering 07/2010; 10(1). DOI:10.1088/1757-899X/10/1/012241
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating ``wet'' regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.
    Review of Modern Physics 05/2009; 81(2):739-805. DOI:10.1103/RevModPhys.81.739 · 42.86 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Drops of a conducting fluid in electrowetting devices tend to spread when a difference of potential V 0 is set between the drop and an electrode external to it. The classical Lippmann theory predicts unlimited spreading, with a decrease of the contact angle between drop and solid substrate, as one increases V 0 . This fact is in contradiction with current experiments, where saturation of the contact angle to a limiting value is found. A further increase of V 0 does not lead to further spreading but to the appearance of instabilities in the form of emitted drops at the contact line. We provide an explanation to these two related phenomena based solely on interfacial and electrostatic energies. A local analysis close to the contact line is also provided and an expression for the most unstable mode is deduced.
    The Quarterly Journal of Mechanics and Applied Mathematics 10/2009; 62(4). DOI:10.1093/qjmam/hbp016 · 0.57 Impact Factor
Show more

Preview

Download
0 Downloads
Available from