Planar Liquid Layer Research Articles

Stability analysis of wall‐attached Bénard–Marangoni convection in a vertical magnetic field

AbstractThe threshold for the onset of thermocapillary flow in a planar liquid layer heated from below is increased by a vertical magnetic field when the liquid is a good electric conductor. The magnetic damping effect is reduced when the induced eddy currents are blocked by insulating side walls. Neutral conditions for this specific Bénard–Marangoni stability problem with a vertical field and side walls are obtained numerically for three‐dimensional perturbations assumed periodic in one horizontal direction. The domain is bounded by a free‐slip wall at the bottom, a free surface at the top and two free‐slip lateral walls in the other horizontal direction. Buoyancy forces and surface deformations are neglected and a constant heat flux is imposed on the free surface. Upon increasing the magnetic induction, the least stable modes become localized near the side walls and the convective threshold increases at a lower rate than for the least stable bulk mode.

The Effects of Small Contaminants on the Formation of Structures during Rayleigh–Bénard–Marangoni Convection in a Planar Liquid Layer

It is shown that convective structures that form upon heating a planar liquid layer from below are determined not only by standard similarity parameters, such as the Prandtl, Rayleigh, and Marangoni numbers, but also by the presence or absence of an elastic film on the surface of the liquid, which occurs because of impurities and stabilizes the surface. The level of impurities contained in distilled water is enough to prevent Marangoni convection, and only additional purification (deionization) of water allows one to induce the thermocapillary effect. Using the method of infrared surface thermography, the mean size of thermal structures that emerge on the surface in different liquids at different temperatures and layer thicknesses is determined. A convection theory that takes the impurities in the linear and nonlinear approximations into account is examined and good compliance of the theoretical calculations with the experimental data obtained in the present work is demonstrated.

Stability of Advective Flow in an Inclined Plane Liquid Layer Bounded by Solid Planes with a Longitudinal Temperature Gradient. 2. Stable Stratification

Stability of Advective Flow in an Inclined Plane Liquid Layer Bounded by Solid Planes with a Longitudinal Temperature Gradient. 2. Stable Stratification

Waves on the surface of a boiling liquid at various medium stratifications

The stability of relatively small perturbations of the stationary state consisting of a plane liquid layer and a vapor film is studied when no liquid evaporation or vapor condensation occurs in the stationary state. In this case, heat from a hot to cold wall is removed through a vapor–liquid layer via heat conduction. The boundary conditions that take into account liquid evaporation (appearance of a mass flux) at the vapor–liquid phase surface and the temperature dependence of the saturation pressure are derived. Dispersion equations are obtained. The wave processes for the stable (light vapor under a liquid layer) and unstable stratifications of the phases at rest and during their relative motion are studied. The deformation of the phase boundary results in liquid evaporation, changes in the boiling temperature and the saturation pressure, and generation of weakly damped low-amplitude waves of a new type. These waves ensure the stability of a vapor film under a liquid layer at rest or a liquid layer moving at a constant velocity in the gravity field. The velocities of these waves are much higher than the gravity wave velocities. The critical heat flows and wavelengths at which wave boiling regimes at normal pressure can exist are determined, and the calculated and experimental data are compared.

Interfacial Temperature Discontinuities in a Thin Liquid Layer during Evaporation

Recent measurements of the temperature profiles across the liquid-vapor interface of a steady evaporating liquid were performed in a thin planar liquid layer subjected to externally imposed horizontal temperature differences when the interface was open to air. Temperature discontinuities have been found to exist at the interface with an growing tendency as the imposed horizontal temperature difference increasing. Under the co-influence of thermocapillary convection and evaporation effect, a thin layer of 0.5 mm thick with approximate uniform temperature was found just below the liquid-vapor interface. Repeated experiments and further comparisons of the interfacial temperature profiles for different spatial positions along the streamwise center line and varying depths of the liquid layer were also carried out. And the temperature discontinuity was found related to the temperature in liquid phase, which was strongly influenced by the coupling of thermocapillary convection and evaporation effect.

Hydrodynamic interactions of evaporating droplet with plane liquid surface

The hydrodynamic interactions between freely evaporating or growing droplet suspended in gas and the infinite plane liquid layer is theoretically studied with allowance for effects that are linear with respect to the Knudsen number. It is assumed that substances comprising droplet and liquid layer are identical, and it is taken into account that these substances can contain dissolved nonvolatile component whose concentration is so low that its presence should necessarily be accounted for only in the calculation of the concentration of saturated vapor. Vapor pressure at large distance from the droplet was assumed to be equal to the pressure of saturated vapor above the plane liquid surface. Results of numerical calculations of the rate of steady motion of water droplet evaporating or growing in the air are reported.

