Showing papers on "Marangoni effect published in 1998"
15 Apr 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: Thermocapillary forces were shown to play a part in the problems of ‘off–centre welding’, ‘porosity’ and ‘arc wander’ in GTA/TIG welding in the surface rippling of welds.
Abstract: The problem of it variable weld penetration or casttocast variation in GTA/TIG welding is discussed. It is shown that for normal GTA/TIG welding conditions the HeipleRoper theory is valid, i.e. tha...
250 citations
TL;DR: In this paper, the spreading of liquid films driven by surface tension gradients induced by evaporation from a two-component mixture was studied and their length was found to depend linearly on the square root of time t.
Abstract: We study the spreading of liquid films driven by surface tension gradients induced by evaporation from a two-component mixture. The films climb from a macroscopic reservoir on a plane tilted surface and their length L is found to depend linearly on the square root of time t: L(t) = (Dt)0.5. We develop a semiquantitative analysis that shows which parameters control the value of D for ideal mixtures and for nonideal ones. We report also experimental results about the time evolution and the spatiotemporal behavior of the interfacial instability that develops at the meniscus between the reservoir and the film. Results agree well with previous experimental and theoretical studies.
133 citations
TL;DR: In this article, a spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton's method for a differentially heated binary mixture.
Abstract: Marangoni convection in a differentially heated binary mixture is studied numerically by continuation. The fluid is subject to the Soret effect and is contained in a two-dimensional small-aspect-ratio rectangular cavity with one undeformable free surface. Either or both of the temperature and concentration gradients may be destabilizing; all three possibilities are considered. A spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton's method. Linear thresholds are compared to those obtained for a pure fluid. It is found that for large enough Soret coefficient, convection is initiated predominantly by solutal effects and leads to a single large roll. Computed bifurcation diagrams show a marked transition from a weakly convective Soret regime to a strongly convective Marangoni regime when the threshold for pure fluid thermal convection is passed. The presence of many secondary bifurcations means that the mode of convection at the onset of instability is often observed only over a small range of Marangoni number. In particular, two-roll states with up-flow at the centre succeed one-roll states via a well-defined sequence of bifurcations. When convection is oscillatory at onset, the limit cycle is quickly destroyed by a global (infinite-period) bifurcation leading to subcritical steady convection.
103 citations
TL;DR: The effects of a sorption-controlled, monolayer-forming surfactant on a drop deforming in an extensional flow are studied numerically and the drop contribution to the volume averaged stress tensor Sigma is calculated.
97 citations
TL;DR: In this article, the authors show that the axial segregation is shifted towards the diffusive case with the application of higher axial magnetic fields, and a pure diffusion-controlled regime cannot be attained even with fields of 5 T.
94 citations
TL;DR: In this paper, temperature fluctuation measurements in a liquid bridge of molten silicon, which shows the Marangoni flow in highly supercritical condition, are performed in a half-zone configuration under microgravity on board a TR-IA-4 rocket and on the ground.
77 citations
TL;DR: In this paper, the critical Marangoni number for the onset of time-dependent thermocapillary convection for the FZ growth was determined: Ma c2 =375±125.
77 citations
TL;DR: In this paper, a numerical study of the flow characteristics of thermocapillary convection in a system composed of two immiscible liquid layers subject to a temperature gradient along their interface is presented.
77 citations
TL;DR: In this article, the authors investigated thermocapillary instabilities on floating half zone convection in microgravity environment by linear instability analysis method and the critical Marangoni numbers were obtained and compared with the experimental ones.
72 citations
TL;DR: In this paper, the transition from two-dimensional thermoconvective steady flow to a time-dependent flow is considered for a liquid with a high Prandtl number (Pr=105) in a liquid bridge with a curved free surface.
