Abstract
In a nonequilibrium multiphase system, the Marangoni effect has important influence on interphase heat and mass transfer induced by interfacial tension gradient associated with either solutal or thermal gradients in numerous applications. Although the basic knowledge of the Marangoni effect has made great progress, its mechanism is not yet fully recognized. An in-depth understanding of the basic principles of heat and mass transport induced by the Marangoni effect is important for better operation of interphase transfer units. This report aims to provide a systematic study of the mechanisms of the Marangoni effect. Special foci are concentrated on the field of material processing, which encompasses the process wherein the raw materials are transformed into useful engineering products. A series of experimental, theoretical, or simulated results are extracted from the literature to elucidate the mechanism of the Marangoni effect and to rationalize the interphase transport phenomena. We examine the major physical explanations and attempt to distinguish the working principle behind the process. Perspectives are also proposed to trigger further innovative thinking about the topics. This work provides new insight into material processing by taking advantage of the Marangoni effect and has far-reaching implications in the design of future nonequilibrium multiphase system.
Funding source: Natural Science Foundation of Anhui Province
Award Identifier / Grant number: 1408085QG138
Funding statement: The authors gratefully acknowledge the support of the National Science Foundation of China (51376008, 51306001, and 51576002) and the Natural Science Foundation of Anhui Province (1408085QG138).
Acknowledgments
The authors gratefully acknowledge the support of the National Science Foundation of China (51376008, 51306001, and 51576002) and the Natural Science Foundation of Anhui Province (1408085QG138).
References
Alhendal Y, Turan A, Hollingsworth P. Thermocapillary simulation of single bubble dynamics in zero gravity. Acta Astronaut 2013; 88: 108–115.10.1016/j.actaastro.2013.03.017Suche in Google Scholar
Andrey P, Michael B, Domnic M, Uwe T. Alternative pathways of dewetting for a thin liquid two-layer film. Phys Rev E Stat Nonlinear Soft Matter Phys 2004; 70: 188–206.10.1103/PhysRevE.70.025201Suche in Google Scholar
Andrey P, Michael B, Domnic M, Uwe T. Morphology changes in the evolution of liquid two-layer films. J Chem Phys 2005; 122: 4973–4978.Suche in Google Scholar
Armijo KM, Carey VP. An analytical and experimental study of heat pipe performance with a working fluid exhibiting strong concentration Marangoni effects. Int J Heat Mass Transfer 2013; 64: 70–78.10.1016/j.ijheatmasstransfer.2013.03.020Suche in Google Scholar
Bammou L, Omari KE, Blancher S, Guer YL, Benhamou B, Mediouni T. A numerical study of the longitudinal thermoconvective rolls in a mixed convection flow in a horizontal channel with a free surface. Int J Heat Fluid Flow 2013; 42: 265–277.10.1016/j.ijheatfluidflow.2013.01.017Suche in Google Scholar
Berthier A, Paillard P, Carin M, Valensi F, Pellerin S. TIG and A-TIG welding experimental investigations and comparison to simulation. Part 1: identification of Marangoni effect. Sci Technol Weld Join 2012; 17: 609–615.10.1179/1362171812Y.0000000024Suche in Google Scholar
Boeck T. Bénard-Marangoni convection at large Marangoni numbers: results of numerical simulations. Adv Space Res 2005; 36: 4–10.10.1016/j.asr.2005.02.083Suche in Google Scholar
Bormashenko ED, Pogreb R, Stanevsky O, Bormashenko Y, Stein T, Gengelman O. Mesoscopic patterning in evaporated polymer solutions: new experimental data and physical mechanisms. Langmuir 2005; 21: 9604–9609.10.1021/la0518492Suche in Google Scholar