Transient Rayleigh–Bénard–Marangoni convection due to evaporation: a linear non-normal stability analysis

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wavenumber and time. The method is applied to transient Rayleigh–Bénard–Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.

Experimental Study on the Combined Evaporation Effect and Thermocapillary Convection in a Thin Liquid Layer

The coupling mechanisms and flow characteristics of thermocapillary convection in a thin liquid layer with evaporating interface were studied. The planar liquid layer, with the upper surface open to air, was imposed externally horizontal temperature differences. The measured average evaporating rates and interfacial temperature profiles indicated the relative importance of evaporation effect and thermocapillary convection under different temperature gradients. A temperature jump was found at the interface, which was thought to be related to the influence of evaporation effect. All above mentioned results were repeated in a rarely evaporating liquid to compare the influence of evaporation effect.

Thermocapillary convection in a plane liquid layer with concentration heat sources

Thermocapillary instability of a plane liquid binary-mixture layer with time-dependent surface tension is studied under weightlessness conditions. The liquid is heated (or cooled) due to heat release by an active admixture. The heat release rate is proportional to the active-component concentration. The admixture is transported by convection and diffusion. The active component “burns up” with time. The neutral curves for monotonous and oscillating disturbances are found for different values of the nondimensional parameters. Some nonlinear convection regimes are studied numerically by a finite-difference method. The dependence of the convective flow intensity on the Marangoni number is determined. The phase portraits of unsteady regimes are found.

CHAOTIC ELECTROCONVECTION IN A LAYER OF DIELECTRIC LIQUID SUBJECTED TO UNIPOLAR INJECTION: MAXIMAL LYAPUNOV EXPONENTS

This paper reviews the studies that have been carried out over the years to analyze the electroconvection of an insulating plane liquid layer subjected to unipolar charge injection from one of the electrodes. We consider in detail the motion near the onset of nonlinear instability that for brevity we call chaotic electroconvection. We also present some recent advances in the characterization of this chaotic motion. In particular, we have computed the maximal Lyapunov exponents for time series obtained from numerical simulation, for weak as well as strong injection regimes, and we discuss the relevance of these results for the characterization of this EHD chaos.

Gas bubble pulsation in a semiconfined space subjected to ultrasound.

In the case of ultrasound application in biological tissues, gas bubbles might form and collapse within cells, in the intercellular spaces and on tissue surfaces. In this work the effect of confined space on the behavior of the gas bubble in the presence of ultrasonic field is studied. A numerical model for bubble pulsation in a planar liquid layer, bounded by two rigid walls, is developed. Surface tension at the interface between the host liquid and the gas in the bubble is considered as well. A mathematical statement and solution technique based on the boundary integral method are presented. In some cases, the bubble divides into two symmetrical parts and high-velocity jets are generated, aimed at the walls. The final velocity of the jets strongly depends on the surface tension of the host liquid. Two new parameters that predict the occurrence of jet formation are developed.

Thermocapillary instability of a liquid layer with allowance for the soret effect

The effect of thermodiffusion on the onset of thermocapillary instability in the presence of a surfactant is investigated with reference to a plane liquid layer. It is shown that taking the Soret effect into account leads to destabilization in the case of heating of both the rigid surface and the free boundary.

Two-dimensional modeling of pulsed-laser irradiated a-Si and other materials.

A previously developed one-dimensional (1D) computational model for heat flow and nonequilibrium phase change phenomena induced by pulsed-laser irradiation has been extended to two dimensions. The 2D modeling focuses attention on the heat flow from localized sources embedded in an otherwise planar matrix. For example, nucleation events occurring in undercooled liquids such as molten Si formed by pulsed-laser melting of amorphous Si (a-Si) and inhomogeneous absorption due to randomly occurring defects in targets used for pulsed-laser ablation can be treated. Concepts introduced in the 1D modeling, such as the state diagram and the state array, have been extended to 2D and refined. As an example of the calculations that are now possible, the laser-induced formation and propagation of buried liquid layers are followed in two dimensions for the case of a-Si on a crystalline silicon substrate. It is demonstrated how solid phase growth, though originating from individual nucleation sites, gives rise to a nearly planar liquid layer propagating through the a-Si. Two other examples briefly address questions related to the early stages of the laser ablation of insulators such as MgO, where it is believed that the absorption of the laser radiation occurs at localized but extended regions of high defect concentrations, and to particulate ejection during laser ablation of many materials. \textcopyright{} 1996 The American Physical Society.