Abstract: The transition from two-dimensional thermoconvective steady flow to a time-dependent flow is considered for a liquid with a high Prandtl number (Pr=105) in a liquid bridge with a curved free surface. Both thermocapillary and buoyancy mechanisms of convection are taken into account. The computer program developed for this simulation transforms the original nonrectangular physical domain into a rectangular computational domain. To solve the problem in body-fitted curvilinear coordinates, the time-dependent Navier–Stokes equations were approximated by central differences on a stretched mesh. For liquid bridges with a flat interface, the instability corresponding to an azimuthal wave number of m=0 is not found for the investigated range of Marangoni numbers. The instability corresponding to an m=0 is found for relatively low Marangoni numbers only in liquid bridges with a nonflat, free surface, and nonzero Rayleigh number. The steady state becomes unstable to axially running waves. It is shown that the onset ...
71 citations
TL;DR: In this article, the authors visualized natural convection in 23 gas-liquid systems in a quiescent cell by Schlieren techniques and analyzed the relationship between the density effect of CO2 saturation and solvent density.
01 Jan 1998
TL;DR: In this paper, the authors studied Marangoni convection in a dierentially heated binary mixture, where the fluid is subject to the Soret eect and is contained in a two-dimensional small-aspect-ratio rectangular cavity with one undeformable free surface.
Abstract: Marangoni convection in a dierentially heated binary mixture is studied numerically by continuation. The fluid is subject to the Soret eect and is contained in a twodimensional small-aspect-ratio rectangular cavity with one undeformable free surface. Either or both of the temperature and concentration gradients may be destabilizing; all three possibilities are considered. A spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton’s method. Linear thresholds are compared to those obtained for a pure fluid. It is found that for large enough Soret coecient, convection is initiated predominantly by solutal eects and leads to a single large roll. Computed bifurcation diagrams show a marked transition from a weakly convective Soret regime to a strongly convective Marangoni regime when the threshold for pure fluid thermal convection is passed. The presence of many secondary bifurcations means that the mode of convection at the onset of instability is often observed only over a small range of Marangoni number. In particular, two-roll states with up-flow at the centre succeed one-roll states via a well-dened sequence of bifurcations. When convection is oscillatory at onset, the limit cycle is quickly destroyed by a global (innite-period) bifurcation leading to subcritical steady convection.
TL;DR: Examination of deformation and breakup of fluid drops suspended in another immiscible fluid under the action of an electric field shows that, although not pronounced in the small deformation limit, nonuniformity in the surfactant distribution is a decisive factor for the breakup mechanism of a prolate spheroid.
TL;DR: In this paper, the axial segregation profiles for phosphorus doped silicon were calculated and it was shown that even high axial magnetic fields B ⩽ 5 T do not establish a diffusive regime due to residual Marangoni convection.
TL;DR: In this article, the amplitude equations of the convective modes are obtained from the continuity, the Navier-Stokes and the Fourier equations in the Boussinesq approximation neglecting surface deformation and buoyancy.
Abstract: A derivation is given of the amplitude equations governing pattern formation in surface tension gradient-driven Benard–Marangoni convection. The amplitude equations are obtained from the continuity, the Navier–Stokes and the Fourier equations in the Boussinesq approximation neglecting surface deformation and buoyancy. The system is a shallow liquid layer heated from below, confined below by a rigid plane and above with a free surface whose surface tension linearly depends on temperature. The amplitude equations of the convective modes are equations of the Ginzburg–Landau type with resonant advective non-variational terms. Generally, and in agreement with experiment, above threshold solutions of the equations correspond to an hexagonal convective structure in which the fluid rises in the centre of the cells. We also analytically study the dynamics of pattern formation leading not only to hexagons but also to squares or rolls depending on the various dimensionless parameters like Prandtl number, and the Marangoni and Biot numbers at the boundaries. We show that a transition from an hexagonal structure to a square pattern is possible. We also determine conditions for alternating, oscillatory transition between hexagons and rolls. Moreover, we also show that as the system of these amplitude equations is non-variational the asymptotic behaviour (t→∞) may not correspond to a steady convective pattern. Finally, we have determined the Eckhaus band for hexagonal patterns and we show that the non-variational terms in the amplitude equations enlarge this band of allowable modes. The analytical results have been checked by numerical integration of the amplitude equations in a square container. Like in experiments, numerics shows the emergence of different hexagons, squares and rolls according to values given to the parameters of the system.