Bormashenko ED, Pogreb R, Musin A, Stanevsky O, Bormashenko Y, Whyman G, Gendelman O, Barkay Z. Self-assembly in evaporated polymer solutions: influence of the solution concentration. J Colloid Interface Sci 2006; 297: 534–540.10.1016/j.jcis.2005.11.025Suche in Google Scholar
Bormashenko ED, Balter S, Pogreb R, Bormashenko Y, Gendelma OV, Aurbach D. On the mechanism of patterning in rapidly evaporated polymer solutions: is temperature-gradient-driven Marangoni instability responsible for the large-scale patterning? J Colloid Interface Sci 2010; 342: 602–607.10.1016/j.jcis.2009.12.005Suche in Google Scholar
Buzek J, Podkański J, Warmuziński K. The enhancement of the rate of absorption of CO2 in amine solutions due to the Marangoni effect. Energy Convers Manage 1997; 38: S69–S74.10.1016/S0196-8904(96)00248-8Suche in Google Scholar
Chen J, Peng J. Velocity of droplet with sorption-controlled surfactant in electrolyte solution. J Chem Ind Eng 2000; 51: 120–125.Suche in Google Scholar
Chen J, Wang Z, Yang C, Mao ZS. Numerical simulation of the solute-induced Marangoni effect with the semi-Lagrangian advection scheme. Chem Eng Technol 2015a; 38: 155–163.10.1002/ceat.201400354Suche in Google Scholar
Chen J, Yang C, Mao ZS. The interphase mass transfer in liquid-liquid systems with Marangoni effect. Eur Phys J Spec Top 2015b; 224: 389–399.10.1140/epjst/e2015-02368-0Suche in Google Scholar
Chen J, Zeng A, Yuan X. Dual-path Schlieren technique on interfacial turbulence phenomena in gas-liquid mass transfer. J Chem Ind Eng 2012; 63: 3040–3044.Suche in Google Scholar
Colinet P, Legros JC, Velarde MG. Nonlinear dynamics of surface-tension-driven instabilities. Berlin, Germany: Wiley-VCH Verlag Berlin GmbH, 2005.Suche in Google Scholar
Davis KE, Huang Y, Houchens BC. Three-dimensional simulations of instabilities in a Marangoni-driven, low Prandtl number liquid bridge with magnetic stabilization to verify linear stability theory. Eur Phys J Spec Top 2013; 219: 13–23.10.1140/epjst/e2013-01776-4Suche in Google Scholar
Dondlinger M, Margerit J, Dauby PC. Weakly nonlinear study of Marangoni instabilities in an evaporating liquid layer. J Colloid Interface Sci 2005; 283: 522–532.10.1016/j.jcis.2004.09.005Suche in Google Scholar PubMed
Dong WC, Lu SP, Li DZ, Li YQ. Numerical simulation of effects of the minor active-oxygen on the Marangoni convection and the weld shape. Acta Metall Sin 2008; 44: 249–256.Suche in Google Scholar
Doumenc F, Guerrier B. Self-patterning induced by a solutal Marangoni effect in a receding drying meniscus. Europhys Lett 2013; 103: 314–318.10.1209/0295-5075/103/14001Suche in Google Scholar
Fang H, Tian J, Zhang Q, Pan Y, Wang S. Study of melt convection and interface shape during sapphire crystal growth by Czochralski method. Int J Heat Mass Transfer 2012; 55: 8003–8009.10.1016/j.ijheatmasstransfer.2012.08.029Suche in Google Scholar
Gambaryan-Roisman T. Marangoni-induced deformation of evaporating liquid films on composite substrates. J Eng Math 2012; 1: 39–52.10.1007/s10665-011-9498-9Suche in Google Scholar
Ganesan S. Simulations of impinging droplets with surfactant-dependent dynamic contact angle. J Comput Phys 2015; 301: 178–200.10.1016/j.jcp.2015.08.026Suche in Google Scholar
Gennes PGD. Instabilities during the evaporation of a film: non-glassy polymer + volatile solvent. Eur Phys J E 2001; 6: 421–424.10.1007/s10189-001-8055-3Suche in Google Scholar
Gennes PGD. Solvent evaporation of spin cast films: “crust” effects. Eur Phys J E 2002; 7: 31–34.10.1140/epje/i200101169Suche in Google Scholar
Gerbeth G, Eckert K, Odenbach S. Electromagnetic flow control in metallurgy, crystal growth and electrochemistry. Eur Phys J Spec Top 2013; 220: 1–8.10.1140/epjst/e2013-01792-4Suche in Google Scholar
