On the use of Galerkin-Eckhaus method to study the nonlinear regime of Marangoni-Bénard instabilities in an evaporating liquid layer

We investigate theoretically Marangoni-Bénard instability in an evaporating liquid layer surmounted by its vapor and an inert gas. A Galerkin-Eckhaus method, based on a slaving principle and an iterative algorithm, and a direct finite element method are used to determine the evaporation rate above the convective threshold. Both methods provide precise quantitative results, even far from the linear stability threshold.     

Scaling and instability analyses on flame spread over liquids

Stability and scaling analyses were applied to experimental data obtained by this group and other researchers on pulsating flame spread over liquids. Data to be analyzed include recent findings of cyclic appearance of a cold temperature valley at the liquid surface-created surface-wave ahead of the spreading flame, and main-pulsation of 0.5–2 Hz and sub-pulsation of 5–10 Hz. Our stability analysis is performed to understand the mechanism of instability on the liquid surface ahead of a flame’s leading edge, which is thought of as the major cause for pulsating flame spread. The scaling analysis is performed to explore the role of four independent (gravity, surface-tension, viscose, and inertia) forces on the mechanisms of flame spread. These four forces form three independent pi-numbers: Marangoni (Ma) number, Weber (We) number, and Froude (Fr) number, all of which include the critical length scale ratio: (height of sub-surface circulation)/(horizontal length of preheated liquid surface). We combined the wave equation obtained from the stability analysis, the three pi-numbers, and the critical length scale ratio, and used them as a universal formula to describe flame spread over liquids. Using this formula, flame spread mechanism over four different types of alcohols was divided into two separate regimes: the thin liquid pool and the thick-liquid pool. For the thin liquid pool, the flame spread rate was correlated with (Fr/Ma^0.5)^−1.0, while for the thick-liquid pool it was correlated with (Fr/Ma^0.5)^−1.5. Change of flame spread pattern from the uniform to the pulsating can be described with temperature difference between the flash point and bulk liquid temperature. For the thin liquid pool this temperature difference is correlated with Ma^−0.5, while for the thick-liquid pool it is correlated with Ma⁻¹. The frequency of pulsation is correlated with We^−1.0 for the thin liquid pool, while it is correlated with We^−1.5 for the thick-liquid pool.     

Vortices on the Surface of Normal He I Generated by the Rayleigh–Bénard Thermogravitational Convection in the Bulk of a Liquid

JETP Letters - It has been experimentally found that the appearance of the Rayleigh–Bénard thermogravitational convection in the bulk of a normal helium He-I layer heated from above in...     

蒸发液面热对流与温度不连续现象的实验研究

实验研究了存在蒸发界面的水平液层中的热毛细对流对汽/液界面处温度不连续的影响.对于单纯的热毛细对流从理论和实验已有深入研究,但目前国际对蒸发与热毛细对流的耦合尚缺乏研究.特别是近期C.A.Ward等人研究发现了蒸发汽液界面处的温度不连续现象.本文以存在蒸发界面的水平薄液层为研究对象,测量了蒸发界面处的温度分布,研究了普...     

Reversals of large-scale circulation in turbulent convection in rectangular cavities

The behavior of large-scale circulation appearing against the background of Rayleigh-Bénard turbulent convection in rectangular cavities of various geometries (from a thin layer to a cubic cell) has been experimentally investigated. It has been shown that the regimes of large-scale circulation with spontaneous reversals separated by long periods of quasistationary circulation appear both in a limited range of the Rayleigh number and in a limited range of the aspect ratio, which determines the ratio of the thickness of a cell to the side in the circulation plane. A regime without reversals is established in a thick layer, whereas a regime characterized by numerous changes in the direction of circulation, which are not separated by intervals with the stable direction of the large-scale flow, arises in a thin layer. The spectra of oscillations of the amplitude of large-scale circulation have been analyzed. It has been shown that a dominant frequency appears in the spectrum of oscillations of the cubic cell.     

