Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T09:37:39.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Contact-line singularities resolved exclusively by the Kelvin effect: volatile liquids in air

Published online by Cambridge University Press:  12 November 2018

A. Y. Rednikov Open the ORCID record for A. Y. Rednikov [Opens in a new window]  and
P. Colinet
A. Y. Rednikov*
Affiliation:
Université Libre de Bruxelles, TIPs Laboratory, CP 165/67, 1050 Brussels, Belgium
P. Colinet*
Affiliation:
Université Libre de Bruxelles, TIPs Laboratory, CP 165/67, 1050 Brussels, Belgium
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The contact line of a volatile liquid on a flat substrate is studied theoretically. We show that a remarkable result obtained for a pure-vapour atmosphere (Phys. Rev. E, vol. 87, 2013, 010401) also holds for an isothermal diffusion-limited vapour exchange with air. Namely, for both zero and finite Young’s angles, the motion- and phase-change-related contact-line singularities can in principle be regularised solely by the Kelvin effect (curvature dependence of saturation conditions). The latter prevents the curvature from diverging and rather leads to its versatile self-adjustment. To illustrate the point, the problem is resolved for a distinguished vicinity of the contact line (‘microregion’) in a ‘minimalist’ way, i.e. without any disjoining pressure, precursor film, Navier slip or any other microphysics. This also leads to the determination of the ‘Kelvin-only’ evaporation- and motion-induced apparent contact angles. With the Kelvin-only microscales actually turning out to be quite nanoscopic, other microphysics effects may nonetheless interfere too in reality. The Kelvin-only results will then yield a limiting case within such a more general formulation.