Gordeeva VY, Lyushnin AV. Influence of Marangoni instability on evaporation of the polar liquid film. Eur Phys J Spec Top 2013; 2191: 45–49.10.1140/epjst/e2013-01779-1Suche in Google Scholar
Grigoriev RO. Control of evaporatively driven instabilities of thin liquid films. Phys Fluids 2002; 14: 1895–1909.10.1063/1.1476304Suche in Google Scholar
Hamid RA, Arifin NM, Bakar NAA, Hamid B. Thermal diffusion and diffusion thermo effects on MHD thermosolutal Marangoni convection boundary layer flow over a permeable surface. J Appl Math 2012; s1: 2607–2645.10.1155/2012/750939Suche in Google Scholar
Hamimid S, Amroune A. Marangoni-Natural convection in liquid metals in the presence of a tilted magnetic field. Fluid Dyn Mater Process 2010; 6: 369–384.Suche in Google Scholar
Hashim I, Kechil SA. Active control of Marangoni instability in a fluid layer with temperature-dependent viscosity in a microgravity environment. Fluid Dyn Res 2009; 41: 730–742.10.1088/0169-5983/41/4/045504Suche in Google Scholar
Hu WQ, Ohta, AT. Aqueous droplet manipulation by optically induced Marangoni circulation. Microfluid Nanofluid 2011; 11: 307–316.10.1007/s10404-011-0797-2Suche in Google Scholar
Hu GH, Zhon ZW. Influences of Marangoni effect on solidification of curved interfaces with constant curvature. Appl Math Mech 2008; 29: 145–151.10.1007/s10483-008-0202-ySuche in Google Scholar
Isa SPM, Arifin NM, Nazar R, Saad MN. Effect of non-uniform temperature gradient and magnetic field on onset of Marangoni convection heated from below by a constant heat flux. Appl Math Mech 2010; 31: 797–804.10.1007/s10483-010-1314-zSuche in Google Scholar
Javadi A, Karbaschi M, Bastani D, Ferri JK, Kovalchuk VI, Kovalchuk NM, Javadi K, Milier R. Marangoni instabilities for convective mobile interfaces during drop exchange: experimental study and CFD simulation. Colloids Surf A Physicochem Eng Aspects 2014; 441: 846–854.10.1016/j.colsurfa.2012.10.032Suche in Google Scholar
Kim J, Yong KT, Chang KC. Effects of gas phase and additive properties on Marangoni instability for absorption process in a horizontal fluid layer. Int J Refrig 2004; 27: 140–149.10.1016/j.ijrefrig.2003.08.002Suche in Google Scholar
Köllner T, Schwarzenberger K, Eckert K, Boeck T. Multiscale structures in solutal Marangoni convection: three-dimensional simulations and supporting experiments. Phys Fluids 2013; 25: 092109-1-31.10.1063/1.4821536Suche in Google Scholar
Köllner T, Schwarzenberger K, Eckert K, Boeck T. Solutal Marangoni convection in a Hele-Shaw geometry: impact of orientation and gap width. Eur Phys J Spec Top 2015; 224: 261–276.10.1140/epjst/e2015-02358-2Suche in Google Scholar
Kozak R, Saghir Z, Viviani A. Marangoni convection in a liquid layer overlying a porous layer with evaporation at the free surface. Acta Astronaut 2004; 55: 189–197.10.1016/j.actaastro.2004.05.017Suche in Google Scholar
Kumacheva E, Li L, Winnik MA, Shinozaki DM, Cheng PC. Direct imaging of surface and bulk structures in solvent cast polymer blend films. Langmuir 1997; 13: 2483–2489.10.1021/la961089iSuche in Google Scholar
Kumar A, Roy S. Effect of three-dimensional melt pool convection on process characteristics during laser cladding. Comput Mater Sci 2009; 46: 495–506.10.1016/j.commatsci.2009.04.002Suche in Google Scholar
Lee SM, Kim SJ, Lee HG. Surface tension and temperature effect on entrapment of bubbles and particles in continuous casting of steel. J Iron Steel Res 2011; S2: 220–226.Suche in Google Scholar
Lei Y, Murakawa H. Numerical investigation of activity element on Marangoni flow and weld pool geometry. Chin J Mech Eng 1999; 35: 29–33.Suche in Google Scholar
Lei Y, Shi Y, Murakawa H. Analysis of weld pool surface velocity singularity induced by Marangoni force. J Xian Jiaotong Univ 1999; 33: 70–74.Suche in Google Scholar