两相流层的Marangoni-Bénard不稳定性分析

关于液层的Marangoni-Bénard不稳定性的研究中,现有文献中普遍采用的是单层流模型。本文建立了一种新的两层流模型,采用线性稳定性方法对带有蒸发界面的两层流的Marangoni-Bénard对流不稳定性进行了分析,得到了在不同蒸发量下临界Marangoni数与波数的关系,重点讨论了蒸发速率对汽液两层流系统Marangoni-Bénard不稳定性的影响。     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

蒸发两层流系统的对流不稳定性分析

关于蒸发液层的Rayleigh-Marangoni-Benard不稳定性的研究中,早期文献中普遍采用的是单层流模型。近年来,一些学者采用两层流模型对蒸发稳定性进行了理论分析,有的文献中没有考虑蒸发率与饱和蒸汽压的耦合关系,所以得到的结果不能完全反应蒸发对系统稳定性的影响。本文建立了一种新的两层流模型,考虑了界面变形对系统稳定性的影响。采用线性稳定性方法对带有蒸发界面的两层流的Rayleigh-Marangoni-Benard对流不稳定性进行了分析,得到了临界 Marangoni数与波数的关系,重点讨论了蒸发系数以及重力对汽液两层流系统的不稳定性的影响。     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

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.     

Heat transport and critical slowing down near the Rayleigh-Bénard instability in cylindrical containers

Measurements of heat transport across layers of liquid He I heated from below show a sharp transition to fluid flow at the gravitationally driven Rayleigh-Bénard instability. The effective thermal conductivity of the convecting fluid is found to be a linear function of the reduced Rayleigh number (R - R_c)/R_c and to have a slope which agrees with calculations. Critical slowing down near R_c is measured and found to be in excellent agreement with theory.     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Oscillation of the convective flow around an air bubble in a vertically stratified surfactant solution

The appearance of oscillatory modes of the concentration convection around an air bubble in an aqueous solution with a vertical gradient of surfactant concentration was revealed experimentally. The solution filled a thin vertical layer containing an air bubble in the form of a short horizontal cylinder with a free lateral surface. Due to a small layer thickness, two-dimensional flows and concentration distributions were generated in the liquid. Their evolution was investigated using an interferometric technique. It was found that the flow oscillation was caused by a specific interaction between the diffusion and two solutal (capillary and gravitational) mechanisms of convective mass transfer, which had quite different characteristic times. The time variation of the oscillation period was analyzed in relation to the surfactant concentration gradient, the average solution concentration, and the concentration Marangoni number. It was shown that the ratio of the dimensionless oscillation frequency to the Marangoni number is time independent and is the same for different liquids and various orientations of the concentration gradient. Published in Russian in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 130, No. 2, pp. 363–370. The text was translated by the authors.     

Influence of the surface deformability and variable viscosity on buoyant - thermocapillary instability in a liquid layer

The primary stationary and oscillatory Bénard-Marangoni instability is investigated in a fluid layer of infinite horizontal extent, bounded below by a rigid plane and above by a deformable upper surface, subjected to a vertical temperature gradient. Since the viscosity is temperature-dependent the consequences of relaxing Oberbeck-Boussinesq approximation and free surface deformability are theoretically examined by means of small disturbance analysis. The problem has been solved numerically by the Taylor series expansion method. The results obtained confirm that when the free surface is undeformable, stationary convection develops in the form of polygonal cells, and oscillatory motion cannot be detected. When the surface deformability is considered, stationary convection sets in, either as a short-wavelength hexagonal instability or as a long-wavelengh mode or as both, and oscillatory convection is also possible. The stability threshold for the short-wavelength mode depends mainly on the viscosity variation while the long-wavelength mode is determined by the surface deformation. Numerically, it is found that the neutral oscillatory Marangoni numbers are only negative. When a variable-viscosity model is used the theoretical and experimental results are in better agreement. Received 15 May 1997     

Convective roll dynamics in liquid 4He near the onset of convection

We present results of experiments on Rayleigh-Bénard convection in liquid 4He at several temperatures. We show visually that with carefully defined boundary conditions the basic convection state consists of parallel rolls which are aligned in one of two directions, the angle thus defined as being temperature dependent and we attempt to explain this behavior. We also show directly the skew-varicose instability acting on the basic state and correlate it with fluctuations in the temperature difference across the fluid layer.     

