Showing papers on "Marangoni effect published in 1986"
Abstract: The stability of thin fibs to long-wavelength, albeit finite-amplitude, initial perturbations is investigated analytically. In contrast to the linear stability analysis for the infinitesimal disturbances, the hydrodynamicand the intermolecular interaction nonlinearities cannot be ignored in such an event. The key idea of the proposed formalism is to determine the stability of a spatially nonhomogeneous stationary solution of the governing equations. It is in the limit of vanishingly small amplitudes that the general stationary solution reduces to the trivial solution (undisturbed, planar interface), and thus the results of the linear stability analysis are recovered. The overall objective of the study is to determine the conditions for the instability, the dominant wavelength of the disturbances, and the time of rupture of the thin films, all as functions of thin-film parameters and the amplitude of the initial disturbances. This set of information is important in the design of flotation, foam, and emulsion systems as well as in the design of thin-film heat-transfer equipment. The analytical results are derived both for a free film with soluble surfactants and for a wetting film (film in contact with a solid) with surfactants present in both the film and the bounding fluid phase. In the case of a wetting film, the effects of the difference in the densities of the film and the bounding fluid (the cause of the Rayleigh-Taylor instability) are shown to be important. For most cases of practical interest, the nonlinear theory predicts a significantly faster rate of thinning and a shorter dominant wavelength compared to the linear theory, because it predicts a greater destabilization due to the van der Waals interaction and a lesser stabilizing influence of the surface tension restoring force. It is deduced that the stabilizing influences of the Marangoni motion (surface elasticity) and the surface viscosity are over- and underestimated by the linear theory in the case of the free and the wetting films, respectively.
75 citations
TL;DR: In this article, a two-dimensional free boundary arising from the steady thermo-capillary flow in a viscous incompressible fluid is studied numerically in the context of the open-boat crystal-growth technique.
Abstract: In this paper a two-dimensional free boundary arising from the steady thermo-capillary flow in a viscous incompressible fluid is studied numerically. The problem is considered in the context of the open-boat crystal-growth technique. The motion of the fluid is governed by the Navier-Stokes equations coupled with the heat equation. The problem is solved numerically by a finite-element-method discretization. Three iterative methods are introduced for the computation of the free boundary. The non-dimensional form of the problem gives rise to the following characteristic parameters: Reynolds, Grashof, Prandtl, Marangoni, Bond, Ohnesorge, Biot numbers. The influence of these parameters on the flow field, the temperature distribution and the shape of the free boundary is studied.
68 citations
TL;DR: In this paper, the authors show that if the temperature and concentration distributions make opposing contributions to the overall surface tension gradient at a free surface, convective motion, as well as heat and mass transfer within the system, is shown to depend on double-diffusive effects.
Abstract: Marangoni convection is important in a variety of physical systems and occurs as a result of surface tension gradients at a liquid free surface. In general, liquid surface tension varies with temperature and species concentration in a binary fluid. If the temperature and concentration distributions make opposing contributions to the overall surface tension gradient at a free surface, convective motion, as well as heat and mass transfer within the system, is shown to depend on double‐diffusive effects. This situation is analogous to double‐diffusive natural convection, in that convection may occur, even though the overall surface tension difference along the free surface suggests stagnant fluid conditions.
59 citations
TL;DR: A phosphorus-doped silicon crystal has been recrystallized under microgravity (μg) by float-zoning aboard a sounding rocket at a rate of 5 mm/min this paper.
50 citations
TL;DR: In this paper, the dissipative layers, called Marangoni boundary layers, that can be formed along the interface of two immiscible fluids, in surface driven flows are studied under the hypothesis that the flow fields of the two interfacing fluids are uncoupled.
Abstract: The paper deals with the dissipative layers, called Marangoni boundary layers, that can be formed, along the interface of two immiscible fluids, in surface driven flows. Under the hypothesis that the flow fields of the two interfacing fluids are uncoupled, similar solutions are studied for the case in which an external pressure gradient is present. The similarity class is derived and the pertinent equations are solved numerically by mean of an algorithm based on a Quasi-Linearization Technique.
39 citations
TL;DR: In this paper, a two-dimensional (2D) model of the Marangoni effect in a one-liquid floating zone is presented, where a concave and a convex cold disk were designed and realized for the DI mission together with two hot disks.
