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The effect of phase change on stability of convective flow in a layer of volatile liquid driven by a horizontal temperature gradient

Published online by Cambridge University Press:  12 January 2018

Roman O. Grigoriev Open the ORCID record for Roman O. Grigoriev [Opens in a new window]  and
Tongran Qin
Roman O. Grigoriev*
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Tongran Qin
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
*
†Email address for correspondence: romgrig@gatech.edu
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Abstract

Buoyancy–thermocapillary convection in a layer of volatile liquid driven by a horizontal temperature gradient arises in a variety of situations. Recent studies have shown that the composition of the gas phase, which is typically a mixture of vapour and air, has a noticeable effect on the critical Marangoni number describing the onset of convection as well as on the observed convection pattern. Specifically, as the total pressure or, equivalently, the average concentration of air is decreased, the threshold of the instability leading to the emergence of convective rolls is found to increase rather significantly. We present a linear stability analysis of the problem which shows that this trend can be readily understood by considering the transport of heat and vapour through the gas phase. In particular, we show that transport in the gas phase has a noticeable effect even at atmospheric conditions, when phase change is greatly suppressed.

JFM classification

Instability: Absolute/convective instability Phase change: Condensation/evaporation Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 248 - 283
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Copyright
© 2018 Cambridge University Press 

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References

Ban Hadid, H. & Roux, B. 1990 Thermocapillary convection in long horizontal layers of low-Prandtl-number melts subject to a horizontal temperature gradient. J. Fluid Mech. 221, 77–103.Google Scholar
Ben Hadid, H. & Roux, B. 1992 Buoyancy- and thermocapillary-driven flows in differentially heated cavities for low-Prandtl-number fluids. J. Fluid Mech. 235, 1–36.Google Scholar
Birikh, R. V. 1966 Thermocapillary convection in a horizontal layer of liquid. Trans. ASME J. Appl. Mech. Tech. Phys. 7, 43–44.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Burguete, J., Mukolobwiez, N., Daviaud, F., Garnier, N. & Chiffaudel, A. 2001 Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient. Phys. Fluids 13, 2773–2787.Google Scholar
Chan, C. L. & Chen, C. F. 2010 Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer. J. Fluid Mech. 647, 91–103.CrossRefGoogle Scholar
Chauvet, F., Dehaeck, S. & Colinet, P. 2012 Threshold of Benard–Marangoni instability in drying liquid films. Europhys. Lett. 99, 34001.Google Scholar
Cross, M. C. & Greenside, H. 2009 Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press.Google Scholar
Daviaud, F. & Vince, J. M. 1993 Traveling waves in a fluid layer subjected to a horizontal temperature gradient. Phys. Rev. E 48, 4432–4436.Google Scholar
De Saedeleer, C., Garcimartín, A., Chavepeyer, G., Platten, J. K. & Lebon, G. 1996 The instability of a liquid layer heated from the side when the upper surface is open to air. Phys. Fluids 8, 670–676.CrossRefGoogle Scholar
Garcimartín, A., Mukolobwiez, N. & Daviaud, F. 1997 Origin of waves in surface-tension-driven convection. Phys. Rev. E 56, 1699–1705.Google Scholar
Ha, J. M. & Peterson, G. P. 1994 Analytical prediction of the axial dryout point for evaporating liquids in triangular microgrooves. ASME J. Heat Transfer 116, 498–503.Google Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 159–229. Cambridge University Press.Google Scholar
Ji, Y., Liu, Q.-S. & Liu, R. 2008 Coupling of evaporation and thermocapillary convection in a liquid layer with mass and heat exchanging interface. Chin. Phys. Lett. 25, 608–611.Google Scholar
Kavehpour, P., Ovryn, B. & McKinley, G. H. 2002 Evaporatively-driven Marangoni instabilities of volatile liquid films spreading on thermally conductive substrates. Colloids Surf. A 206, 409–423.Google Scholar