Interfacial analysis of InP surface preparation using atomic hydrogen cleaning and Si interfacial control layers prior to MgO deposition

The objective of this study is to investigate how the surface characteristics of indium phosphide (InP) can be modified through the use of atomic hydrogen (H^*) cleaning and silicon interfacial control layers (Si ICL), prior to the deposition of MgO dielectric layers. X-ray photoelectron spectroscopy (XPS) analysis shows that the InP native oxide can be successfully removed using atomic hydrogen cleaning at a substrate temperature of 300 °C. However, atomic force microscopy (AFM) images display evidence for the growth of metallic In island features after H^* cleaning, and subsequent deposition of MgO thin films on the H^* cleaned surface resulted in high levels of interfacial indium oxide growth. It has also been shown that the deposition of thin (∼1 nm) Si layers on InP native oxide surfaces results in the transfer of oxygen from the InP substrate to the Si ICL and the formation of Si-InP bonds. XPS analysis indicates that MgO deposition and subsequent 500 °C annealing results in further oxidation of the Si layer. However, no evidence for the re-growth of interfacial In or P oxide species was observed, in contrast to observations on the H^* cleaned surface.     

Large-scale patterns in Rayleigh-Bénard convection

Rayleigh-Bénard convection at large Rayleigh number is characterized by the presence of intense, vertically moving plumes. Both laboratory and numerical experiments reveal that the rising and descending plumes aggregate into separate clusters so as to produce large-scale updrafts and downdrafts. The horizontal scales of the aggregates reported so far have been comparable to the horizontal extent of the containers, but it has not been clear whether that represents a limitation imposed by domain size. In this work, we present numerical simulations of convection at sufficiently large aspect ratio to ascertain whether there is an intrinsic saturation scale for the clustering process when that ratio is large enough. From a series of simulations of Rayleigh-Bénard convection with Rayleigh numbers between 10⁵ and 10⁸ and with aspect ratios up to 12π, we conclude that the clustering process has a finite horizontal saturation scale with at most a weak dependence on Rayleigh number in the range studied.     

Droplet migration: Quantitative comparisons with experiment

An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H^*, of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H^* be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H^* near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H^* and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.     

Interfacial instability in bilayer films due to solvent evaporation

We perform a linear analysis of the Marangoni instability of a deformable interface between two fluid layers of finite depths, submitted to a gradient of solvent concentration induced by evaporation at the top layer, in the presence of convective as well as diffusive solvent transport. We discuss, in turn, the influence on the onset of the instability of the solvent evaporation rate, of the ratios of viscosity and diffusivity, of the rate of convection and of the layer depths. Qualitative comparison with experimental observations of spin-coating processes of solution of two immiscible polymers are then performed, yielding satisfactory agreement.     

Measurement of temperature distribution in thermocapillary instability

Summary We report the measurement of the temperature field inside a fluid layer with a free surface, heated from below, in the unstable regime (thermocapillary instability or Marangoni effect). The measurements have been done when the convective flow was time dependent. We show the evolution of the temperature spatial distribution in the periodic and biperiodic regimes. We also discuss the main differences of the temperature field between Rayleigh-Benard and Marangoni instabilities.

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Riassunto Si riporta la misura del campo di temperatura in uno strato di fluido scaldato dal di sotto e con una superficie libera nel regime instabile (instabilità termocapillare o effetto Marangoni). Le misure sono state effettuate quando il moto convettivo non era stazionario. L’evoluzione della distribuzione spaziale della temperatura è stata seguita nel regime periodico e biperiodico. Si discutono inoltre le prineipali differenze del campo di temperatura fra l’instabilità di Rayleigh-Benard e quella di Marangoni.