Li M, Xu SA, Kumacheva E. Convection in polymeric fluids subjected to vertical temperature gradients. Macromolecules 2000; 33: 4972–4978.10.1021/ma992156tSuche in Google Scholar
Li L, Kang Q, Duan L, Hu L. Interface tension effect in two-layer Bénard-Marangoni convection. J Exp Fluid Mech 2009; 23: 5–9.Suche in Google Scholar
Li D, Lu S, Li D, Li Y. Tracer investigation of convection in weld pool under TIG welding process. Trans China Welding Inst 2011; 8: 45–158.Suche in Google Scholar
Li ZY, Liu LJ, Nan XH, Kakimoto K. Role of Marangoni tension effects on the melt convection in directional solidification process for multi-crystalline silicon ingots. J Cryst Growth 2012; 346: 40–44.10.1016/j.jcrysgro.2012.02.031Suche in Google Scholar
Li Z, Peng L, Li YR, Tu JY. Characteristics of convection in detached solidification on the ground. J Huazhong Univ Sci Technol Nat Sci Ed 2013; 41: 93–97.Suche in Google Scholar
Lin XP, Peng XF, Wang BX, Christopher DM. Influence of Marangoni flow on the melting process. Prog Nat Sci 1997; 7: 616–623.Suche in Google Scholar
Liu D, Guo YC, Lin WY. Surface tension gradients on mixing processes after coalescence of binary equal-sized droplets. Chin Phys Lett 2013; 30: 1–4.10.1088/0256-307X/30/7/074701Suche in Google Scholar
Malkin AY. Surface instabilities. Colloid J 2008; 70: 673–689.10.1134/S1061933X0806001XSuche in Google Scholar
Mao ZS, Chen J. Numerical simulation of the Marangoni effect on mass transfer to single slowly moving drops in the liquid-liquid system. Chem Eng Sci 2004; 59: 1815–1828.10.1016/j.ces.2004.01.035Suche in Google Scholar
Mao ZS, Lu P, Zhang GJ, Yang C. Numerical simulation of the Marangoni effect with interphase mass transfer between two planar liquid layers. Chin J Chem Eng 2008; 16: 161–170.10.1016/S1004-9541(08)60057-9Suche in Google Scholar
Mat NA, Arifin NM, Nazar, Ismail F, Pop I. Radiation effects on Marangoni convection boundary layer over a permeable surface. Meccanica 2013; 48: 83–89.10.1007/s11012-012-9585-7Suche in Google Scholar
Melnikov DE, Shevtsova VM, Legros JC. Effect of gravity on oscillatory Marangoni convection in half-zone formed by high Pr-number liquids. Adv Space Res 2005; 36: 43–47.10.1016/j.asr.2005.02.078Suche in Google Scholar
Mitov Z, Kumacheva E. Convection-induced patterns in phase-separating polymeric fluids. Phys Rev Lett 1998; 81: 3427–3430.10.1103/PhysRevLett.81.3427Suche in Google Scholar
Moatimid GM, Hassan MA. The Instability of an electrohydrodynamic viscous liquid micro-cylinder buried in a porous medium: effect of thermosolutal Marangoni convection. Math Probl Eng 2013; 20: 27–53.10.1155/2013/416562Suche in Google Scholar
Momin O, Shuja SZ, Yilbas BS. Laser heating of titanium and steel: phase change at the surface. Int J Thermal Sci 2012; 54: 230–241.10.1016/j.ijthermalsci.2011.12.003Suche in Google Scholar
Muhmood L, Viswanathan NN, Seetharaman S. Some investigations into the dynamic mass transfer at the slag-metal interface using sulfur: concept of interfacial velocity. Metallurg Mater Trans B Process Metallurg Mater Proces Sci 2011; 42: 460–470.10.1007/s11663-011-9482-9Suche in Google Scholar
Nanjundappa EC, Shivakumara IS, Arunkumar R. Bénard-Marangoni ferroconvection with magnetic field dependent viscosity. J Magnet Magnet Mater 2010; 322: 2256–2263.10.1016/j.jmmm.2010.02.021Suche in Google Scholar
Nanjundappa CE, Shivakumara IS, Arunkumar R. Onset of Bénard-Marangoni ferroconvection with internal heat generation. Microgravity Sci Technol 2011; 27: 29–39.10.1007/s12217-010-9218-5Suche in Google Scholar
Nanjundappa CE, Shivakumara IS, Shivakumara K. On the penetrative Bénard-Marangoni convection in a ferromagnetic fluid layer. Aerospace Sci Technol 2013; 27: 57–66.10.1016/j.ast.2012.06.007Suche in Google Scholar