Kirdyashkin, A. G. 1984 Thermogravitational and thermocapillary flows in a horizontal liquid layer under the conditions of a horizontal temperature gradient. Intl J. Heat Mass Transfer 27, 1205–1218.Google Scholar
Klentzman, J. & Ajaev, V. S. 2009 The effect of evaporation on fingering instabilities. Phys. Fluids 21, 122101.Google Scholar
Li, Y., Grigoriev, R. O. & Yoda, M. 2014 Experimental study of the effect of noncondensables on buoyancy-thermocapillary convection in a volatile low-viscosity silicone oil. Phys. Fluids 26, 122112.Google Scholar
Li, Y.-R., Zhang, H.-R., Wu, C.-M. & Xu, J.-L. 2012 Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity. Heat Mass Transfer 48, 241–251.CrossRefGoogle Scholar
Lu, X. & Zhuang, L. 1998 Numerical study of buoyancy- and thermocapillary-driven flows in a cavity. Acta Mechanica Sin. 14, 130–138.Google Scholar
Markos, M., Ajaev, V. S. & Homsy, G. M. 2006 Steady flow and evaporation of a volatile liquid in a wedge. Phys. Fluids 18, 092102.Google Scholar
Mercier, J. & Normand, C. 2002 Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows. Intl J. Heat Mass Transfer 45, 793–801.Google Scholar
Mercier, J. F. & Normand, C. 1996 Buoyant-thermocapillary instabilities of differentially heated liquid layers. Phys. Fluids 8, 1433–1445.Google Scholar
Mundrane, M. & Zebib, A. 1994 Oscillatory buoyant thermocapillary flow. Phys. Fluids 6, 3294–3306.Google Scholar
Normand, C., Pomeau, Y. & Velarde, M. 1977 Convective instability: a physicist’s approach. Rev. Mod. Phys. 49, 581–624.Google Scholar
Parmentier, P. M., Regnier, V. C. & Lebon, G. 1993 Buoyant-thermocapillary instabilities in medium-Prandtl-number fluid layers subject to a horizontal gradient. Intl J. Heat Mass Transfer 36, 2417–2427.Google Scholar
Priede, J. & Gerbeth, G. 1997 Convective, absolute, and global instabilities of thermocapillary-buoyancy convection in extended layers. Phys. Rev. E 56, 4187–4199.Google Scholar
Qin, T. & Grigoriev, R. O. 2015 The effect of noncondensables on buoyancy-thermocapillary convection of volatile fluids in confined geometries. Intl J. Heat Mass Transfer 90, 678–688.CrossRefGoogle Scholar
Qin, T., Tuković, Z̆. & Grigoriev, R. O. 2014 Buoyancy-thermocapillary convection of volatile fluids under atmospheric conditions. Intl J. Heat Mass Transfer 75, 284–301.CrossRefGoogle Scholar
Qin, T., Tuković, Z̆. & Grigoriev, R. O. 2015 Buoyancy-thermocapillary convection of volatile fluids under their vapors. Intl J. Heat Mass Transfer 80, 38–49.CrossRefGoogle Scholar
Riley, R. J. & Neitzel, G. P. 1998 Instability of thermocapillarybuoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. J. Fluid Mech. 359, 143–164.Google Scholar
Schatz, M. F. & Neitzel, G. P. 2001 Experiments on thermocapillary instabilities. Annu. Rev. Fluid Mech. 33, 93–127.Google Scholar
Schrage, R. W. 1953 A Theoretical Study of Interface Mass Transfer. Columbia University Press.Google Scholar
Shevtsova, V. M. & Legros, J. C. 2003 Instability in thin layer of liquid confined between rigid walls at different temperatures. Acta Astron. 52, 541–549.Google Scholar
Shevtsova, V. M., Nepomnyashchy, A. A. & Legros, J. C. 2003 Thermocapillary-buoyancy convection in a shallow cavity heated from the side. Phys. Rev. E 67, 066308.Google Scholar
Smith, M. K. & Davis, S. H. 1983a Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. J. Fluid Mech. 132, 119–144.Google Scholar
Smith, M. K. & Davis, S. H. 1983b Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities. J. Fluid Mech. 132, 145–162.Google Scholar
Suman, B. & Kumar, P. 2005 An analytical model for fluid flow and heat transfer in a micro-heat pipe of polygonal shape. Intl J. Heat Mass Transfer 48, 4498–4509.Google Scholar
Villers, D. & Platten, J. K. 1987 Separation of marangoni convection from gravitational convection in earth experiments. Phys. Chem. Hydrodyn. 8, 173–183.Google Scholar
Villers, D. & Platten, J. K. 1992 Coupled buoyancy and marangoni convection in acetone: experiments and comparison with numerical simulations. J. Fluid Mech. 234, 487–510.CrossRefGoogle Scholar
Yaws, C. L. 2003 Yaws’ Handbook of Thermodynamic and Physical Properties of Chemical Compounds (Electronic Edition): Physical, Thermodynamic and Transport Properties for 5,000 Organic Chemical Compounds. Knovel.Google Scholar
Yaws, C. L. 2009 Yaws’ Thermophysical Properties of Chemicals and Hydrocarbons (Electronic Edition). Knovel.Google Scholar