TL;DR: In this paper, a preliminary model of pulmonary airway reopening was developed that includes the physicochemical influence of surfactant under bulk-equilibrium conditions, and the results indicate that El can have a dual, contrasting influence on the airway Reopening behavior.
Abstract: A preliminary model of pulmonary airway reopening is developed that includes the physicochemical influence of surfactant under bulk-equilibrium conditions. The airway is modeled following Gaver et al. [J. Fluid. Mech. 319, 25–65 (1996)] as a flexible-walled channel, where walls are membranes under longitudinal tension T, and supported with elasticity E with a stress-free separation distance 2H. The lining fluid has viscosity μ and surface tension γ*. Airway reopening occurs when a semi-infinite bubble of air with pressure Pb* progresses steadily at velocity U and separates the walls. Surfactant exists in the lining fluid (C*) and at the air–liquid interface (Γ*). Bulk equilibrium is assumed (C*=C0) and the kinetic transfer of surfactant between the bulk and interface occurs with a rate k. The equilibrium relationship between Γ* and C* is based upon Henry’s isotherm (Γeq=KC0). The surface tension equation of state, a relationship between γ* and Γ*, is assumed to be linear near Γeq. Marangoni stresses develop from the transport of surfactant at the interface, leading to interfacial rigidification and changes in the airway reopening behavior. The behavior is governed by the following dimensionless parameters: the capillary number Ca=μU/γeq, the surface elasticity number El=−(dγ*/dΓ*)(Γeq/γeq), the modified Stanton number Stλ=(k/K)/(U/H), the wall elastance parameter β=EH2/γeq, the wall tension ratio η=T/γeq, and the surface Peclet number Peint=UH/Dint. The results indicate that El can have a dual, contrasting influence on the airway reopening behavior. By increasing El through an increase in dγ*/dΓ* (method 1), larger Pb* are predicted from the resulting interfacial surfactant gradients and interfacial rigidification. In contrast, increasing Γeq (method 2) increases El but reduces Pb* due to the global reduction of γ*; however, the reduction in Pb* is augmented by the increasing importance of viscous, elastic, tension and Marangoni stresses. Furthermore, for Stλ>10 the interface remains mobile due to rapid surfactant adsorption and the elimination of Marangoni stresses, which minimizes Pb*. This behavior may be important in the development of improved exogenous surfactants for the treatment of a variety of pulmonary diseases.
TL;DR: In this paper, the authors demonstrated that the free surface temperature perturbations and the periodic addition of heat along lines parallel to the crests of the hydrothermal waves can suppress the instability produced in the model system of Part 1 (Riley & Neitzel 1998).
Abstract: Hydrothermal-wave instabilities in thermocapillary convection are known to produce undesirable effects when they occur during the float-zone crystal-growth process, and perhaps in other situations. Suppression of the hydrothermal-wave instability produced in the model system of Part 1 (Riley & Neitzel 1998) is demonstrated through the sensing of free-surface temperature perturbations and the periodic addition of heat at the free surface along lines parallel to the crests of the hydrothermal waves.
TL;DR: In this article, a lubrication analysis for the near-contact axisymmetric motion of spherical drops covered with an insoluble non-diffusing surfactant is presented.
Abstract: A lubrication analysis is presented for the near-contact axisymmetric motion of spherical drops covered with an insoluble non-diffusing surfactant. Detailed results are presented for the surfactant distribution, the interfacial velocity, and the gap width between the drop surfaces. The effect of surfactant is characterized by a dimensionless force parameter: the external force normalized by Marangoni stresses. Critical values of the force parameter have been established for drop coalescence and separation. Surfactant-covered drops are stable to rapid coalescence for external forces less than 4πkTac0, where c0 is the surfactant concentration at the edge of the near-contact region and a is the reduced drop radius.For subcritical forces, the behaviour of surfactant-covered drops is described by two time scales: a fast time scale characteristic of near-contact motion between drops with clean interfaces and a slow time scale associated with rigid particles. The surfactant distribution evolves on the short time scale until Marangoni stresses approximately balance the external force. Supercritical values of the external force cannot be balanced; coalescence and separation occur on the fast time scale. The coalescence time normalized by the result for drops with clean interfaces is independent of the viscosity ratio and initial gap width.Under subcritical force conditions, a universal long-time behaviour is attained on the slow time scale. At long times, the surfactant distribution scales with the near-contact region and the surface velocity is directed inward which impedes the drop approach and accelerates their separation compared to rigid particles. For drops pressed together with a sufficiently large subcritical force, a shrinking surfactant-free clean spot forms.Surfactant-covered drops exhibit an elastic response to unsteady external forces because of energy stored in the surfactant distribution.