Nepomnyashchy AA, Velarde MG, Colinet P. Interfacial phenomena and convection. New York: Chapman & Hall/CRC, 2002.10.1201/9781482296303Suche in Google Scholar
Nepomnyashchy AA, Simanovskii I, Legros JC. Interfacial convection in multilayer systems. New York: Springer, 2012.10.1007/978-0-387-87714-3Suche in Google Scholar
Peng XF, Lin XP, Lee DJ, Yan Y, Wang BX. Effects of initial molten pool and Marangoni flow on solid melting. Int J Heat Mass Transfer 2001; 44: 457–470.10.1016/S0017-9310(00)00070-3Suche in Google Scholar
Peng L, Li YR, Zeng DL. Effect of dynamic viscosity on Marangoni convection in liquid bridge with liquid encapsulation. J Chongqing Univ 2004; 27: 97–100.Suche in Google Scholar
Raghuram S, Raghavan V, Pope DN, Gogos G. Numerical study of Marangoni convection during transient evaporation of two-component droplet under forced convective environment. Int J Heat Mass Transfer 2012; 55: 7949–7957.10.1016/j.ijheatmasstransfer.2012.08.025Suche in Google Scholar
Rahni MT, Karbaschi M, Miller R. Computational methods for complex liquid-fluid interfaces. New York: CRC Press, 2015.10.1201/b19337Suche in Google Scholar
Sang IJ, Lee HS. The effect of Bénard-Marangoni convection on percolation threshold in amorphous polymer-multiwall carbon nanotube composites. Curr Appl Phys 2012; 12: 467–472.10.1016/j.cap.2011.08.002Suche in Google Scholar
Savino R, Cecere A, Paola RD. Surface tension-driven flow in wickless heat pipes with self-rewetting fluids. Int J Heat Fluid Flow 2009; 30: 380–388.10.1016/j.ijheatfluidflow.2009.01.009Suche in Google Scholar
Schwarzenberger K, Köllner T, Linde H, Boeck T, Odenbach S, Eckert K. Pattern formation and mass transfer under stationary solutal Marangoni instability. Adv Colloid Interface Sci 2014; 206: 344–371.10.1016/j.cis.2013.10.003Suche in Google Scholar PubMed
Sha Y, Cheng H. Sun Z, Guo YU, Wang Y, Zhang Z. Observation of Rayleigh-Bénard-Marangoni flow patterns in mass transfer by the laser Schlieren device. J Tianjin Univ 2002; 35: 155–158.Suche in Google Scholar
Shivakumara IS, Suma SP, Indira R, Gangadharaiah YH. Effect of internal heat generation on the onset of Marangoni convection in a fluid layer overlying a layer of an anisotropic porous medium. Transport Porous Media 2012; 92: 727–743.10.1007/s11242-011-9930-7Suche in Google Scholar
Slavtchev S, Mendes MA. Marangoni instability in binary liquid-liquid systems. Int J Heat Mass Transfer 2004; 47: 3269–3278.10.1016/j.ijheatmasstransfer.2004.02.003Suche in Google Scholar
Son G. Numerical simulation of particle-laden droplet evaporation with the Marangoni effect. Eur Phys J Spec Top 2015; 224: 401–413.10.1140/epjst/e2015-02369-ySuche in Google Scholar
Tam D, Arnim VV, Mckinley GH, Hosoi AE. Marangoni convection in droplets on superhydrophobic surfaces. J Fluid Mech 2009; 624: 101–123.10.1017/S0022112008005053Suche in Google Scholar
Tang JW, Fan JY, Lan P, Li YR. Numerical simulation of thermocapillary-buoyancy convection in detached solidification. Microgravity Sci Technol 2010; 22: 171–177.10.1007/s12217-009-9171-3Suche in Google Scholar
Tang Z, Zhan B, Zhang S, Zhang H, Yuan X. Microconvection phenomena accompanying CO2 desorption from nanofluids. J Chem Ind Eng 2012; 63: 1691–1696.Suche in Google Scholar
Tang J, Zhu G, Sun L. Microbubble emission boiling in subcooled pool boiling and the role of Marangoni convection in its formation. Exp Thermal Fluid Sci 2013; 50: 97–106.10.1016/j.expthermflusci.2013.05.009Suche in Google Scholar
Trouette B, Chénier E, Delcarte C, Guerrier B. Numerical study of convection induced by evaporation in cylindrical geometry. Eur Phys J Spec Top 2011; 192: 83–93.10.1140/epjst/e2011-01362-xSuche in Google Scholar
Velarde MG, Zeytounian RK. Interfacial phenomena and the Marangoni effect. New York: Springer, 2002.10.1007/978-3-7091-2550-2Suche in Google Scholar
