Experimental Investigation of Thermocapillary Convection in a Liquid Layer with Evaporating Interface

Thermocapillary convection coupling with the evaporation effect of evaporating liquids is studied experimentally. This study focused on an evaporation liquid layer in a rectangular cavity subjected to a horizontal temperature gradient when the top evaporating surface is open to air, while most previous works only studied pure thermocapillary convection without evaporation. Two liquids with different evaporating rates are used to study the coupling of evaporation and thermocapillary convection, and the interfacial temperature profiles for different temperature gradients are measured. The experimental results indicate evidently the influence of evaporation effect on the thermocapillary convection and interfacial temperature profiles. The steady multicellular flow and the oscillatory multicellular flow in the evaporation liquid layer are observed by using the particle-image-velocimetry method.     

Thermographic investigation of the temperature field dynamics at the liquid-air interface in drops of water solutions drying on a glass substrate

The temperature field distribution at the liquid-air interface in drops of water and water solutions drying on a glass substrate is studied with thermal imaging means. It is shown that irrespective of the liquid composition, the circumferential temperature of the drops (along the boundary line) is always higher than the temperature on the top. The temperature field on the surface of the drops is nonstationary and varies chaotically during water evaporation. It is found that the dynamics of histograms for albumin-containing and albumin-free liquids differ. Mechanisms behind the origination of thermocapillary liquid flows and their directivity in the drying drops are discussed.     

Steady parallel flow in an evaporating fluid heated from sidewalls

Evaporation is ubiquitous in nature, but very few attempts have been made in the past to couple the effects of evaporation with fluid flow behavior. In this theoretical paper we have discussed the effects of evaporation on the dynamics of steady state thermocapillary convection in a two-dimensional rectangular container. The liquid is heated by differentially heated sidewalls and mass loss from the interface due to evaporation is compensated by the liquid entering into the container through a lower inlet, thus keeping the thickness of the liquid layer constant. We show that for an evaporating liquid one can obtain a plane parallel base state profile which depends on the evaporative mass flux.     

On derivation of the analytical expression for damping ratios in a low-viscosity approximation

The damping ratios of waves and oscillations in nonlinear dispersion equations are found for planar, cylindrical, and spherical geometries as applied to finite-volume liquids. For a cylindrical jet and a plane interface between viscous liquids, the damping ratios are determined for the first time. When the radius of curvature of the liquid jet surface decreases, so does the damping ratio of capillary waves. In a system of immiscible liquids, the damping ratio may be both larger and smaller than that for the pure liquid depending on the viscosity of the liquids and the ratio of their densities. This is because the damping ratio depends on the kinematic viscosities of pure liquids. The damping ratio is also estimated for waves arising at the liquidgas interface due to a tangential discontinuity of the velocity field.     

Nonlinear asymptotic calculation of the Kelvin-Helmholtz instability

The problem of periodic capillary-gravitational wave motion on the uniformly charged interface between two ideal immiscible incompressible liquids is solved in the third order of smallness. The lower liquid is assumed to be ideally conducting, while the upper one is a dielectric executing translational motion parallel to the interface with a constant velocity. A nonlinear frequency correction in the resonance form is found. It is shown that the positions of internal nonlinear resonances depend on the sum of the field and Weber parameters, the density ratio of the liquids, and the wave number. When the upper liquid is denser than the lower one, resonances are absent.     

Gravitational and thermocapillary mechanisms of hydrodynamic motions in liquid crystals induced by laser with a spatially periodic intensity structure

A possibility of excitation of hydrodynamic convective motions of the Rayleigh-Benard and Marangoni type in isotropic liquids and nematic liquid crystals upon absorption of light with a spatially periodic intensity distribution is demonstrated theoretically and experimentally. The opportunity of control and the stability of convective motions are studied. Benard cells become unstable when the light intensity is high. These instabilities are of the thermal origin because the Prandtl number for the medium under study is considerably larger than unity. The competition between the gravitational and thermocapillary mechanisms of photohydrodynamic reorientation of nematic liquid crystal director is also studied. The reorientation of the molecules due to the thermocapillary mechanism causes an optical nonlinearity which is three orders of magnitude stronger than the well-known direct orientational optical nonlinearity.     

Low-frequency sound transmission through a gas-liquid interface

Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.     