15 Apr 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this article, a large thermal gradient in the region where the electron beam intercepts the melt is introduced, which leads to variations in the surface energy of the melt close to the be...
Abstract: Electron beam melting processes exhibit large thermal gradients in the region where the electron beam intercepts the melt; this leads to variations in the surface energy of the melt close to the be...
TL;DR: In this paper, a modified form of the Marangoni number, Ma*, is proposed and its critical values, Ma* c, for alcohol and Freon-113 evaporating layers are determined experimentally.
Abstract: Marangoni-Benard instability and convection in evaporating liquid layers have been studied experimentally through flow visualization and temperature profile measurement. Benard cells have been observed in an evaporating thin liquid layer whether it is heated, adiabatic, or cooled from below. This experimental study has revealed a different mechanism from the traditional Rayleigh-Benard and Marangoni-Benard instabilities and convections, which require a negative temperature gradient in the thin liquid layer. Evaporation rate and enthalpy of evaporation have been found to be important parameters of instability and convection in an evaporating liquid layer. A modified form of Marangoni number, Ma*, is proposed and its critical values, Ma* c, for alcohol and Freon-113 evaporating layers are determined experimentally. A quantitative comparison between Ma* and the traditional Marangoni number, Ma, shows that Ma* is an adequate indicator of the stability status in evaporating liquid layers.
TL;DR: In this article, the interaction of solutal and thermal Marangoni convections that occur inside a metal melt during directional solidification was studied, where the melt was assumed to be incompressible and to have constant properties, except for surface tension.
Abstract: This study is concerned with the interaction of solutal and thermal Marangoni convections that occur inside a metal melt during directional solidification. In order to simplify the problem, the melt was assumed to be incompressible and to have constant properties, except for surface tension. Using the HSMAC algorithm, we carried out simulations for two cases: one is that the flow directions of solutal and thermal Marangoni convections are the same (acceleration case), and the other is that the flow directions are opposite (deceleration case). The effects of solutal Marangoni convection on flow and mass transport phenomena are discussed.
TL;DR: In this article, the authors present results of a transient growth study which reveals enormous amplification of initially infinitesimal disturbances in the film thickness, and for the first time, evidence of an instability resembling experimental patterns.
Abstract: The spreading of surfactant coated thin liquid films is often accompanied by an instability producing significant film corrugation, fingering and branching. Marangoni stresses, responsible for the rapid and spontaneous spreading, are suspected as the main cause of unstable flow. Traditional eigenvalue analysis of a self-similar solution describing Marangoni driven spreading has predicted only stable modes. We present results of a transient growth study which reveals enormous amplification of initially infinitesimal disturbances in the film thickness. This analysis provides, for the first time, evidence of an instability resembling experimental patterns.
TL;DR: Results indicate that under dynamic conditions, the Marangoni effect and the hydrophobic interaction at the surface become important for foam film rupture.
15 Apr 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: An overview is given of recent results about the onset and development of steady and time–dependent flow motions past an instability threshold induced by the Marangoni effect.
Abstract: An overview is given of recent results about the onset and development of steady and timedependent flow motions past an instability threshold induced by the Marangoni effect. First, I consider the ...
15 Apr 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this article, dynamic Xray imaging of a metal droplet in a slag phase is an elegant way to monitor the rate of the interfacial reactions of dephosphorization.
Abstract: Dynamic Xray imaging of a metal droplet in a slag phase is an elegant way to monitor the rate of the interfacial reactions. In an attempt to follow the kinetics of dephosphorization, the changes in...
15 Nov 1998
TL;DR: Experiments and simulations prove that marginal regeneration cannot be the result of thickness fluctuations, and that it is due to surface tension gradients between the film and its borders.
