Two-parametric family of exact solutions for the profile of the surface of a conducting liquid in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid in an external nonuniform electric field are investigated. The liquid is at the tip of a wedge-shaped electrode, and the counter-elecrode is a thin straight conducting filament parallel to the edge of the wedge. The conformal mapping method is used to obtain a two-parametric family of exact solutions for the shape of the surface. The solutions describe the deformation of the surface right to separation of a drop from the electrode.     

Analysis of shape perturbations of a drop on a vibrating substrate for different wetting angles

An exact solution is obtained to the problem of axisymmetric normal modes and natural frequencies characterizing surface perturbations of a drop that sits with an arbitrary wetting angle on a substrate and experiences only gravity and surface tension. The resulting mode solutions are used to calculate and analyze different shapes of the perturbed surface for the same drop placed on a vibrating base. The distinctive feature of the present study is the explicit representation of the results in the form of calculated shapes of the surface of a vibrating drop, comparison of the parameters of actual drops with resonance frequencies, and comparison with experimental data.     

Transfer of smectic films to a solid substrate by the method of Maclennan

We investigate monolayers of 2-alcohols (2-C9 to 2-C16) obtained by placing a drop of pure alcohol at the water surface. These alcohols are chiral molecules and we study the racemic mixtures. By ellipsometry and surface tension measurements we are able to characterize the 2D crystallization-melting transition with temperature. We find a first order transition. Using X-ray under grazing incidence we show that the racemic mixture crystallizes at 2D on a hexagonal cell. We find a parity effect on the lateral pressure at the transition and on the stability of the Bragg peak. We compare all results with those observed for 1-alcohols. Received: 11 April 1997 / Revised: 18 August 1997 / Accepted: 9 October 1997     

Nonstationary periodic spatial waves on the surface of a viscous liquid film falling down a vertical cylinder

The flows of viscous liquid film over the outer surface of a vertical cylinder are examined. Investigation of wave regimes in the case of low flow rates and large cylinder radii is reduced to the analysis of solutions to a nonlinear evolution equation for the film thickness. There are countable numbers of steady-state traveling solution families in the considered model. In turn, most of them are unstable to 2D and 3D perturbations. Thus, evolution of initial perturbations in different ranges of parameter values differs significantly. Some typical scenarios of perturbation development are presented in this work. Initial perturbations with some symmetries, kept in the process of evolution, are of a particular interest. In these cases, solutions are drawn up to the steady-state traveling solutions with similar symmetry.     

表面单分子膜的垂悬液滴方法研究

提出一种扩展或收缩气/液界面单分子层的分子密度，用荧光成像技术检测单分子层的扩展或收缩效果的新方法——垂悬液滴分析方法-此方法通过改变液滴体积，对液滴界面上的表面活性剂分子实施扩展和收缩，具有Langmuir-Blodgett(LB槽)的功能-对表面活性剂荧光分子，用液滴的激光感生荧光图像，可以实时测量液滴界面的相对分子密度变化；用偏振荧光分析技术，可获取荧光偶极矩在液滴界面的相对取向-对罗丹明(B)表面活性剂分子ODRB的实验结果表明：1) 表面单分子层分子密度在压缩过程中遵循σ/σ_{0关键词：}     

Stability of negative ions near the surface of a solid

Stationary states of molecular negative ions (anions) near the surface of a solid are investigated. The lone electron is assumed to interact with a diatomic molecule and the surface of the solid. The energies of electron levels are determined by solving the 2D Schrödinger equation. It is shown that its stable solutions exist at distances from the surface greater than some critical distance, otherwise the electron is detached from the anion. In the case of attraction between the electron and the solid, the interaction potential between the anion and the solid appears to have the Lennard-Jones form and the ion is separated from the surface by some equilibrium distance.     

Step-Wise Concentration Influence of Fullerenes C60 and C70 on the Various Parameters of Condensed Systems

A step-wise changing concept is developed of the influence of fullerenes C₆₀and C₇₀ on various properties of condensed systems, liquid, and solid. In this, Part I is considered the step-wise character for three parameters: (1) the density of solutions; (2) the boiling points of solutions, and (3) the coefficient of the surface tension of solutions. The sharp drop of the density of solutions at very small fullerene concentrations is pointed out and considered. A step change in the coefficients of the surface tension of fullerene solutions with concentration were determined and are discussed. In Part II, to follow, the influence of fullerene concentrations on the freezing and melting of solutions will be considered.     

Statistical equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.     

A level-set continuum method for two-phase flows with insoluble surfactant

A level-set continuum surface force method is presented to compute two-phase flows with insoluble surfactant. Our method recasts the Navier–Stokes equations for a two-phase flow with insoluble surfactant as “one-fluid” formulation. Interfacial transport and interfacial jump conditions are treated using the level-set method and the discrete Dirac function. Based on the density-weighted projection method, a stable semi-implicit scheme is used to decouple the velocity components in solving the regularized Navier–Stokes equations. It allows numerical simulations for a wide range of viscosity ratios and density ratios.Numerical simulations on single drop deformation in a 2D shear flow are presented. Simulations on two drop interaction shows that surfactants can play a critical role in preventing drop coalescence. A fully 3D simulation demonstrating the physical interactions of multiple surfactant-laden drops is presented.     

