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Spreading dynamics and contact angle of completely wetting volatile drops

Published online by Cambridge University Press:  12 April 2018

Etienne Jambon-Puillet Open the ORCID record for Etienne Jambon-Puillet [Opens in a new window] ,
Odile Carrier ,
Noushine Shahidzadeh ,
David Brutin ,
Jens Eggers  and
Daniel Bonn
Etienne Jambon-Puillet*
Affiliation:
Institute of Physics, Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Odile Carrier
Affiliation:
Institute of Physics, Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Noushine Shahidzadeh
Affiliation:
Institute of Physics, Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
David Brutin
Affiliation:
Aix-Marseille University, IUSTI UMR 7343, 13453 Marseille, France
Jens Eggers
Affiliation:
School of Mathematics – University of Bristol, University Walk, Bristol BS8 1TW, UK
Daniel Bonn
Affiliation:
Institute of Physics, Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The spreading of evaporating drops without a pinned contact line is studied experimentally and theoretically, measuring the radius $R(t)$ of completely wetting alkane drops of different volatility on glass. Initially the drop spreads ($R$ increases), then owing to evaporation reverses direction and recedes with an almost constant non-zero contact angle $\unicode[STIX]{x1D703}\propto \unicode[STIX]{x1D6FD}^{1/3}$, where $\unicode[STIX]{x1D6FD}$ measures the rate of evaporation; eventually the drop vanishes at a finite-time singularity. Our theory, based on a first-principles hydrodynamic description, well reproduces the dynamics of $R$ and the value of $\unicode[STIX]{x1D703}$ during retraction.

JFM classification

Phase change: Condensation/evaporation Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 817 - 830
Copyright
© 2018 Cambridge University Press 