Abstract: Marginal regeneration is the rate-determining drainage mechanism in mobile vertical liquid films stabilized with surfactants. Mysels, Frankel, and Shinoda explained this process from (thermal) thickness fluctuations, like capillary waves. The Laplace underpressure in the Plateau border would exert a larger force on a thick, rather than on a thinner film element. This force unbalance would make film elements of different thicknesses move in opposite directions so that they are exchanged at the border. However, experiments and simulations prove that marginal regeneration cannot be the result of thickness fluctuations. Our alternative view is, that marginal regeneration is due to surface tension gradients between the film and its borders. Drainage of film elements into the lower Plateau border causes a local excess of surfactant, and thereby local differences in surface tension. This causes film elements to flow and generates the thickness differences between the absorbed and emerging film elements. The rates of the Marangoni flows reflect the surface dilational properties. This Marangoni effect is a consequence of the compression of the film surface when a film element flows into the lower Plateau border. Marginal regeneration is then a mechanism which returns the surfactant back into the film.
TL;DR: In this article, the authors examined the motion of a gas bubble in a non-Newtonian fluid and determined the conditions for the possible existence of a discontinuity in the bubble velocity-bubble volume log-log plot.
Abstract: The motion of a gas bubble in a non-Newtonian fluid has been further examined in order to determine the conditions for the possible existence of a discontinuity in the bubble velocity-bubble volume log–log plot. It has been proposed in the past that this phenomenon was the result of a sudden change in the hydrodynamics of the moving bubble, resulting in a transition from a Stroke to a Hadamard regime. Furthermore, this abrupt transition was only qualitatively attributed to the elasticity of the fluid. Using our data as well as those of Leal et al., we demonstrate here that the discontinuity results as a balance between elastic and Marangoni instabilities, providing another major difference between Newtonian and non-Newtonian hydrodynamics.
TL;DR: In this paper, the role of the Marangoni number on the evolution of the free surface in space and time has been investigated for a thin viscous liquid layer bounded from below by a heated solid surface and on the top by a free surface subject to a temperature dependent surface tension.
Abstract: Physically, there are two main mechanisms responsible for driving the instability in the coupled buoyancy (Benard) and thermocapillary (Marangoni) convection problem for a weakly expansible viscous liquid layer bounded from below by a heated solid surface and on the top by a free surface subject to a temperature-dependent surface tension. The first mechanism is density variation generated by the thermal expansion of the liquid; the second results from the surface-tension gradients due to temperature fluctuations along the upper free-surface. In the present paper we consider only the second effect as in the Benard experiments [the so-called Benard–Marangoni (BM) problem]. Indeed, for a thin layer we show that it is not consistent to consider both effects simultaneously, and we formulate an alternative concerning the role of buoyancy. In fact, it is necessary to consider two fundamentally distinct problems: the classical shallow-convection problem for a non-deformable upper surface with partial account of the Marangoni effect (the RBM problem), and the full BM problem for a deformable free surface without the buoyancy effect. We shall be mostly concerned with the thermocapillary BM instabilities problem on a free-falling vertical film, since most experiments and theories have focused on this (in fact, wave dynamics on an inclined plane is quite analogous). For a thin film we consider three main situations in relation to the magnitude of the characteristic Reynolds number (Re) and we derive various model equations. These model equations are analyzed from various points of view but the central intent of this paper is to elucidate the role of the Marangoni number on the evolution of the free surface in space and time. Finally, some recent numerical results are presented.
TL;DR: In this paper, an alternative model for convection in a porous medium layer driven by the Marangoni effect is presented, and the predictions of the two models are significantly different.
Abstract: Comments are made about limitations of the model proposed by Hennenberg et al for convection in a porous medium layer driven by the Marangoni effect, and an alternative model for this problem is presented The predictions of the two models are significantly different
15 Apr 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the active motion of slag film formed by the wettability between the refractory and slag was investigated in SiO2(s)(PbOSiO...
Abstract: Local corrosion of refractory at slaggas and slagmetal interfaces is caused by active motion of slag film formed by the wettability between the refractory and slag. In the systems of SiO2(s)(PbOSiO...