Showing papers on "Marangoni effect published in 1982"
TL;DR: In this article, the stability of axisymmetric states in a circular cylinder with a nonlinear Marangoni flow was investigated, where the upper free surface of the liquid was taken to have large enough surface tension that surface deflections were neglected.
Abstract: We consider liquid in a circular cylinder that undergoes nonlinear Marangoni insta- bility. The upper free surface of the liquid is taken to have large-enough surface tension that surface deflections are neglected. The side walls are adiabatic and impenetrable, and for mathematical simplicity the liquid is allowed to slip on the side walls. The linearized stability theory for heating from below gives the critical Marangoni number Mc as a function of cylinder dimensions, surface-cooling condition and Rayleigh number. The steady nonlinear convective states near Mc are calculated using an asymptotic theory, and the stability of these states is examined. At simple eigenvalues Mc the finite-amplitude states are determined. We find th at the Prandtl number of the liquid influences the stability of axisymmetric states, distinguishing upflow at the centre from downflow. Near those aspect ratios corresponding to double eigenvalues Me, where two convective states of linear theory are equally likely, the nonlinear theory predicts sequences of transitions from one steady convective state to another as the Marangoni number is increased. These transitions are determined and discussed in detail. Time-periodic convection is possible in certain cases.
107 citations
TL;DR: In this article, a nonlinear Marangoni instability in a circular cylinder is examined, with attention given to roll-cell development and interaction, and the observed roll cell amplitudes and transport properties are shown to be available from simple eigenvalues, with double eigen values, indicating the existence of two roll states as predicted by linear theory, while nonlinear theory indicates transitions from one steady convective state to another.
Abstract: Liquid undergoing nonlinear Marangoni instability in a circular cylinder is examined, with attention given to roll-cell development and interaction. Surface deflections are neglected and the side walls are considered as adiabatic and impenetrable, allowing the liquid to freely slip. The nonlinear convective states are calculated and their stability is defined. The behavior and amplitude of cells forming in the liquid, heated from below, are modeled in order to derive all the transport properties. A new small parameter is formulated which is related to the critical Marangoni number of the infinite matrix expressing the eigenvalue expansion of the problem. The observed roll cell amplitudes and transport properties are shown to be available from simple eigenvalues, with double eigenvalues, indicating the existence of two roll-states as predicted by linear theory, nonlinear theory indicates transitions from one steady convective state to another.
85 citations
TL;DR: In this paper, the authors considered the surface-tension-driven convection in a liquid film and showed that if the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater than the film thickness.
77 citations
TL;DR: In this paper, a system of two interfacing immiscible fluids subject to an imposed temperature difference in a gravity field is considered, and an order of magnitude analysis is applied to determine: (i) the types of flow regimes that can be attained in natural, Marangoni or combined free convection; (ii) how the problem's data identify which type of free convective and of flow regime prevails in each specific case.
73 citations
TL;DR: In this paper, the authors propose to superimpose rotating flows induced by single or iso-rotation of the coaxial disks which represent the upper and lower solid boundaries of the floating zone.
62 citations
TL;DR: In this article, the authors investigated the oscillatory thermocapillary convection in a floating zone in a sounding rocket experiment (TEXUS IIIb) on 30 April 1981.
58 citations
TL;DR: In this paper, it was shown theoretically that Marangoni convection may exist in a human tear film due to the diffusion of mucin, but the temperature drop across the tear film is not capable of generating MARANGONI convection.
39 citations
01 May 1982
TL;DR: In this paper, a freely floating liquid drop is subjected at its surface to an axial temperature field inducing a thermal Marangoni-convection due to the variation of the surface tension.
Abstract: A freely floating liquid drop is subjected at its surface to an axial temperature field inducing a thermal Marangoni-convection due to the variation of the surface tension. Streamfunction and velocity distribution are analytically determined for steady and unsteady temperature fields, by solving the equation for the Streamfunction with the help of associated Legendre functions of the first kind. The special case of a steady linear axial temperature field is evaluated numerically and exhibits a single quadratic velocity profile, which in radial direction is proportional to cos ϑ and in ϑ-direction proportional to sin ϑ.
30 citations
TL;DR: In this paper, an infinite at both ends closed cylindrical liquid column is subjected to various axial temperature fields, such as linear, quadratic, sinusoidal and exponential temperature changes.
Abstract: An infinite at both ends closed cylindrical liquid column is subjected to various axial temperature fields, such as linear, quadratic, sinusoidal and exponential temperature changes. Due to the Marangoni effect surface tension driven flow is created. The velocity distribution for the various cases is presented in closed form. Streamlines are exhibited for the different cases.