JFM classification

Phase change: Condensation/evaporation Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 881 - 916
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ajaev, V. S. 2005 Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528, 279–296.Google Scholar
Ajaev, V. S., Gambaryan-Roisman, T. & Stephan, P. 2010 Static and dynamic contact angles of evaporating liquids on heated surfaces. J. Colloid Interface Sci. 342, 550–558.Google Scholar
Berteloot, G., Pham, C.-T., Daerr, A., Lequeux, F. & Limat, L. 2008 Evaporation-induced flow near a contact line: consequences on coating and contact angle. Europhys. Lett. 83, 14003.Google Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739–805.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Effect of solid properties and contact angle in dropwise condensation and evaporation. J. Fluid Mech. 195, 463–494.Google Scholar
Colinet, P. & Rednikov, A. 2011 On integrable singularities and apparent contact angles within a classical paradigm. Partial and complete wetting regimes with or without phase change. Eur. Phys. J. (Special Topics) 197, 89–113.Google Scholar
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flows. J. Fluid Mech. 168, 169–194.Google Scholar
DasGupta, S., Kim, I. Y. & Wayner, P. C. 1994 Use of the Kelvin–Clapeyron equation to model an evaporating curved microfilm. Trans. ASME J. Heat Transfer 116 (4), 1007–1015.Google Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827–829.Google Scholar
Dehaeck, S., Rednikov, A. & Colinet, P. 2014 Vapor-based interferometric measurement of local evaporation rate and interfacial temperature of evaporating droplets. Langmuir 30, 2002–2008.Google Scholar
Derjaguin, B. V., Churaev, N. V. & Muller, V. M. 1987 Surface Forces. Consultants Bureau.Google Scholar
Doumenc, F. & Guerrier, B. 2011 A model coupling the liquid and gas phases for a totally wetting evaporative meniscus. Eur. Phys. J. (Special Topics) 197, 281–293.Google Scholar
Doumenc, F. & Guerrier, B. 2013 Numerical simulation of an evaporative meniscus on a moving substrate. Eur. Phys. J. (Special Topics) 219, 25–31.Google Scholar
Duffy, B. R. & Wilson, S. K. 1997 A third-order differential equation arising in thin-film flows and relevant to Tanner’s law. Appl. Maths Lett. 10, 63–68.Google Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K. 2009 The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623, 329–351.Google Scholar
Eggers, J. 2004 Hydrodynamic theory of forced dewetting. Phys. Rev. Lett. 93, 094502.Google Scholar
Eggers, J. & Pismen, L. M. 2010 Nonlocal description of evaporating drops. Phys. Fluids 22, 112101.Google Scholar
Eggers, J. & Stone, H. A. 2004 Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact agle. J. Fluid Mech. 505, 309–321.Google Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
Guéna, G., Poulard, C. & Cazabat, A. M. 2007 The leading edge of evaporating droplets. J. Colloid Interface Sci. 312, 164–171.Google Scholar
Hervet, H. & de Gennes, P. G. 1984 Dynamique du mouillage: films précurseurs sur solide ‘sec’. C. R. Acad. Sci. Paris II 299, 499–503.Google Scholar
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36 (1), 55–69.Google Scholar
Hocking, L. M. 1992 Rival contact-angle models and the spreading of drops. J. Fluid Mech. 239, 671–681.Google Scholar
Hocking, L. M. 1995 On contact angles in evaporating liquids. Phys. Fluids 7 (12), 2950–2955.Google Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.Google Scholar
Jambon-Puillet, E., Carrier, O., Shahidzadeh, N., Brutin, D., Eggers, J. & Bonn, D. 2018 Spreading dynamics and contact angle of completely wetting volatile drops. J. Fluid Mech. 844, 817–830.Google Scholar
Janeček, V., Andreotti, B., Pražák, D., Bárta, T. & Nikolayev, V. S. 2013 Moving contact line of a volatile fluid. Phys. Rev. E 88, 060404.Google Scholar
Janeček, V., Doumenc, F., Guerrier, B. & Nikolayev, V. S. 2015 Can hydrodynamic contact line paradox be solved by evaporation–condensation? J. Colloid Interface Sci. 460, 329–338.Google Scholar
Janeček, V. & Nikolayev, V. S. 2012 Contact line singularity at partial wetting during evaporation driven by substrate heating. Europhys. Lett. 100, 14003.Google Scholar
Janeček, V. & Nikolayev, V. S. 2013 Apparent-contact-angle model at partial wetting and evaporation: impact of surface forces. Phys. Rev. E 87, 012404.Google Scholar
Lugg, G. A. 1968 Diffusion coefficient of some organic and other vapors in air. Anal. Chem. 40 (7), 1072–1077.Google Scholar
Machrafi, H., Rednikov, A., Colinet, P. & Dauby, P. 2015 Importance of wave-number dependence of Biot numbers in one-sided models of evaporative Marangoni instability: horizontal layer and spherical droplet. Phys. Rev. E 91, 053018.Google Scholar
Machrafi, H., Sadoun, N., Rednikov, A., Dehaeck, S., Dauby, P. & Colinet, P. 2013 Evaporation rates and Bénard–Marangoni supercriticality levels for liquid layers under inert gas flow. Microgravity Sci. Technol. 25, 251–265.Google Scholar
Moosman, S. & Homsy, G. M. 1980 Evaporating menisci of wetting fluids. J. Colloid Interface Sci. 73, 212–223.Google Scholar
Morris, S. J. S. 2001 Contact angles for evaporating liquids predicted and compared with existing experiments. J. Fluid Mech. 432, 1–30.Google Scholar
Morris, S. J. S. 2014 On the contact region of a diffusion-limited evaporating drop: a local analysis. J. Fluid Mech. 739, 308–337.Google Scholar
Oliver, J. M., Whiteley, J. P., Saxton, M. A., Vella, D., Zubkov, V. S. & King, J. R. 2015 On contact-line dynamics with mass transfer. Eur. J. Appl. Maths 26, 1–49.Google Scholar
Pham, C.-T., Berteloot, G., Lequeux, F. & Limat, L. 2010 Dynamics of complete wetting liquid under evaporation. Europhys. Lett. 92, 54005.Google Scholar
Pismen, L. M. & Pomeau, Y. 2000 Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics. Phys. Rev. E 62, 2480–2492.Google Scholar
Pomeau, Y. 2011 Contact line moving on a solid. Eur. Phys. J. (Special Topics) 197, 15–31.Google Scholar
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71, 036313.Google Scholar
Potash, M. & Wayner, P. C. 1972 Evaporation from a two dimensional extended meniscus. Intl J. Heat Mass Transfer 15, 1851–1863.Google Scholar
Raj, R., Kunkelmann, C., Stephan, P., Plawsky, J. & Kim, J. 2012 Contact line behavior for a highly wetting fluid under superheated conditions. Intl J. Heat Mass Transfer 55, 2664–2675.Google Scholar
Rednikov, A. & Colinet, P. 2013 Singularity-free description of moving contact lines for volatile liquids. Phys. Rev. E 87, 010401.Google Scholar
Rednikov, A. Y. & Colinet, P. 2017 Asymptotic analysis of the contact-line microregion for a perfectly wetting volatile liquid in a pure-vapor atmosphere. Phys. Rev. Fluids 2, 124006.Google Scholar
Rednikov, A. Y., Rossomme, S. & Colinet, P. 2009 Steady microstructure of a contact line for a liquid on a heated surface overlaid with its pure vapor: parametric study for a classical model. Multiphase Sci. Technol. 21, 213–248.Google Scholar
Ristenpart, W. D., Kim, P. G., Domingues, C., Wan, J. & Stone, H. A. 2007 Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99, 234502.Google Scholar
Savva, N., Rednikov, A. & Colinet, P. 2017 Asymptotic analysis of the evaporation dynamics of partially-wetting droplets. J. Fluid Mech. 824, 574–623.Google Scholar
Saxton, M. A., Whiteley, J. P., Vella, D. & Oliver, J. M. 2016 On thin evaporating drops: when is the d 2 -law valid? J. Fluid Mech. 792, 134–167.Google Scholar
Schiaffino, S. & Sonin, A. A. 1997 On the theory for the arrest of an advancing molten contact line on a cold solid of the same material. Phys. Fluids 9 (8), 2227–2233.Google Scholar
Sibley, D. N., Nold, A., Savva, N. & Kalliadasis, S. 2013 On the moving contact line singularity: asymptotics of a diffuse-interface model. Eur. Phys. J. E 36, 26.Google Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269–292.Google Scholar
Stephan, P. C. & Busse, C. A. 1992 Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Intl J. Heat Mass Transfer 35, 383–391.Google Scholar
Tsoumpas, Y., Dehaeck, S., Rednikov, A. & Colinet, P. 2015 Effect of Marangoni flows on the shape of thin sessile droplets evaporating into air. Langmuir 31, 13334–13340.Google Scholar
Voinov, O. V. 1976 Hydrodynamics of wetting. Fluid Dyn. 11, 714–721.Google Scholar
Wayner, P. C. 1993 Spreading of a liquid film with a finite contact angle by the evaporation/condensation process. Langmuir 9, 294–299.Google Scholar