The buoyant marangoni convection heat transfer in a differentially heated cavity is numerically studied. Marangoni convection which is independent of orientation with respect to the gravity vector. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the. Fluid flows from a region with low surface tension to a region with high surface tension as seen clearly in the following video. The marangoni effect is flow of a liquid due to gradients in the surface tension of the liquid. Publishers pdf, also known as version of record includes final page, issue. Linear stability analysis of marangoni convection with freeslip boundary conditions at the bottom was first investigated by boeck and thess 5. Convective instability in a ferrofluid layer can also be induced by surface tension forces provided it is a function of temperature andor. Onset of convection article pdf available in physics of fluids 223 march 2010 with 261 reads how we measure reads. Experimental work on marangoni convection in thin liquid layers is somewhat prob lematic, because flow measurements in such layers are very difficult and in thick layers the simultaneous presence of rayleigh convection is an obstacle. Pdf marangoni convection in binary mixtures with soret effect.
The analysis includes the complete effects of interface deformation. However, marangoni convection rapidly relieves the driving concentration gradients. Pdf effect of internal heat generation on marangoni. Pdf series solutions for marangoni convection on a vertical. Surface tension driven convection known as the marangoni effect needs to be included in the model owing to its. The results determined for large biot and zero marangoni zero prandtl numbers show that steady convection may exist for reynolds numbers re larger than, and for capillary numbers ca. The dual solutions in thermosolutal marangoni boundary layer flow towards a flat plate with suctioninjection effect can be given in hamid et al. Solutal marangoni convection is caused by variations in the concentration of a surfactant at the interface between two liquids or a liquid and a gas. Davis and koschmieder have suggested that the convection should be rightfully called the pearsonbenard convection. Marangoni convection, which is induced by a surface tension gradient on the interface, is an important physical phenomenon under microgravity conditions.
Marangoni instability in a liquid layer with two free surfaces. In the case of temperature dependence, this phenomenon may be called thermocapillary convection or benardmarangoni convection. Mixed buoyancymarangoni convection wiley online library. Surface flow marangoni convection was always found from the high to low temperature region at the surface as far as the liquid bridge had a free surface. Nov 30, 2015 using a cahnhilliardnavierstokes model with a capillary tensor to account for solutal marangoni force, we observe an interfacial wave at the interface of two immiscible liquids. Zhang, in modeling and analysis of modern fluid problems, 2017. Pdf marangoni convection and fragmentation in laser. The marangoni instability is introduced by the temperature dependence of surface tension. In this paper, we study the onset of cellular convection in a horizontal fluid layer heated from below, with a freeslip boundary condition at the bottom when the driving mechanism is surface tension at the upper free surface, in the light of the modified analysis of banerjee et al. Marangoni convection with the objective of understanding the control of convective instability which is important in many engineering and applications in the heat and momentum transfer research.
Effect of marangoni convection generated by voids on. Microscopic simulation of the effect of process parameters. Characterization of the thermal and solutal marangoni flows. In contrast to a large amount of experimental work on marangoni convection in pure liquids, such experiments in binary mixtures are not available in the literature, to our knowledge. At a 0, the critical marangoni number is zero and in this case, conductive state does not exist. Thus as the marangoni number compares flow and diffusion timescales it is a type of peclet number. Marcello lappa, in fluids, materials and microgravity, 2004.
The marangoni effect also called the gibbs marangoni effect is the mass transfer along an interface between two fluids due to a gradient of the surface tension. Use of a ctitious marangoni number for natural convection. Numerical analysis of marangoni convection with freeslip. Marangoni instabilities in binary mixtures are different from those in pure liquids. Marangoni convection with variable viscosity can be delayed and the critical marangoni number can be increased through the use of feedback control.
Marangoni convection in a fluid layer with internal heat generation nor. It is figured out that the heat transfer rate is enhanced for stronger marangoni convection and nanoparticle volume fraction. 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. Moreover, at low scanning speeds, the liquid pool becomes larger than the beam diameter and the development of marangoni eddies leads to a widening and deepening of the pool. Buoyant marangoni convection of nanofluids in square cavity. A critical marangoni number is defined above which the oscillatory modes of solutal marangoni. Moreover, at low scanning speeds, the liquid pool becomes larger than the beam diameter and the development of marangoni vortices leads to a widening and deepening of the pool. Surface tension is a property of a liquid that causes the surface portion of liquid to be attracted to another surface, such as a drop of mercury that forms a cohesive ball in a thermometer or droplets of water on a wellwaxed car. There is a unique solution v0, q0 of the stokes system for a given f. The resulting tx,y may destabilize the layer to figure 9. We consider a small droplet of water sitting on top of a heated superhydrophobic surface. Oscillatory regimes of solutocapillary marangoni convection 537 in gustafson et al. It is usually expected that surface tension driven flow dominates at small scales.