Relaxation auto-oscillations in a fluidized bed

Oscillations of nonuniform fluidized bed in the slugging regime are considered. A nonlinear one-dimensional model of bed oscillations is developed and investigated, including the equations of the bed surface motion and the oscillations of the pressure drop in the bed for the phase of the surface ascent and for the phase of its fall. A quasi-discrete process of the gas escape from the layer with large bubble and the relaxation (discontinuous) type of oscillations of the bed surface and of the pressure, which are related to the above process, are shown based on the model analysis, the obtained numerical solutions, and the comparison with experiment.     

Limiting phenomena for the spreading of water on polymer films by electrowetting

This paper is about fundamental limitations in electrowetting, used as a tool for spreading water solutions on hydrophobic surfaces, like the surface of a polymer film. Up to which point can an electric voltage decrease the contact angle? The first limitation comes when using pure water, above a threshold voltage, little droplets are emitted at the perimeter of the mother drop. We present an analysis of the drop contour line stability, involving competition between electrostatic and capillary forces, which is compatible with observations. The use of salted water solutions suppresses this instability, then one faces a second limitation: the evolution of the contact angle saturates before complete wetting. We show that this saturation is caused by ionisation of the air in the vicinity of the drop edge. We analyse the luminescence induced by gas ionization and measure the related electrical discharges. We explain how air ionization suppresses the driving force for electrowetting and how it induces the formation of an hydrophillic ring around the drop.     

On the oscillations of a charged drop of a finite-conductivity viscous liquid

A dispersion relation for the capillary oscillations of a charged spherical drop of a viscous incompressible finite-conductivity liquid is derived and analyzed. It is found that electric currents inside the charged drop equalize its potential and produce liquid flows interacting with both potential and eddy poloidal liquid flows inside the drop that are due to drop oscillations. Taking into account the finiteness of the rate of potential equalization over the drop surface leads to an additional damping of the capillary oscillations that arises because of the increased role of energy dissipation.     

The wetting angle of very small and large drops

On the basis of Born-Green-Yvon integral equations for the density distribution functions, an approximate integral equation is established for the profile of the surface of the drop. Numerical solutions and analytical solutions for limiting cases are obtained for this profile. Equations relating the angle at the leading edge and in its vicinity to parameters characterizing the interaction forces between the molecules of the liquid and between those of the liquid and solid are derived for large and for very small drops on a horizontal solid surface. One concludes that there is a rapid spatial variation of shape near the leading edge, that for large drops the measured macroscopic wetting angle is reached at a distance of about 20 to 40 Å from the leading edge, and that for very small drops the wetting angle is weakly size dependent. A condition for drop stability is established, which if not satisfied, the liquid will spread over the surface of the solid.     

A kinetic approach to the calculation of surface tension of a spherical drop

In literature, surface tension has been investigated mainly from a Thermodynamics standpoint, more rarely with kinetic methods. In the present work, surface tension of drops is studied in the framework of kinetic theory, starting from the Sutherland approximation to Van Der Waals interaction between molecules. Surface tension is calculated as a function of drop radius: it is found that it approaches swiftly an asymptotic value, for radii of several times the distance of minimum approach D of the Sutherland potential. This theoretical asymptotic value is compared to experimental values of surface tension in plane surfaces of a few liquids, and is found in reasonable agreement.     

Exact solutions of the equations of motion of liquid helium with a charged free surface

The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and its magnitude is much larger than the instability threshold, the asymptotic behavior of the system can be described by the well-known 3D Laplacian growth equations. The integrability of these equations in 2D geometry makes it possible to describe the evolution of the surface up to the formation of singularities, viz., cuspidal point at which the electric field strength, the velocity of the liquid, and the curvature of its surface assume infinitely large values. The exact solutions obtained for the problem of the electrocapillary wave profile at the boundary of liquid helium indicate the tendency to a change in the surface topology as a result of formation of charged bubbles.     

Surface tension effects in the zero gravity inflow of a drop into a fluid

As a drop of fluid is deposited on the surface of a miscible fluid (that we call the solvent), it undergoes a strong pulling due to its surface rupture and it acquires a kinetic energy independently of gravity. For the drop and the solvent being of the same fluid we observe a drop injection at an initial velocity which scales as the square root of the surface tension of the drop against air. Once injected, the drop develops a transverse instability giving rise to an expanding ring. Viscosity terminates the process and stops the ring. We show that the final ring height follows a scaling law whereas two asymptotical scaling regimes can be identified for the ring radius. Received 31 August 1999     

Sound generation as a drop falls on a water surface

Impact of a drop on a water surface is accompanied by a series of sound pulses propagating in air and underwater. Depending on the falling mode (drop size and initial velocity), pulses substantially differ in amplitude, duration, and modulation frequency. We study falling modes in which in addition to conventional sound packets—the shock pulse and single resonance sound packets—several packets are observed. Experiments were conducted with simultaneous recording of sound in air and underwater and were accompanied by synchronous video depiction of currents in the drop impact region. Comparison of videograms and phonograms demonstrate that the sources of sound packets are gas cavities of arbitrary shape detached from the underwater cavern under the action of large accelerations (several km/s²) during a sharp change in its surface area, which gradually achieve equilibrial elliptical and spherical shapes.     

On nonlinear corrections to the frequencies of oscillations of a charged drop in an external incompressible medium

Analytical expressions are derived for the shape generatrix of an ideally conducting drop immersed in an incompressible dielectric medium as well as for nonlinear corrections to the frequencies of the oscillations of the drop. The solutions are obtained in an approximation of the third order of smallness with respect to the amplitude of the initial deformation of the equilibrium spherical shape of the drop. It is shown that the presence of the ambient liquid results in a reduction of the absolute magnitudes of corrections both to the oscillation frequencies and the self-charge critical for the development of instability of the drop.     

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.