Wang JF, Yang C, Mao ZS. Numerical simulation of Marangoni effects of single drops induced by interphase mass transfer in liquid-liquid extraction systems by the level set method. Sci China 2008; 51: 684–694.10.1007/s11426-008-0012-9Suche in Google Scholar
Wang J, Yan J, Li Y, Hu S. Experimental investigation of Marangoni condensation of ethanol-water mixture vapors on vertical tube. Heat Mass Transfer 2009; 45: 1533–1541.10.1007/s00231-009-0528-3Suche in Google Scholar
Wang S, Li C, Ye X. Spreading of a liquid drop containing insoluble surfactant driven by thermocapillary. Proc CSEE 2011a; 31: 63–70.Suche in Google Scholar
Wang Z, Lu P, Zhang G, Yong Y, Yang C, Mao ZS. Experimental investigation of Marangoni effect in 1-hexanol/water system. Chem Eng Sci 2011b; 66: 2883–2887.10.1016/j.ces.2011.03.048Suche in Google Scholar
Wang F, Peng L, Zhang QZ, Liu J. Effect of the vertical heat transfer on the thermocapillary convection in a shallow annular pool. Microgravity Sci Technol 2015; 27: 107–114.10.1007/s12217-015-9415-3Suche in Google Scholar
Warmuziński K, Tańczyk M. Marangoni instability during the absorption of carbon dioxide into aqueous solutions of monoethanolamine. Chem Eng Process Process Intensif 1991a; 30: 113–121.10.1016/0255-2701(91)80018-KSuche in Google Scholar
Warmuziński K, Tańczyk M. Oscillatory Marangoni instability during absorption accompanied by chemical reaction. Chem Eng Sci 1991b; 46: 2031–2039.10.1016/0009-2509(91)80162-RSuche in Google Scholar
Warmuziński K, Buzek J, Podkański J. Marangoni instability during absorption accompanied by chemical reaction. Chem Eng J Biochem Eng J 1995; 58: 151–160.10.1016/0923-0467(94)02944-XSuche in Google Scholar
Wegener M, Fevre M, Paschedag AR, Kraume M. Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets. Int J Heat Mass Transfer 2009a; 52: 2543–2551.10.1016/j.ijheatmasstransfer.2008.11.022Suche in Google Scholar
Wegener M, Paschedag AR, Kraume M. Mass transfer enhancement through Marangoni instabilities during single drop formation. Int J Heat Mass Transfer 2009b; 52: 2673–2677.10.1016/j.ijheatmasstransfer.2009.01.005Suche in Google Scholar
Weh L. Surface structures in thin polymer layers caused by coupling of diffusion-controlled Marangoni instability and local horizontal temperature gradient. Macromol Mater Eng 2005; 290: 976–986.10.1002/mame.200500165Suche in Google Scholar
Wi HS, Cingarapu S, Klabunde KJ, Sorenden CM, Law BM. Observation of nanoparticle-enhanced Marangoni transport near a freezing out front. J Phys Chem C 2012; 116: 6052–6057.10.1021/jp211691qSuche in Google Scholar
Xu B, Wang H, Xu G, Xu C, Zhang Z. Numerical modeling of laser-induced molten pool for laser interaction with metal material. J Jiangsu Univ 2010; 313: 358–362.Suche in Google Scholar
Yang C, Mao ZS. Numerical simulation of interphase mass transfer with the level set approach. Chem Eng Sci 2005; 60: 2643–2660.10.1016/j.ces.2004.11.054Suche in Google Scholar
Yang L, Peng X. Numerically modeling and characteristics of molten pool during laser processing. J Basic Sci Eng 2001; 9: 215–221.Suche in Google Scholar
Yang Y, Zhen K, Yan J, Liu J, Hu S. Marangoni condensation heat transfer for binary mixture vapor at different vapor pressures. J Chem Ind Eng 2006; 57: 2816–2822.Suche in Google Scholar
Yao L, Zeng Z, Zhang YX. Effects of transverse rotating magnetic field on thermocapillary flow under microgravity. J Chongqing Univ 2012; 35: 115–120.Suche in Google Scholar
Ye XH, Chen X. Three-dimensional modelling of heat transfer and fluid flow in laser full-penetration welding. J Phys D Appl Phys 2002; 35: 1049–1056.10.1088/0022-3727/35/10/313Suche in Google Scholar