Accumulation of particles in time-dependent thermocapillary flow in a liquid bridge. Modeling of experiments

The study addresses the phenomenon of accumulation of rigid tracer particles suspended in a time-dependent thermocapillary flow in a liquid bridge. We report the results of the three-dimensional numerical modeling of recent experiments [1,2] in a non-isothermal liquid column. Exact physical properties of both liquids and particles are used for the modeling. Two liquids are investigated: sodium nitrate (NaNO₃) and n-decane (C₁₀H₂₂). The particles are modeled as perfect spheres suspended in already well developed time-dependent thermocapillary flow. The particle dynamics is described by the Maxey-Riley equation. The results of our simulations are in excellent agreement with the experimental observations. For the first time we reproduced numerically formation of the particle accumulation structure (PAS) both under gravity and under weightlessness conditions. Our analysis confirms the experimental observations that the existence of PAS depends on the strength of the flow field, on the ratio between liquid and particle density, and on the particle size.     

Instability of a charged plane interface between two liquids with respect to the tangential discontinuity of a time-dependent velocity field

The differential equation that describes the evolution of perturbations of a charged plane boundary between immiscible liquids when the upper liquid moves relative to the lower one with a time-dependent velocity parallel to the boundary is the Hill equation. In this system, the interface can exhibit instabilities of three types at various values of physical parameters: the Kelvin-Helmholtz, Tonks-Frenkel, and parametric instability. When physical parameters have certain values, the interface that is unstable with respect to surface charge and the tangential discontinuity of the velocity field across the interface can be parametrically stabilized.     

Evaluation of the possibility of using the laser-induced thermocapillary effect for photothermal spectroscopy

A new approach to the photothermal spectroscopy of solids and liquids is proposed on the basis of the thermocapillary effect, which arises when a laser beam excites a layer of liquid several hundreds of millimeters thick lying on a solid surface. The method uses the measurement of the diameter of a thermocapillary response or the counting of the number of fringes of equal thickness observed in the light reflected from a thermocapillary depression. The detectability threshold and the resolution of the method correspond to absorbed optical powers of, respectively, 500 and 100 μW in the first case and 500 and 10 μW in the second case.     

Experimental measurement of variations in the optical reflection coefficient of water-magnetic liquid interface in an electric field,wave motion,and surface instability

A variation in the reflection coefficient of an interface of two liquids (water and magnetic liquid) in the presence of an electric field is experimentally studied. An increase in the reflection coefficient of the interface is demonstrated. A surface instability of the water-magnetic liquid interface, the wave motion at the interface, and wave interference are observed.     

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.     

Modeling of the vaporization front on a heater surface

The boiling-up of a metastable liquid with appearing vaporization fronts is theoretically considered. The boiling-up occurs usually on the surface of a heater. At the initial stage, growth of a spherical vapor bubble is observed. If the temperature of the liquid exceeds a threshold value, the vaporization fronts develop near the line of contact of a vapor bubble and the heater. The vaporization fronts extend along the heater with a constant speed. A model of steady propagation of the vaporization front is developed. The temperature and propagation velocity of the interface are determined from the balance equations of mass, momentum, and energy in the neighborhood of the vaporization front and from the stability condition of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The propagation velocity of the vaporization front also has the threshold value. The calculated velocity of interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid.     

On the structure of waves at the charged interface between two viscous liquids at the solid bottom

The solutions to the equation describing the wave motion in a bilayer system of immiscible liquids are obtained in the first order of the theory of approximations. The hydrodynamic potentials, current functions, generatrix of the shape, and electrostatic potential of the charged interface between two viscous liquids, one of which conducts current and the other being a dielectric, on the solid bottom, are determined. It is shown that in the case when the density of the upper medium is three or more orders of magnitude lower than that of the lower liquid or when the kinematic viscosity of the upper medium is negligibly low as compared to that of the lower medium, the effect of the upper medium on the flow of the liquid in the lower medium is negligibly small. The structure of the wave motion generated by the interface between the two media is analyzed.     