The marangoni effect also called the gibbsmarangoni effect is the mass transfer along an interface between two fluids due to a gradient of the surface tension. Parks department of engineering, university of cambridge trumpington street, cambridge, cb2 1pz, united kingdom in this paper, a method based on the use of a ctitious marangoni number is proposed for. Underdamped capillary wave caused by solutal marangoni. Note that some authors do not favor the name of electric marangoni convection, like jones 11, because it is not formally rigorous. Pdf the effect of coriolis force on marangoni convection. Magnetothermomarangoni convective flow of cu h2o nanoliquid past an. Apr 19, 2014 solutal marangoni convection is caused by variations in the concentration of a surfactant at the interface between two liquids or a liquid and a gas. Magnetothermomarangoni convective flow of cuh2o nanoliquid. The marangoni effect takes place when there is a gradient of surface tension at the interface between two phases in most situations, a liquidgas interface. This study is focused on a steady dissipative layer, which is generated by marangoni convection flow over the surface resulted from an imposed temperature. In this system, the solutal marangoni convection develops in the direction opposite to the thermal marangoni convection along the free surface in the bridge, i.
Pdf marangoni convection in binary mixtures with soret. It is necessary to clarify the effect of marangoni convection on single crystal growth from a melt in order to improve the quality of the grown crystal. Pearson 18 obtained the critical marangoni number, mc 79. Marangoni convection in a differentially heated binary mixture is studied numerically by continuation. Golia and viviani 19 have studied the marangoni convection effect in the nonisobaric boundary layers. The cavity is filled with waterag, watercu, wateral 2 o 3, and watertio 2 nanofluids.
Linear stability theory, marangoni convection, variable viscosity, feedback control, freeslip, deformable free surface 1 introduction convection is the transfer of heat by the motion of. Impact of the marangoni and thermal radiation convection on. Pdf modeling by using comsol of natural and combined. They also mentioned the instability of marangoni convection and found oscillations of the temperature. Experiments carried out on the ground with microscale facilities and model liquids have shown that if the ambient gas air surrounding the droplets is replaced by an immiscible liquid, the marangoni effects at the liquidliquid interface e. Marangoni convection in a relatively hotter or cooler liquid. A modified form of marangoni number, ma, is proposed and its critical values, ma c, for alcohol and freon1 evaporating layers are determined experimentally. Marangoni convection an overview sciencedirect topics. Feedback control of marangoni convection with magnetic field. At and above the critical marangoni number m a c h t w, which is completely different from a critical marangoni number m a c m b for the onset of marangonibenard convection in section 22. Marangoni convection in a relatively hotter or cooler. Oscillatory regimes of solutocapillary marangoni convection. The surface tension being a function of the local surface concentration of surfactant, a variation in the latter will affect the value of surface tension locally and therefore give rise to. Figure 3 shows the critical marangoni number at the onset of convection as a function of the wave number, a, for a range of values of the controller gains, k when in the case of c r 0.
The gradient in surface tension can be caused by a gradient in temperature or chemical concentration 1,2. In such a cuvette, the interference pattern is formed only due to inhomogeneity of the medium enclosed between the mirror coatings of the cuvette walls and is not affected by. A 3d transient finite element model of inconel 718 nickelbased superalloy processed by selective laser melting was developed to study the heat flux in the molten pool under the condition of different process parameters and its effect on the temperature field and the shape of molten pool, in which a solid heat transfer module and a laminar flow module in the finite element simulation software. Modeling marangoni convection with comsol multiphysics. Marangoni convection in a cavity with differentially heated sidewalls has been investigated. The effect of coriolis force on marangoni convection. Pdf modelling marangoni convection in laser heat treatment.
View marangoni convection research papers on academia. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquidsolid contact point. The fluid is subject to the soret effect and is contained in a twodimensional smallaspectratio rectangular cavity with one undeformable free surface. Effects of nonuniform temperature gradients on triple. Microscopic simulation of the effect of process parameters by.