Abstract: T he experiment on Marangoni flows was designed to continue the investigation performed during the first Spacelab mission (SL1), namely to study surface-driven convection phenomena under microgravity conditions to exploit the unique environment offered by space laboratories. In fact, on earth free convection is mostly caused by buoyancy forces that generally "mask" all the others, while in space such forces may not be the governing ones and free convective flows may be induced by other forces. In the case of liquid systems presenting fluid-fluid interface, one of these forces is the surface tension gradient and the corresponding convective flow is the well-known Marangoni effect. The scientific objectives of the D1 experiment include the qualitative and quantitative extension of the studies related to the SL1 and the investigation of new phenomenologies essentially concerned with the formation of a two-liquid floating zone. Once the SL1 experiment was performed, together with other experiments, both under microgravity conditions (on board sounding rocket and airplane) and on ground (at the Microgravity Laboratory of the Institute Umberto Nobile), the objectives of the DI experiment were defined; they can be summarized as follows: Study of thermal Marangoni flows in a one-liquid floating zone. Study of thermal and/or solutal Marangoni flows in a two-liquid floating zone. For each of the previous cases, analysis of the effects of some parameters, such as geometry of the supporting disks, imposed temperature differences, heating modalities, shape of the liquid-gas interfaces and breaking and reforming of the liquid bridge, was performed. With respect to the first objective, the D1 experiment was intended to increase the ranges of the values of the relevant parameters with respect to the SLI experiment; such increases can be obtained, for example, in the case of the conditional Peclet number Peu, by forming liquid bridges with different volumes, aspect ratios (length divided by diameter of the supporting disk) and shapes, or by temperature differences and/or disk rotational velocities. According to the third objective, it was intended to analyze the effects of parameters (new with respect to the SLI experiment and never considered before), such as the shape of the supporting disks and the heat flux distribution over the heating disk. In particular, a concave and a convex cold disk were designed and realized for the DI mission together with two hot disks characterized, respectively, by a radial and an azimuthal distribution of temperature (however, time limitation allowed the use in space of only the concave and the radially heated disks). The reason for such boundary conditions was the need to better simulate the real configuration of the molten zone during a typical floating zone process. With respect to the two-liquid floating zone, the experiment was intended to analyze the effects of the presence of a liquid-liquid interface. The relevance of such a configuration comes from the possibility of studying many interesting fluid phenomena: from the dynamics of different surface phases to the dynamics of three-phase confluent lines, to the solutal Marangoni effects, to mass diffusion and its interaction with the Marangoni effect as in miscible liquids.
35 citations
TL;DR: In this article, the steady surface tension-driven flow (Marangoni convection) under gravity in an axisymmetric, non-cylindrical floating zone is numerically studied for two melts with different Prandtl numbers: a Si melt and NaNO3 melt.
32 citations
TL;DR: In this paper, 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.
32 citations
TL;DR: In this article, the surface tension at a liquid/gas interface is decreasing with temperature and the influence of this property on hydrodynamic stability and on surface tension induced flows is studied as well theoretically as experimentally.
18 citations
TL;DR: In this paper, the critical Marangoni number for the steady mode can be expressed by a simple function of the wave-number when the two boundaries of the sheet are flat and when the surface deformations are taken into account.
Abstract: The Marangoni instability of a thin liquid sheet driven by the surface tension gradient (due to variations of temperature or of mass concentration) is studied by means of a linear theory. It is found that the critical Marangoni number for the steady mode can be expressed by a simple function of the wave-number when the two boundaries of the sheet are flat. When the surface deformations are taken into account, another type of instability may occur for small values of the Biot number. The effect of deviation of the surface tension coefficient from the mean value at the free surfaces and the resulting surface patterns made up by the surface deformations at small wave-numbers are also discussed.
16 citations
TL;DR: It is proposed that the coupling between potential, pH and interfacial Gibbs energy can provide an elementary driving force for cell and organelle motility, phagocytosis and streaming effects.
TL;DR: In this article, the effects of temperature dependence of the diffusion coefficients on the solution fields of Thermal Marangoni Flows in micro-gravity are analyzed by using an unsteady variable mesh and finite difference numerical code to solve the full Navier-Stokes equations.
TL;DR: In this article, the second order Marangoni number is derived for a thin horizontal fluid layer exhibiting a nonlinear dependence of the surface-tension with respect to the temperature.
Abstract: Marangoni instability in a thin horizontal fluid layer exhibiting a nonlinear dependence of the surface-tension with respect to the temperature is studied. This behaviour is typical of some aqueous long chain alcohol solutions. The band of allowed steady convective solutions is determined as a function of the wavenumber and a new dimensionless number, called the second order Marangoni number. We show that the cells which take the shape of rolls and rectangles are unstable while hexagonal planforms remain allowed. The field equations are expressed as Euler-Lagrange equations of a variational principle which serves as the starting point of the numerical procedure, based on the Rayleigh-Ritz method On etudie l'instabilite de Marangoni dans une mince lame horizontale de fluide lorsque la tension de surface est une fonction non lineaire de la temperature. Un tel comportement est typique de solutions aqueuses d'alcools a longue chaine. La zone des solutions stationnaires convectives est determinee en fonction du nombre d'onde et d'un nouveau nombre sans dimension, le nombre de Marangoni du second ordre. On montre que les cellules prenant la forme de rouleaux et de rectangles sont instables alors que les hexagones sont stables. Les equations de champ sont exprimees sous forme d'equations d'Euler-Lagrange d'un principe variationnel qui constitue le point de depart de la procedure numerique, basee sur la methode de Rayleigh-Ritz
TL;DR: In this paper, various contributions of spreading, of capillarity and of Marangoni convection on the mixing and demixing of transparent liquids exhibiting a miscibility gap are reported.