Study of dynamics of thin liquid layer breakdown under conditions of spot heating and formation of a droplet cluster

Breakdown dynamics was studied experimentally for the horizontal layers of various liquids (ethanol, water) with the thickness of 300 μm under the conditions of spot heating from the substrate. The main stages of the process of liquid layer breakdown were determined, and time of dry spot formation was measured. Time of dry spot formation for ethanol at the heat flux of 12.6 W/cm² was 7.85 s, and for water at the heat flux of 117 W/cm², it was 0.13 s. It was found that for both working liquids, a residual layer appears in the region of spot heating before liquid layer breakdown. It is shown that together with the thermocapillary effect, evaporation is one of the main factors affecting dynamics of liquid layer breakdown and dry spot formation.     

On capillary motion of a viscoelastic liquid with a charged free surface

The structure of the capillary-relaxation motion spectrum in a liquid with a charged free surface has been investigated taking into account the viscosity relaxation effect. On the basis of numerical analysis of the dispersion equation for the wave motion in a viscoelastic incompressible liquid, it is shown that for a given wave number the range of characteristic relaxation times in which relaxation-type wave motion exists is limited and expands with increasing wave number. The growth rate of instability of the charged liquid surface markedly depends on the characteristic relaxation time and increases with its growth; in liquids with elastic properties, the energy dissipation rate of capillary motion is enhanced. At a surface charge density that is supercritical for the onset of Tonks-Frenkel instability, both purely gravitational waves and waves of a relaxational nature exist.     

Thermocapillary deformation of a thin locally heated horizontal liquid layer

In this paper, steady thermocapillary flow in a thin horizontal layer of a viscous incompressible liquid with a free surface is considered. An axially symmetric steady problem with a localized thermal action on a horizontal liquid layer with a deformable free surface is solved in a thin-layer approximation. In addition to the thermocapillary effect, the model takes into account the capillary pressure caused by the free surface variable curvature and the convective mechanism of heat transfer in the liquid. Analytical expressions for the velocity vector components as functions of the liquid layer thickness and surface temperature are obtained. The free surface and velocity profiles caused by various kinds of heating are calculated. The influence of convective heat transfer on the flow pattern is analyzed.     

Excitation of oscillations of an immiscible liquid interface by a pulsed ultrasound beam parallel to the interface

For several pairs of immiscible liquids, a new opportunity to excite oscillations of their interface by ultrasound pulses propagating parallel to the interface has been discovered experimentally. A plane ultrasound transducer is placed so that the interface between liquids halves its aperture. The evolution of the shape of the interface oscillations under the variation of the amplitude and duration of excitation pulses, as well as of the distance from the transducer, has been analyzed. The possibility of the excitation of various modes of the interface oscillations in a bounded volume has been revealed.     

Droplet ejection from an interface between two immiscible liquids under pulsed ultrasound

The emphasis of this study is on the ejection of single droplets of a certain size under pulsed ultrasound. Droplet ejection from an interface of two immiscible liquids in this mode, which differs from the well-known ultrasonic fountain (where liquid droplets arise spontaneously), has been experimentally implemented and investigated. The spatial and time evolution of the interface deformation and violation of interface integrity, caused by pulsed acoustic radiation pressure, has been recorded with a high-speed video camera. It is shown that, depending on the ultrasound intensity, three characteristic modes of interface response can be distinguished. In the first (low-intensity)mode, the interface undergoes forced oscillations, without violation of its integrity. In the second (intermediate-intensity) mode, which is in the focus of our study, the interface integrity is violated due to the ejection of a single droplet of a certain size; the latter continuously changes its shape when moving in the second liquid. In the third (high-intensity) mode, the predictable ejection of droplets of a predictable size turns into stochastic ejection of multiple droplets with unpredictable sizes. The dependence of the sizes of single droplets on the parameters of focused ultrasound beam have been measured in the second (stable) mode of ultrasound ejection. Based on these measurements, the range of ultrasound parameters providing controlled generation of single droplets of a specified size is estimated. Differences in the dynamics of interface motion and specific features of droplet generation for the liquid/liquid interface in comparison with the liquid/gas interface are indicated. Possible applications of the observed effects are discussed.     

微重力下液封对液桥内热毛细对流影响的研究

本文建立了具有液封的液桥（不相溶混的双层同轴液柱）内热毛细对流的物理模型和数学模型。采用涡量－流函数法对微重力条件下具有液封的液桥内热毛细对流进行了数值模拟，得到了双层液柱主流区的温度场和流场，证实了液封能够削弱液桥内热毛细对流，从而提高浮区晶体生长质量，并得到液封厚度对液桥内热毛细对流的影响规律。