Marangoni convection in binary mixtures with soret effect. Marangoni convection technische universiteit eindhoven. Nonetheless in modern usage rayleighbenard convection refers to the effects due to temperature, whereas benardmarangoni convection refers specifically to the effects of surface tension. Moreover, at low scanning speeds, the liquid pool becomes larger than the beam diameter and the development of marangoni vortices leads to. Consider a liquid layer heated from below and bounded by a free surface above. Unexpectedly absence of marangoni convection in an evaporating. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. In chapters 2 and 3 chapter 2 chapter 3, we discuss the different types of marangoni convection. Georis et alas studied the marangoni instability of a trilayer in microgravity analyti cally in the linear regime and numerically in the nonlinear one under the assumption that. Evaporation from the meniscus of ethanolmethanol confined in a capillary induces marangoni convection at the meniscus which has been investigated by previous researchers. Surface tension driven convection known as the marangoni effect needs to. In the case of temperature dependence, the marangoni effect is also called thermocapillary convection.
A fourier analysis shows that the interfacial wave is induced by oscillatory modes of solutal marangoni convection. The surface tension typically changes due to variations in solute concentration, surfactant concentration, and temperature variations along the interface. Marangoni convection in a fluid layer with internal heat. The problem of triple diffusive marangoni convection is investigated in a composite layer comprising an incompressible three component fluid saturated, sparsely packed porous layer over which lies a layer of the same fluid. Diffusion is of whatever is creating the gradient in the surface tension. Marangoni convection occurs when the surface tension of an interface generally liquidair depends on the concentration of a species or on the temperature distribution.
Marangoni convection in a rectangular container springerlink. Effect of coriolis force on benardmarangoni convection in. Buoyant marangoni convection of nanofluids in square. Doublediffusive marangoni convection in a rectangular cavity. However, marangoni convection is unexpectedly absent at an evaporating water meniscus confined inside a small. The role of marangoni convection in crystal growth. Due to the types of metals used and the extremely high temperatures involved, performing experiments to analyze marangoni convection often proves to be rather challenging. The fluid is subject to the soret effect and is contained in a twodimensional smallaspect. Marangoni convection is a ubiquitous feature in droplet microfluidics. Marangoni convection is the tendency for heat and mass to travel to areas of higher surface tension within a liquid. Jul 07, 2015 marangoni convection also called thermocapillary convection is important in a number of processes, including welding, crystal growth, and electron beam melting. Marangoni convection in a variable viscosity fluid layer. The lower rigid surface of the porous layer and the upper free surface are considered to be insulating to temperature, insulating to both salute concentration. Pdf the problem of steady, laminar, thermal marangoni convection flow of newtonian fluid over a flat surface is investigated.
Users may download and print one copy of any publication from the public portal for. Marangoni convection also called thermocapillary convection is important in a number of processes, including welding, crystal growth, and electron beam melting. Pdf marangoni convection and fragmentation in laser treatment. In general, surface tension is a decreasing function of temperature. A critical marangoni number exists leading to cellullar patterns and, for realistic values of the permeability, it is proportional to the inverse of this last parameter. Marangoni convection and fragmentation in laser treatment. At and above the critical marangoni number m a c h t w, which is completely different from a critical marangoni number m a c m b for the onset of marangoni benard convection in section 22. Marangoni mixed convection flow with joule heating mafiadoc. In the mid1860s, marangoni found the phenomenon that the natural convection dominated by liquid gravity gradually disappeared in a microgravity environment, whereas at the interface of liquid. Use of a ctitious marangoni number for natural convection simulation francisco j. Theoretical analysis of marangoni convection was started with the linear analysis by pearson 1 who assumed. Modeling by using comsol of natural and combined natural marangoni convection flows in a low prandtl number material filled in a square mold. Marangoni convection in droplets on superhydrophobic surfaces.
It is defined by the marangoni number is defined as. Impact of the marangoni and thermal radiation convection. The marangoni effect is the flow of fluid caused by a gradient in surface tension 1,2. The governing equations are based on the equations involving the stream function, vorticity, and temperature.
Having established that marangoni convection is the dominant instability within the. Effect of internal heat generation on marangoni convection in a superposed fluidporous layer with deformable free surface. Impact of the marangoni and thermal radiation convection on the grapheneoxidewaterbased and ethyleneglycolbased nanofluids taza gul, waqas noman, muhammad sohail, and muhammad altaf khan advances in mechanical engineering 2019 11. A 3d transient finite element model of inconel 718 nickelbased superalloy processed by selective laser melting was developed to study the heat flux in the molten pool under the condition of different process parameters and its effect on the temperature field and the shape of molten pool, in which a solid heat transfer module and a laminar flow module in.
291 140 900 435 271 181 263 70 825 11 782 633 495 869 276 629 940 395 603 1240 126 444 222 1286 258 315 883 49 898 727 43 1057 635 36 139 513 528 203 452 870 645 860 945