Abstract
Evaporation characteristics of working fluid in capillaries are of great significance for high efficiency of heat transfer system. Currently, numerous works have been done mainly focusing on the macro-convection behavior of fluid in capillary tubes considering constant shapes of meniscus. The effects of the natural evaporation with meniscus shape evolution on the convection and temperature distribution are still quite insufficient. Thus, the present paper aims to experimentally investigate the Marangoni convection in thin films during ethanol natural evaporation in a capillary tube with the evolution of different meniscus shapes. The flow pattern and interfacial temperature distribution of Marangoni convection were measured by means of the infrared camera and μPIV, respectively, through focal plane in both horizontal and vertical views. The capillary tube was made of quartz glass with an inner diameter of 1 mm. As a result, the Marangoni macro-flow of ethanol in the capillary presents 2 symmetrical and opposite vortices flowing from center to edge along with the interface on the horizontal cross-section. On the vertical cross-section, a single clockwise vortex appears in convex and flat cases. However, in the case of concave liquid surface, the single clockwise vortex can be broken affected by the gravity, and another small vortex generates intermittently with the time ratio of 2:1. In addition to the experimental work, theoretical analysis was conducted to validation the effects of different meniscus shapes on Marangoni convection, and a good agreement has been achieved qualitatively.
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Abbreviations
- T :
-
Temperature (℃)
- P :
-
Total pressure in the gas phase (N/m2)
- C p :
-
Specific heat capacity (J/kg K)
- θ :
-
Contact angle during evaporation (°)
- μ :
-
Dynamic viscosity (N s/m2)
- ρ :
-
Density (kg/m3)
- κ :
-
Thermal conductivity (W/m K)
- σ :
-
Surface tension coefficient (N/m)
- U :
-
Vertical velocity components (m/s)
- d :
-
Diameter (mm)
- g :
-
Gravitational acceleration (m/s2)
- R :
-
Capillary radius (mm)
- ▽ T :
-
Thermal gradient (K/m)
- \(\frac{\partial \sigma }{{\partial T}}\) :
-
Partial derivative of the surface tension with temperature (mJ/m2 k)
- τ:
-
Time scale(s)
- a:
-
Air
- l:
-
Liquid
- w:
-
Wall
- P:
-
Particles
- conv:
-
Convection
- diff:
-
Diffusion
- Ma:
-
Marangoni number
References
Bennacer R, Sefiane K, El-Ganaoui M, Buffone C (2004) Numerical investigation of the role of non-uniform evaporation rate in initiating marangoni convection in capillary tubes. Int J Numer Method H 14(7):879–892. https://doi.org/10.1108/09615530410546281
Buffone C, Sefiane K (2004) IR measurements of interfacial temperature during phase change in a confined environment. Exp Therm Fluid Sci 29(1):65–74. https://doi.org/10.1016/j.expthermflusci.2004.02.004
Buffone C, Sefiane K, Bennacer R, Liu B (2017) Effect of external convection on evaporating cooling for a volatile meniscus. Exp Therm Fluid Sci 89:181–188. https://doi.org/10.1016/j.expthermflusci.2017a.08.006Get
Buffone C, Sefiane K, Christy J (2017) Infra-Red measurements of an evaporating meniscus with imposed contact angle. Int J Therm Sci 121:89–98. https://doi.org/10.1016/j.ijthermalsci.2017b.07.005
Buffone C, Sefiane K, Easson W (2005) Marangoni-driven instabilities of an evaporating liquid-vapor interface. Phys Rev E 71:5. https://doi.org/10.1103/PhysRevE.71.056302
Buffone C, Minetti C, Boussemaere L, Roudgar M, De Coninck J (2014) Marangoni convection in evaporating meniscus with changing contact angle. Exp Fluids 55(10):1833. https://doi.org/10.1007/s00348-014-1833-2
Buffone C (2004) An experimental and numerical investigation of thermocapillary driven phenomena for evaporating menisci in capillary tubes related to microelectronics cooling. The University of Edinburgh (United Kingdom).
Chamarthy P, Dhavaleswarapu HK, Garimella SV, Murthy JY, Wereley ST (2008) Visualization of convection patterns near an evaporating meniscus using μPIV. Exp Fluids 44(3):431–438. https://doi.org/10.1007/s00348-007-0376-1
Cook R, Tung C, Wayner P Jr (1981) Use of scanning microphotometer to determine the evaporative heat transfer characteristics of the contact line region. J Heat Transfer 103(2):325–330. https://doi.org/10.1115/1.3244461
DasGupta S, Schonberg J, Wayner P Jr (1993) Investigation of an evaporating extended meniscus based on the augmented young-laplace equation. J Heat Transfer 115(1):201–208. https://doi.org/10.1115/1.2910649
Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR, Witten TA (2000) Contact line deposits in an evaporating drop. Phys Rev E 62:756–765. https://doi.org/10.1103/physreve.62.756
Dhavaleswarapu HK, Murthy JY, Garimella SV (2012) Numerical investigation of an evaporating meniscus in a channel. Int J Heat Mass Transf 55(4):915–924. https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.017
Gazzola D, Franchi Scarselli E, Guerrieri R (2009) 3D visualization of convection patterns in lab-on-chip with open microfluidic outlet. Microfluid Nanofluid 7(5):659–668. https://doi.org/10.1007/s10404-009-0426-5
Höhmann C, Stephan P (2002) Microscale temperature measurement at an evaporating liquid meniscus. Exp Therm Fluid Sci 26(2–4):157–162. https://doi.org/10.1016/S0894-1777(02)00122-X
Kazemi MA, Nobes DS, Elliott JAW (2017) Experimental and numerical study of the evaporation of water at low pressures. Langmuir 33(18):4578–4591. https://doi.org/10.1021/acs.langmuir.7b00616
Kim M, Kaviany M (2017) Multi-artery heat-pipe spreader: monolayer-wick receding meniscus transitions and optimal performance. Int J Heat Mass Transf 112:343–353. https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.131
Kim SH, Wang T, Zhang L, Jiang YY, Li ZG (2019) Micro-particle image velocimetry visualization study of thermal buoyant-marangoni flow in microtubes. Int J Heat Mass Transf 137:765–774. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.126
Medici EF, Allen JS (2013) Evaporation, two phase flow, and thermal transport in porous media with application to low-temperature fuel cells. Int J Heat Mass Transf 65:779–788. https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.035
Miller C A, P Neogi (2007) Interfacial phenomena: equilibrium and dynamic effects (2nd Edition), CRC Press. https://doi.org/10.1002/aic.11631
Molenkamp, T (1998) Marangoni convection, mass transfer and microgravity. Groningen.