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References

Alizadeh Pahlavan, A., Cueto-Felgueroso, L., McKinley, G. H. & Juanes, R. 2015 Thin films in partial wetting: internal selection of contact-line dynamics. Phys. Rev. Lett. 115, 034502.10.1103/PhysRevLett.115.034502Google Scholar
Allen, J. S. 2003 An analytical solution for determination of small contact angles from sessile drops of arbitrary size. J. Colloid Interface Sci. 261 (2), 481–489.10.1016/S0021-9797(03)00127-9Google Scholar
Berezhnoi, A. N. & Semenov, A. V. 1997 Binary Diffusion Coefficients of Liquid Vapors in Gases. Begell House.Google Scholar
Beverley, K. J., Clint, J. H. & Fletcher, P. D. I. 1999 Evaporation rates of pure liquids measured using a gravimetric technique. Phys. Chem. Chem. Phys. 1, 149–153.10.1039/a805344hGoogle Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739–805.10.1103/RevModPhys.81.739Google Scholar
Bonn, D. & Meunier, J. 1997 Comment on ‘evaporation preempts complete wetting’. Europhys. Lett. 39 (3), 341–342.10.1209/epl/i1997-00358-9Google Scholar
Bourges-Monnier, C. & Shanahan, M. E. R. 1995 Influence of evaporation on contact angle. Langmuir 11 (7), 2820–2829.10.1021/la00007a076Google Scholar
Cachile, M., Bénichou, O. & Cazabat, A. M. 2002a Evaporating droplets of completely wetting liquids. Langmuir 18 (21), 7985–7990.10.1021/la020231eGoogle Scholar
Cachile, M., Bénichou, O., Poulard, C. & Cazabat, A. M. 2002b Evaporating droplets. Langmuir 18 (21), 8070–8078.10.1021/la0204646Google Scholar
Carruth, G. F. & Kobayashi, R. 1973 Vapor pressure of normal paraffins ethane through n-decane from their triple points to about 10 mm mercury. J. Chem. Engng Data 18 (2), 115–126.10.1021/je60057a009Google Scholar
Cazabat, A. M. & Guena, G. 2010 Evaporation of macroscopic sessile droplets. Soft Matt. 6, 2591–2612.10.1039/b924477hGoogle 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 (6653), 827–829.10.1038/39827Google Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 2000 Contact line deposits in an evaporating drop. Phys. Rev. E 62, 756–765.Google Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2009 Evaporation of a thin droplet on a thin substrate with a high thermal resistance. Phys. Fluids 21 (5), 052101.10.1063/1.3121214Google Scholar
Eggers, J. & Fontelos, M. A. 2015 Singularities: Formation, Structure, and Propagation. Cambridge University Press.10.1017/CBO9781316161692Google Scholar
Eggers, J. & Pismen, L. M. 2010 Nonlocal description of evaporating drops. Phys. Fluids 22 (11), 112101.10.1063/1.3491133Google Scholar
Elbaum, M., Lipson, S. G. & Wettlaufer, J. S. 1995 Evaporation preempts complete wetting. Europhys. Lett. 29 (6), 457–462.10.1209/0295-5075/29/6/005Google Scholar
Erbil, H. Y. 2012 Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170 (1–2), 67–86.10.1016/j.cis.2011.12.006Google Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.10.1103/RevModPhys.57.827Google Scholar
Hu, H. & Larson, R. G. 2006 Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110 (14), 7090–7094.10.1021/jp0609232Google Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
Jackson, J. D. 1975 Classical Electrodynamics. Wiley.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
Kelly-Zion, P. L., Pursell, C. J., Vaidya, S. & Batra, J. 2011 Evaporation of sessile drops under combined diffusion and natural convection. Colloids Surf. A 381 (1–3), 31–36.10.1016/j.colsurfa.2011.03.020Google Scholar
Larson, R. G. 2014 Transport and deposition patterns in drying sessile droplets. AIChE J. 60 (5), 1538–1571.10.1002/aic.14338Google Scholar
Lee, K. S., Cheah, C. Y., Copleston, R. J., Starov, V. M. & Sefiane, K. 2008 Spreading and evaporation of sessile droplets: universal behaviour in the case of complete wetting. Colloids Surf. A 323 (1–3), 63–72.10.1016/j.colsurfa.2007.09.033Google Scholar
Morris, S. J. S. 2014 On the contact region of a diffusion-limited evaporating drop: a local analysis. J. Fluid Mech. 739, 308–337.10.1017/jfm.2013.577Google Scholar
Perrin, H., Lhermerout, R., Davitt, K., Rolley, E. & Andreotti, B. 2016 Defects at the nanoscale impact contact line motion at all scales. Phys. Rev. Lett. 116, 184502.10.1103/PhysRevLett.116.184502Google Scholar
Poulard, C., Guéna, G., Cazabat, A. M., Boudaoud, A. & Ben Amar, M. 2005 Rescaling the dynamics of evaporating drops. Langmuir 21 (18), 8226–8233.10.1021/la050406vGoogle Scholar
Rednikov, A. & Colinet, P. 2013 Singularity-free description of moving contact lines for volatile liquids. Phys. Rev. E 87, 010401.Google Scholar
Savino, R. & Fico, S. 2004 Transient Marangoni convection in hanging evaporating drops. Phys. Fluids 16 (10), 3738–3754.10.1063/1.1772380Google 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, 134–167.10.1017/jfm.2016.76Google Scholar
Semenov, S., Starov, V. M., Rubio, R. G. & Velarde, M. G. 2012 Computer simulations of evaporation of pinned sessile droplets: influence of kinetic effects. Langmuir 28 (43), 15203–15211.10.1021/la303916uGoogle Scholar
Shahidzadeh-Bonn, N., Rafai, S., Azouni, A. & Bonn, D. 2006 Evaporating droplets. J. Fluid Mech. 549, 307–313.10.1017/S0022112005008190Google Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45 (1), 269–292.10.1146/annurev-fluid-011212-140734Google Scholar