Yiantsios SG, Serpetsi SK, Doumenc F, Guerrier B. Surface deformation and film corrugation during drying of polymer solutions induced by Marangoni phenomena. Int J Heat Mass Transfer 2015; 89: 1083–1094.10.1016/j.ijheatmasstransfer.2015.06.015Suche in Google Scholar
Yin H, Emi T. Marangoni flow at the gas/melt interface of steel. Metallurg Mater Trans B Process Metallurg Mater Proces Sci 2003; 34: 483–493.10.1007/s11663-003-0015-zSuche in Google Scholar
Yoshimune N, Shigeki C, Eri S, Hiroyuki M. Anomalous spreading with Marangoni flow on agar gel surfaces. Langmuir 2012; 28: 3799–3806.10.1021/la2049597Suche in Google Scholar PubMed
Zhang Y, Zheng LC. Analysis of MHD thermosolutal Marangoni convection with the heat generation and a first-order chemical reaction. Chem Eng Sci 2012; 69: 449–455.10.1016/j.ces.2011.10.069Suche in Google Scholar
Zhang F, Zhao X, Geng J, Wu Y, Zhang Z. A new insight into Marangoni effect in non-isothermal falling liquid films. Exp Thermal Fluid Sci 2007; 31: 361–365.10.1016/j.expthermflusci.2006.05.008Suche in Google Scholar
Zhang Y, Zheng L, Wang X, Song G. Analysis of Marangoni convection of non-Newtonian power law fluids with linear temperature distribution. Thermal Sci 2011; 15: 45–52.10.2298/TSCI11S1045ZSuche in Google Scholar
Zhao S, Liu Q. Marangoni instability in vertically inhomogeneous porous media. Chin J Space Sci 2008; 8: 33–37.10.11728/cjss2008.01.033Suche in Google Scholar
Zhao G, Pumera M. Liquid-liquid interface motion of a capsule motor powered by the interlayer Marangoni effect. J Phys Chem B 2012; 116: 10960–10963.10.1021/jp3057702Suche in Google Scholar PubMed
Zhao X, Zhang Z. Characteristic of the threshold of Marangoni effect on heated falling film. Chem Ind Times 2010; 24: 1–6.Suche in Google Scholar
Zhao CX, Kwakernaak C, Pan Y, Richardson IM, Saldi Z, Kenjeres S. The effect of oxygen on transitional Marangoni flow in laser spot welding. Acta Mater 2010; 58: 6345–6357.10.1016/j.actamat.2010.07.056Suche in Google Scholar
Zheng L, Lin Y, Zhang X. Marangoni convection of power law fluids driven by power-law temperature gradient. J Franklin Inst 2012; 349: 2585–2597.10.1016/j.jfranklin.2012.07.004Suche in Google Scholar
Zhou X, Huai X. Thermosolutocapillary convection in an open rectangular cavity with dynamic free surface. J Heat Transfer 2015; 137: 082901-1-9.10.1115/1.4029270Suche in Google Scholar
Zhou X, Huang H. Numerical simulation of steady thermocapillary convection in a two-layer system using level set method. Microgravity Sci Technol 2010; 22: 223–232.10.1007/s12217-010-9178-9Suche in Google Scholar
Zhou B, Liu Q, Tang Z. Rayleigh-Bénard-Marangoni instability in two-layer fluid system. Acta Mech Sin 2004; 20: 366–373.10.1007/BF02489374Suche in Google Scholar
Zhu Z, Chen S, Liu Q, Tong S. Experimental investigation and simulation on the Marangoni convection in a binary mixture. Chin J Theor Appl Mech 2011; 43: 674–679.Suche in Google Scholar
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Artikel in diesem Heft
- Frontmatter
- In this issue
- A critical analysis on palm kernel shell from oil palm industry as a feedstock for solid char production
- Survey of supercritical fluid techniques for producing drug delivery systems for a potential use in cancer therapy
- Electroconductive and electroresponsive membranes for water treatment
- Marangoni effect in nonequilibrium multiphase system of material processing
Artikel in diesem Heft
- Frontmatter
- In this issue
- A critical analysis on palm kernel shell from oil palm industry as a feedstock for solid char production
- Survey of supercritical fluid techniques for producing drug delivery systems for a potential use in cancer therapy
- Electroconductive and electroresponsive membranes for water treatment
- Marangoni effect in nonequilibrium multiphase system of material processing