Morris SJS (2003) The evaporating meniscus in a channel. J Fluid Mech 494:297–317. https://doi.org/10.1017/S0022112003006153
Pan Z, Wang H (2010) Symmetry-to-asymmetry transition of Marangoni flow at a convex volatizing meniscus. Microfluid Nanofluid 9(4–5):657–669. https://doi.org/10.1007/s10404-010-0579-2
Potash M Jr, Wayner P Jr (1972) Evaporation from a two-dimensional extended meniscus. Int J Heat Mass Transf 15(10):1851–1863. https://doi.org/10.1016/0017-9310(72)90058-0
Pratt DM, Brown JR, Hallinan KP (1998) Thermocapillary effects on the stability of a heated, curved meniscus. J Heat Transfer 120(1):220–226. https://doi.org/10.1115/1.2830045
Preiss G, Wayner P Jr (1976) Evaporation from a capillary tube. J Heat Transfer 98(2):178–181. https://doi.org/10.1115/1.3450515
Qu W, Ma TZ, Miao JY, Wang JL (2002) Effects of radius and heat transfer on the profile of evaporating thin liquid film and meniscus in capillary tubes. Int J Heat Mass Transf 45(9):1879–1887. https://doi.org/10.1016/S0017-9310(01)00296-4
Raffel M, Willert CE, Kompenhans J (1998) Particle image velocimetry: a practical guide. Springer. https://doi.org/10.1007/978-3-319-68852-7
Rusanov AI, Krotov VV (2000) Capillary effects of surfactants at curved interfaces. Adv Colloid Interface Sci 85(1):35–59. https://doi.org/10.1016/S0001-8686(99)00024-X
Sefiane K, Snodgrass M, Steinchen A (2004) Evaporation self-induced Marangoni motion in fed capillaries for volatile liquids in open air. J Non-Equil Thermody 29:2. https://doi.org/10.1515/JNETDY.2004.011
Sefiane K, Steinchen A (2002) On the thermocapillary effects in the evaporation of a meniscus from a capillary tube. Heat Tranf Conf. Begel House Inc., Int. https://doi.org/10.1615/IHTC12.2510
Steinchen A, Sefiane K (2005) Self-organised marangoni motion at evaporating drops or in capillary menisci—thermohydrodynamical model. J Non-Equil Thermody 30(1):39–51. https://doi.org/10.1515/JNETDY.2005.003
Tang YC, Min JC, Zhang X, Liu GL (2018) Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries. Chin J Chem Eng 26(10):2014–2022. https://doi.org/10.1016/j.cjche.2018.04.031
Wayner P Jr, Kao Y, LaCroix L (1976) The interline heat-transfer coefficient of an evaporating wetting film. Int J Heat Mass Transf 19(5):487–492. https://doi.org/10.1016/0017-9310(76)90161-7
Wong H, Morris S, Radke C (1992) Three-dimensional menisci in polygonal capillaries. J Colloid Interface Sci 148(2):317–336. https://doi.org/10.1016/0021-9797(92)90171-H
Acknowledgements
Support from CMSA and ESA (TGMTYY00-RW-03) supported by the Integrated Projects utilizing the Space Environment on ISS and CSS, the Open Fund Project of the Key Laboratory of Agricultural Products Storage and Preservation of the Ministry of Agriculture and Rural Affairs (Kf2021004), and the Tianjin Research Innovation Project for Postgraduate Students (2021YJSS292) is gratefully acknowledged.
Funding
The work of Bin Liu was supported by Integrated Projects utilizing the Space Environment on ISS and CSS, under Grant TGMTYY00-RW-03, the work of Aiqiang Chen was supported by The Open Fund Project of the Key Laboratory of Agricultural Products Storage and Preservation of the Ministry of Agriculture and Rural Affairs, under Grant Kf2021004, and the work of Haoyan Zhang was supported by Tianjin Research Innovation Project for Postgraduate Students, under Grant 2021YJSS292.
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AC: methodology, review, funding acquisition, and supervision; HZ: data curation, and writing—review and editing; JS: review; CZ: investigation, formal analysis, and visualization; BL: funding acquisition; JY: funding acquisition. All authors read and approved the final manuscript.
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Chen, A., Zhang, H., Song, J. et al. Marangoni convection analysis during ethanol natural evaporation in a capillary tube. Microfluid Nanofluid 26, 98 (2022). https://doi.org/10.1007/s10404-022-02597-1
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DOI: https://doi.org/10.1007/s10404-022-02597-1