Marangoni flow regimes in liquid metals

Marangoni flows in liquid metals are studied in two complementary ways: 1. 1. An order of magnitude analysis of the flow regimes is performed on the basis of the concepts of the boundary layer theory, as previously performed for the case of buoyancy driven flows in Bridgman solidification. This analysis is applied to the case of a planar liquid layer under 1 g conditions. Particularly, the parameter range (layer thickness d and thermal gradient G) under which pure Marangoni flows can be observed at 1 g is thus determined. 2. 2. An experimental method is developed to measure the velocities of inert particles at the surface of thin liquid metal layers at 1 g. Experimental results for liquid tin with 0.3 < H < 4 mm and 5 < G < 40 K/cm are reported, and their consistency with the predicted scaling laws is discussed.

Instability of a planar liquid layer in an alternating longitudinal magnetic field with non-zero mean

The conducting liquid interface is found to undulate in an alternating magnetic field. It was shown earlier that ifM =B 0 2/μηω, B0, ω, μ andη being the amplitude (complex) of the alternating longitudinal magnetic field imposed at the interface, the angular frequency of the field, the magnetic permeability and the viscosity respectively, and ifM c was the critical value ofM then the planar layer was stable or unstable according asM < M c orM > M c. In this paper we have determined the stability criterion when in addition to the alternating longitudinal field there acts a uniform field in the same direction. After comparing our results with those obtained earlier, in the absence of the uniform field, we find that the additional uniform field has a significant destabilizing effect.

Instability of a planar liquid layer in a magnetic field with alternating longitudinal and uniform transverse components

In many cases of levitation, melting of metals and shaping of the liquid metal interface to form certain materials like glass, the interface is found to undulate in an alternating magnetic field. As undulations have undesirable effects, it is of considerable importance to study the stability of the liquid under similar circumstances. Earlier, investigations had been made to determine the stability criterion of a planar conducting liquid layer in an alternating longitudinal field and the critical value of the parameter M = B 0 2 μηω ( B 0, ω, μ and η are the amplitude of the alternating field, the angular frequency of the field, the magnetic permeability and the viscosity, respectively) was determined. It was shown that if M c was the critical value of M then the layer was stable or unstable according as M < or > M c . Since there is some possibility of additional magnetic fields such as the geomagnetic field or any other stray field to act along with the alternating field and affect the stability, we have investigated in this note the stability of a planar liquid layer in the presence of a uniform transverse field acting along with the alternating longitudinal field. The layer has been considered as thick with a perfectly conducting rigid boundary. After comparing with the earlier results we find that the critical value M c minimized with respect to the wave number decreases from the approximate value of 425 to an approximate value 80 even when B 1 is as small as 10 −4, where B 1 is the ratio of the strength of the uniform transverse field to the amplitude of the alternating field. It is also found that M c decreases further as B 1 increases and for B 1 = 10 there is no stability.

Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to surface-wave instabilities that couple the interfacial deflection to the underlying shear flow. These instabilities are found to be directly related to the two-dimensional waves on an isothermal layer subject to wind shear as described by Miles and by Smith &amp; Davis. Hence the surface-tension gradients are important only in that they drive the basic shear flow. The surface-wave stability characteristics for liquid layers with and without return-flow profiles are presented, and special attention is paid to long-wave instabilities. Comparisons are made with available experimental observations.

Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.

Instability of a planar liquid layer in an alternating magnetic field

Instability of a planar liquid layer in an alternating magnetic field

Heat Flow and Convection Demonstration Experiments Aboard Apollo 14

A group of experiments was conducted by Apollo 14 astronaut Stuart A. Roosa during the lunar flyback on 7 Fehruary 1971 to obtain information on heat flow and convection in gases and liquids in an environment of less than 10-(6)g gravity. Flow observations and thermal data have shown that: (i) there are, as expected, convective motions caused by surface tension gradients in a plane liquid layer with a free upper surface; (ii) heat flow in enclosed liquids and gases occurs mainly by diffusive heat conduction; and (iii) some convective processes, whose characteristics are not fully known, add to the heat transfer.