TL;DR: In this article, a nonlinear diffusion equation governing surface deformation was derived theoretically for the Marangoni convection, which has been derived numerically for the surfaces deformation by solving an initial value problem under a periodic boundary condition.
Abstract: A nonlinear diffusion equation governing a surface deformation, which has been derived theoretically for the Marangoni convection, is investigated numerically. By solving an initial value problem under a periodic boundary condition, it is found that the numerical solutions for the surface deformation are classified into three types, i.e., damping, steady and explosive ones depending upon various values of parameters.
TL;DR: In this article, a detailed analysis of this development and its influence on mass transfer will lead to new insights in this transfer process, which might lead to a better understanding of the influence of side walls on the stability of the system.
Abstract: We are very satisfied with the experimental results thus far obtained. The stability of the flat interface was unexpected and might lead to a better understanding of the influence of side walls on the stability of the system. The movement induced by curvature, the development of the roll cells, were obtained in these experiments under microgravity. A detailed analysis of this development and its influence on mass transfer will lead to new insights in this transfer process.
01 Jan 1986
TL;DR: In this article, a thermal imaging system using a liquid-liquid interface has been studied, which utilizes the extreme temperature sensitivity of surface tension (Marangoni Effect), and theoretical considerations for the design and operating conditions of the device are given.
Abstract: A thermal imaging system using a liquid-liquid interface has been studied, which utilizes the extreme temperature sensitivity of surface tension (Marangoni Effect). Theoretical considerations for the design and the operating conditions of the device are given. The experimental results using a detection by polarization interferometer indicate that the limitations on such a device are primarily due to the finite film thickness of the upper solution (on the order of 50–80 μm). This system was able to image 1°C with a limiting resolution of ten lines pair per millimeter.
TL;DR: In this article, the effects of a non-uniform temperature gradient and the Coriolis force on the onset of convection driven by combined surface-tension and buoyancy force in a horizontal layer of Boussinesq fluid with upper boundary free and adiabatic and the lower boundary rigid and isothermal is studied by means of linear stability analysis.
Abstract: The effects of a non-uniform temperature gradient and the Coriolis force on the onset of convection driven by combined surface-tension and buoyancy force in a horizontal layer of Boussinesq fluid with upper boundary free and adiabatic and the lower boundary rigid and isothermal is studied by means of linear stability analysis. The Galerkin technique is used to obtain the eigenvalues. A mechanism for suppressing or augmenting convection is discussed in detail. It is found that as the rotation increases the coupling between the two agencies causing instability becomes weaker even in the presence of a non-uniform temperature gradient. A discontinuous change in cell size occurs at a certain value of Rayleigh number as a result of sudden change over from convection dominated by one of the two agencies to that dominated by the other. The results obtained in the limiting case of uniform temperature gradient or in the absence of rotation agree with the existing ones and found that even a single-term Galerkin expansion gives reasonable results with minimum mathematics.
Journal Article•
TL;DR: In this article, the effects of uniform rotation and non-uniform temperature gradient on the onset of India according to Marangoni convection driven by surface tension in a horizontal layer of fluid is studied subjected to infinitesimal amplitude analysis assuming both the bounding surfaces free and adiabatic.
Abstract: The effects of uniform rotation and non-uniform temperature gradient on the onset of India according of Marangoni convection driven by surface tension in a horizontal layer of fluid is studied subjected to infinitesimal amplitude analysis assuming both the bounding surfaces free and adiabatic. A single term Galerkin technique with single term expansion is used to obtain the eigenvalues which are then computed numerically. Attention is focused on the situation where the. Critical Marangoni number is greatest or least than that for the uniform temperature gradient. Numerical results are obtained for special cases and some general conclusions about the destabilizing effects or various basic temperature profiles and the stabilizing effect of Coriolis force are presented. It was round that the most destabilizing temperature gradient is one for which the temperature gradient is a step function of the depth and the most stabilizing temperature gradient is inverted parabola and the Coriolis force has inhibiting effect on the onset of Marangom convection.
TL;DR: The microscopic interpretation of the driving force of bubble motion is still a matter of debate as mentioned in this paper, but it is known that it is located at the gas-liquid interface in a layer of atomic dimensions.