Eine unendliche an beiden Enden geschlossene zylindrische Flussigkeitssaule ist einem axialen Temperaturfeld ausgesetzt. Aufgrund des thermischen Marangonieffektes tritt eine von der Oberflachenspannung angetriebene Konvektion in der Flussigkeit auf. Fur lineares, parabolisches, sinusformiges und exponentielles axiales Temperaturfeld werden die Stromungsgeschwindigkeitsverteilung und Stromlinien in geschlossener Form angegeben.
29 citations
TL;DR: In this paper, a purley angular temperature field at the free surface of the liquid is analyzed for the case of a simple stationary sinusoidal temperature field, and the stream function is evaluated numerically for arbitrary stationary and time-periodic temperature fields.
Abstract: Thermal Marangoni convection inside a liquid bridge is analytically determined for a purley angular temperature field at the free surface of the liquid. Radial- and angular velocity components as well as the stream function are presented for arbitrary stationary and time-periodic temperature fields. The case of a simple stationary sinusoidal temperature field has been evaluated numerically.
TL;DR: In this paper, a variational principle describing marginal stability is proposed, and the amplitude of the supercritical temperature and velocity fields are calculated in the framework of Stuart's shape approximation, with the possibility of subcritical instability with respect to disturbances of arbitrary amplitude is investigated by the method of energy.
Abstract: Benard-Marangoni instabilities are theoretically discussed: emphasis is placed on the role of negative Rayleigh and Marangoni numbers. Marginal, supercritical and subcritical instabilities are respectively examined. The first part is concerned with the response of an unbounded fluid layer with respect to small disturbances. A variational principle describing marginal stability is proposed. Rayleigh-Ritz method is used to obtain approximate solutions for the critical Rayleigh and Marangoni numbers. In a second part, corrections to the linear theory, by including weak nonlinearities, are introduced. The amplitude of the supercritical temperature and velocity fields are calculated in the framework of Stuart's shape approximation. Finally, the possibility of subcritical instability with respect to disturbances of arbitrary amplitude is investigated by the method of energy.
TL;DR: In this paper, the effects of surface tension forces and buoyant forces have been separated by suppression of MC with a surface contamination in a NaNO3-floating zone by flow visualization and temperature measurements under 1-g and under 0.4 g.
TL;DR: The Marangoni wave as discussed by the authors is a solution of the characteristic equation for ripple motion on an air-water interface covered by a film, and it possesses a condition of minimum damping when the loss angle φ is negative and nears −45°.
Abstract: The Marangoni wave, brought forth as a solution of the characteristic equation for ripple motion on an air-water interface covered by a film, is shown to possess a condition of minimum damping when the loss angle φ is negative, and nears −45°. Experimental evidence of this phenomenon was observed in the waving of a tank filled with distilled water and covered with a film of oleic alcohol.
TL;DR: This technique is applied to a study of Benard-Marangoni convection and isotherms of convective cells (hexagons as well as pentagonal and heptagonal defects) are presented.
Abstract: Thermovision is a technique which visualizes the superficial temperatures of materials through the infrared radiation emitted by their surface. This technique is applied to a study of Benard-Marangoni convection. Isotherms of convective cells (hexagons as well as pentagonal and heptagonal defects) are presented. A few thermal pictures displaying the temperature profile along a line of surface and the thermal reliefs of the surface are also presented.
TL;DR: In this article, the stability of a thin horizontal fluid layer subjected to rotation about a vertical axis, when the thermal (or concentration) gradient is not uniform is examined by linear stability analysis.
Abstract: In view of the interesting possibilities of controlling surface tension-driven convection, anticipated in space experiments involving fluid interfaces, the problem of the stability of a thin horizontal fluid layer subjected to rotation about a vertical axis, when the thermal (or concentration) gradient is not uniform is examined by linear stability analysis. Attention is focussed on the situation where the critical Marangoni number is greater than that for the case of uniform thermal gradient and the convection is not, in general, maintained. The case of adiabatic boundary condition is examined because it brings out the effect of surface tension at the free surfaces and allows a simple application of the Galerkin technique, which gives useful results. Numerical results are obtained for special cases and some general conclusions about the destabilizing effects of various basic temperature profiles and the stabilizing effect of coriolis force are presented. The results indicate that the most destabilizing temperature gradient is one for which the temperature gradient is a step function of the depth. Increase in Taylor number and the inverted parabolic basic temperature profile suppress the onset of convection.
TL;DR: In this article, the authors deal with the analysis of physical features of ingots fabrication with the aid of an undirectional crystallisation method in microgravity, and the effect of heat exchange features in the melt on the crystallization front rate value has been treated.
TL;DR: In this article, the physical mechanisms of flows generated by surface-tension gradients are clearly defined and the relevant dimensionless parameters are derived, which are used to indicate the qualitative nature of possible flows.
