Influence of a surface tension minimum as a function of temperature on the marangoni convection

Legros, Jean Claude; Limbourg-Fontaine, M.C.; Pétré, Georges

doi:10.1016/0094-5765(84)90005-5

Cited by 46 publications

(15 citation statements)

References 8 publications

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“…It has been recently discovered that dilute aqueous solutions of long-chain alcohols exhibit nonmonotonic dependence of surface tension on temperature (Legros et al, 1984;Legros, 1986). This dependence can be approximated quite well by the quadratic polynomial…”

Section: F Thermocapillarity Surface Tension and Body Force Onlymentioning

confidence: 98%

Long-scale evolution of thin liquid films

1997

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Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation f...

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Section: F Thermocapillarity Surface Tension and Body Force Onlymentioning

confidence: 98%

Long-scale evolution of thin liquid films

1997

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“…Therefore the signs of <r g and a i may be arbitrary, but conditions (4.1) must be always valid because they express the maximum entropy principle. At first sight, the inequality cr m < 0 contradicts the work of Legros et al (1984), wherein the surface tension minimum has been established for aqueous long chain alcohol solutions. To overcome this apparent difficulty, it suffices to conjecture that there has been an experimental measurement of the compound function a(8) = <r(d, £(#)), where the chemical potential £ = £(#) of the alcohol is defined from the condition TV = constant.…”

Section: Capillaritymentioning

confidence: 90%

“…The general symmetrization procedure presented there, and in this paper, is very familiar. The study arose from the author's interest in capillary phenomena, which led him to investigate the so-called anomalous thermocapillary effect (Legros et al 1984). In this paper the surface tension minimum has been experimentally established for aqueous long chain alcohol solutions.…”

Section: Introductionmentioning

confidence: 99%

Symmetrization of interface dynamics equations

Antanovskiĭ

1992

Eur. J. Appl. Math

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The system of conservation laws governing heat and mass transfer processes in a continuous medium is obtained in a symmetric form on the basis of the successive application of fundamental thermodynamic principles. This approach involves reformulating the problem in intensive thermodynamic variables such as the temperature and chemical potential. The equations of capillary fluid mechanics and phase transitions with moving free boundaries are analysed in detail. The unsteady motion of a drop driven by buoyancy forces in an unbounded ambient fluid with dilute surfactants is investigated where the LeChatelier principle is established for an arbitrary surfactant. The general procedure for construction of self-similar solutions for the thermodiffusive Stefan problem with piecewise constant matrices of coefficients is described

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“…La ecuación anterior da cuenta de la dependencia espacial del esfuerzo de Marangoni que queda fuertemente determinado por la distribución de temperatura en el sustrato, T s . Los líquidos comúnmente denominados self-rewetting, compuestos por una solución de agua y alcohol con una gran concentración de carbono (n-heptanol), exhiben una dependencia cuadrática con la temperatura, [8,9]…”

Section: Modelounclassified

“…1. Por el contrario, en este trabajo analizamos fluidos que presentan una dependencia cuadrática de la tensión superficial con la temperatura, comúnmente llamados líquidos "self-rewetting" [8,9], ver Fig. 1.…”

Section: Introductionunclassified

Driven Droplets by Thermocapillary Effect: Quadratic Dependence of the Surface Tension on the Temperature

Intyre¹,

Gomba²,

Perazzo³

2020

AnAFA

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We study the migration of droplets on a solid surface which is under a uniform temperature gradient. The present article focus on partial wetting fluids which surface tension depends on the squared temperature. These type of liquids, called self-rewetting, show a complex dynamics and here we will compare with those liquids of linear dependence in the temperature. Unlike to the latter ones, the droplet width increases with the time.

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Influence of a surface tension minimum as a function of temperature on the marangoni convection

Cited by 46 publications

References 8 publications

Long-scale evolution of thin liquid films

Long-scale evolution of thin liquid films

Symmetrization of interface dynamics equations

Driven Droplets by Thermocapillary Effect: Quadratic Dependence of the Surface Tension on the Temperature

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