Abstract: in which all buoyancy effects are neglected. Grad T in this expression is the temperature gradient inside the liquid, not considering the disturbances caused by the flow around the bubble. R is the radius of the bubble and a the surface tension; / , / ~ are the viscosities inand outside the bubble, respectively; and h', h are the corresponding heat conductivities. The driving force is located at the gas-liquid interface in a layer of atomic dimensions. The microscopic interpretation of the driving force is still a matter of debate. Observation of the bubble motion of different chemical systems can provide us with information about processes in the liquid-gas interface, so that the chemical and physical properties of the systems can be correlated with the deviations in the bubble velocity from that calculated according to Eq. (1). Table 1. The silicon oil AK 100 is a pure methyl-siloxane, with 6% phenyl groups on the free valences of the siloxane chain, which are increased to 28% in the oil AP 100
01 Jan 1986
TL;DR: In this paper, the authors examined nonlinear effects on the stability of a free thin liquid film in a simplified situation where only the influence of Van der Waals interaction is taken into account.
Abstract: The authors examine nonlinear effects on the stability of a free thin liquid film in a simplified situation where only the influence of Van der Waals interaction is taken into account. First, in the limit of long wavelength of the perturbation, we obtain a nonlinear evolution equation describing the temporal variation of the film thickness along the lateral space dimension in the case of tangentially immobile surfaces. We determine numerically the time of rupture for the film through the amplification of the squeezing mode, this latter being the more appropriate mode leading to rupture. Secondly, we analyze the stability of a film submitted to solutal Marangoni effects at the two surfaces which allows predicting bifurcations to new flow patterns.
TL;DR: In the parabolic flights of march 1986, the main interest was to perform experiments with Marangoni convection due to concentration gradients along the gas-liquid interface under isothermal conditions.
TL;DR: In this paper, the onset of Marangoni convection in an electrically conducting liquid is studied theoretically for the case that the liquid is subjected to a vertical temperature gradient and a magnetic field with arbitrary orientation.
TL;DR: Marangoni-Effekte sind somit natfirliche, gravitationsunabhfingige Konvektionserscheinungen, die unter Schwerelosigkeit Bedeutung gewinnen, weil dort die Auftriebskonvektion unterdriickt ist.
Abstract: U nter Marangoni-Effekten versteht man Fliissigkeitsbewegungen, die durch Inhomogenit/iten der Grenzfl/ichenspannung in freien Flfissigkeitsoberfl/ichen (Grenzfl/ichen) zustande kommen. Die Inhomogenit/iten k6nnen thermischer und chemischer Natur sein. Die Marangoni-Effekte sind daher ein Ph/inomen yon allgemeiner Bedeutung fiir alle Flfissigkeiten mit freier Oberfl/iche (Grenzfl/iche flfissig-gasf6rmig oder flfissigfliissig). Die Marangoni-Effekte geh6ren zu den natfirlichen Konvektionserscheinungen wie die Auftriebskonvektion. Wfihrend die Auftriebskonvektion darauf beruht, dab das Kr~iftegleichgewicht in der Fliissigkeit durch Dichteunterschiede (verursacht durch lokale Temperaturunterschiede oder Konzentrationsunterschiede) im Gravitationsfeld der Erde gest6rt ist, beruhen MarangoniEffekte darauf, dab lediglich das Grenzfl/ichenspannungsgleichgewicht gest6rt ist. Marangoni-Effekte sind somit natfirliche, gravitationsunabhfingige Konvektionserscheinungen, die unter Schwerelosigkeit Bedeutung gewinnen, weil dort die Auftriebskonvektion unterdriickt ist. Konvektionserscheinungen sind bei vielen W/irmeoder Stofftransportprozessen yon Bedeutung, weil die konvektiven Transportraten die diffusen in der Regel um Gr613enordnungen fibersteigen. Unter Schwerelosigkeit k6nnen Marangoni-Effekte den Transport iiberall dort effektiv fibernehmen, wo freie Fliissigkeitsgrenzfl/ichen vorhanden sind. Da Marangoni-Effekte Oberfl/icheneffekte sind, ist ihre Wirkung nahe der Oberfl/iche oder in kleinen Volumen besonders grog. Die St/irke der Marangoni-Konvektion wird durch die Marangoni-Zahl M a angegeben:
TL;DR: In this article, the temperature field inside a fluid layer with a free surface, heated from below, in the unstable regime (thermocapillary instability or Marangoni effect) was measured when the convective flow was time dependent.
Abstract: 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.
TL;DR: In this paper, a model of a gas well containing liquid is considered, the nature of the steady-state regimes is investigated, and the causes of cyclical output are analyzed.
Abstract: A model of a gas well containing liquid is considered, the nature of the steady-state regimes is investigated, and the causes of cyclical output are analyzed. In formulation the problem resembles the oil well gushing problem studied in [1].