Abstract: The physical mechanisms of flows generated by surface-tension gradients are clearly defined and the relevant dimensionless parameters are derived. These are used to indicate the qualitative nature of possible flows.
TL;DR: In this article, it was proposed that immiscible droplets in a host fluid in which a temperature gradient exists move in the direction of increasing temperature, and this thermocapillary migration could be used to construct a "liquid wick" that would return the condensed vapor at the condenser end of a heat pipe back to the evaporator, thus completing the fluid circuit.
Abstract: In accordance with the Marangoni effect, immiscible droplets in a host fluid in which a temperature gradient exists move in the direction of increasing temperature. It is proposed that this thermocapillary migration could be used to construct a ‘‘liquid wick’’ that would return the condensed vapor at the condenser end of a heat pipe back to the evaporator, thus completing the fluid circuit. The droplets would be formed by capillary pressure forcing the condensate through a perforated diaphragm whose temperature would control the droplet flux, and hence the heat flux between the two ends of the heat pipe, thus making it a controllable heat valve.
01 Dec 1982
TL;DR: An infinitely long liquid bridge, observing a non-Newtonian flow law (Ostwald-de-Waal and Bingham), is subjected under weightless condition to a linear temperature field, which yields due to the local change of the surface tension a Marangoni convection as mentioned in this paper.
Abstract: An infinitely long liquid bridge, observing a Non-Newtonian flow law (Ostwald-de-Waal and Bingham), is subjected under weightless condition to a linear temperature field, which yields due to the local change of the surface tension a Marangoni convection. The velocity- and temperature distribution inside the liquid bridge is determined analytically.
01 Jan 1982
TL;DR: In this paper, the role of thermal gradients, crystal rotation, and surface tension driven (Marangoni) convection in the Czochralski growth of single crystals from large melts is discussed.
Abstract: In the Czochralski growth of single crystals from large melts, fluid flow phenomena have a major effect on interface shape, growth striations, defect density and the length of crystals which can be grown from a melt of given volume and thermal geometry. Because of the technical difficulties encountered in making direct measurements in molten oxides, simulation experiments have been extensively utilized to gain insight into melt behavior. Both temperature profile and flow geometry results from simulation experiments are discussed. This data is supported by direct melt observations and results from the characterization of grown crystals. When reviewed together, this information offers new insights into the complex behavior of Czochralski growth processes, including the role of thermal gradients, crystal rotation, and surface tension driven (Marangoni) convection.
TL;DR: In this paper, the rates of evaporation of alloying elements from Fe-Cu, Fe-Sn and Fe-Cr melts under vacuum have been investigated by using an experimental apparatus which was made up of a Langmuir's Evaporation cell and of target plates for collecting evaporated material.
07 Jun 1982
TL;DR: In this paper, the axial momentum equation is solved to account for axial variation in surface tension forces due to changes in meniscus length and liquid-channel wall friction due to recirculating Marangoni flow in the gas-blocked region.
Abstract: An analysis is developed for the Marangoni effect, due to surface tension variation with temperature, in axially grooved variableconductance heat pipes (VCHP) and compared with test data. The axial momentum equation is solved, accounting for the axial variation in surface tension forces due to changes in meniscus length, as well as changes in surface tension and liquid-channel wall friction due to the recirculating Marangoni flow in the gas-blocked region. The NASA groove analysis program has been modified to include these changes. Results indicate very substantial reductions in transport capacity for VCHPs compared with original isothermal values. Nomenclature A = cross-sectional area, m^ F = force in axial direction, N k = nondimensional constant, Eq. (13) tb = diffusion zone length, m ^m = total meniscus length in cross section, m m = nondimensional summation parameter, Eq. (14) N = number of axial grooves n = nondimensional summation integer, Eq. (14)
01 Sep 1982
TL;DR: In this article, the combined effects of buoyancy and Marangoni thermal stresses for Stokes regimes in a plane Plateau type configuration are studied and the appropriate mathematical formulation for arbitrary immiscible interfacing liquids in the presence of temperature differences and gravity field is given and conditions for which the temperature field is uncoupled from the velocity field derived.
Abstract: The combined effects of buoyancy and Marangoni thermal stresses for Stokes regimes in a plane Plateau type configuration are studied. The appropriate mathematical formulation for Stokes regimes of arbitrary immiscible interfacing liquids in the presence of temperature differences and gravity field is given and the conditions for which the temperature field is uncoupled from the velocity field derived. It is then proved that for Plateau configurations the zeroth order problem is fully linear so that Marangoni and buoyant effects are superposable. The special case of a plane geometry is then solved analytically by means of Papkovich-Faddle bi-orthogonal complex functions. The relevant features of the flow are analyzed and discussed in terms of streamlines, velocity profiles, dynamic interface shapes with particular emphasis in the comparison between purely Marangoni, purely buoyant and combined free convection.