Skip to main content Accessibility help

Role of natural convection in the dissolution of sessile droplets

  • Erik Dietrich (a1) (a2), Sander Wildeman (a1), Claas Willem Visser (a1), Kevin Hofhuis (a2), E. Stefan Kooij (a2), Harold J. W. Zandvliet (a2) and Detlef Lohse (a1) (a3)...


The dissolution process of small (initial (equivalent) radius $R_{0}<1$  mm) long-chain alcohol (of various types) sessile droplets in water is studied, disentangling diffusive and convective contributions. The latter can arise for high solubilities of the alcohol, as the density of the alcohol–water mixture is then considerably less than that of pure water, giving rise to buoyancy-driven convection. The convective flow around the droplets is measured, using micro-particle image velocimetry ( ${\rm\mu}$ PIV) and the schlieren technique. When non-dimensionalizing the system, we find a universal $Sh\sim Ra^{1/4}$ scaling relation for all alcohols (of different solubilities) and all droplets in the convective regime. Here $Sh$ is the Sherwood number (dimensionless mass flux) and $Ra$ is the Rayleigh number (dimensionless density difference between clean and alcohol-saturated water). This scaling implies the scaling relation ${\it\tau}_{c}\propto R_{0}^{5/4}$ of the convective dissolution time ${\it\tau}_{c}$ , which is found to agree with experimental data. We show that in the convective regime the plume Reynolds number (the dimensionless velocity) of the detaching alcohol-saturated plume follows $Re_{p}\sim Sc^{-1}Ra^{5/8}$ , which is confirmed by the ${\rm\mu}$ PIV data. Here, $Sc$ is the Schmidt number. The convective regime exists when $Ra>Ra_{t}$ , where $Ra_{t}=12$ is the transition $Ra$ number as extracted from the data. For $Ra\leqslant Ra_{t}$ and smaller, convective transport is progressively overtaken by diffusion and the above scaling relations break down.


Corresponding author

Email address for correspondence:


Hide All
Bejan, A. 1993 Heat Transfer. John Wiley & Sons.
van der Bos, A., van der Meulen, M.-J., Driessen, T., van den Berg, M., Reinten, H., Wijshoff, H., Versluis, M. & Lohse, D. 2014 Velocity profile inside piezoacoustic inkjet droplets in flight: comparison between experiment and numerical simulation. Phys. Rev. Appl. 1, 014004.
Cazabat, A.-M. & Guéna, G. 2010 Evaporation of macroscopic sessile droplets. Soft Matt. 6, 25912612.
Crittenden, E. D. Jr & Hixson, A. N. 1954 Extraction of hydrogen chloride from aqueous solutions. Ind. Engng Chem. 46, 265274.
Dehaeck, S., Rednikov, A. & Colinet, P. 2014 Vapor-based interferometric measurement of local evaporation rate and interfacial temperature of evaporating droplets. Langmuir 30, 20022008.
Demond, A. H. & Lindner, A. S. 1993 Estimation of interfacial tension between organic liquids and water. Environ. Sci. Technol. 27, 23182331.
Dietrich, E., Kooij, E. S., Zhang, X., Zandvliet, H. J. W. & Lohse, D. 2015 Stick–jump mode in surface droplet dissolution. Langmuir 31, 46964703.
Enríquez, O. R., Sun, C., Lohse, D., Prosperetti, A. & van der Meer, D. 2014 The quasi-static growth of bubbles. J. Fluid Mech. 741, R1.
Epstein, P. S. & Plesset, M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18, 15051509.
Erbil, H. Y. 2012 Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170, 6786.
Fujii, T. 1963 Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source. Intl J. Heat Mass Transfer 6, 597606.
Gelderblom, H., Marín, Á. G., Nair, H., van Houselt, A., Lefferts, L., Snoeijer, J. H. & Lohse, D. 2011 How water droplets evaporate on a superhydrophobic substrate. Phys. Rev. E 83, 026306.
Guéna, G., Poulard, C. & Cazabat, A.-M. 2006 The leading edge of evaporating droplets. J. Colloid Interface Sci. 312, 164171.
Hao, L. & Leaist, D. G. 1996 Binary mutual diffusion coefficients of aqueous alcohols. Methanol to 1-heptanol. J. Chem. Engng Data 41, 210213.
Høiland, H. & Vikingstad, E. 1976 Partial molal volumes and additivity of group partial molal volumes of alcohols in aqueous solution at $25\,^{\circ }\text{C}$ and $35\,^{\circ }\text{C}$ . Acta Chem. Scand. A 30, 182186.
Hu, H. & Larson, R. G. 2002 Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 106, 13341344.
Karpitschka, S.2012 Dynamics of liquid interfaces with compositional gradients. PhD thesis, Universität Potsdam.
Kelly-Zion, P. L., Batra, J. & Pursell, C. J. 2013a Correlation for the convective and diffusive evaporation of a sessile drop. Intl J. Heat Mass Transfer 64, 278285.
Kelly-Zion, P. L., Pursell, C. J., Hasbamrer, N., Cardozo, B., Gaughan, K. & Nickels, K. 2013b Vapor distribution above an evaporating sessile drop. Intl J. Heat Mass Transfer 65, 165172.
Kinoshita, K., Ishikawa, H. & Shinoda, K. 1958 Solubility of alcohols in water determined the surface tension measurements. Bull. Chem. Soc. Japan 31, 10811082.
Kostarev, K., Zuev, A. & Viviani, A. 2004 Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratification. C. R. Méc. 332, 17.
Lohse, D. & Zhang, X. 2015 Surface nanobubbles and nanodroplets. Rev. Mod. Phys. 87, 9811035.
Peñas López, P., Parrales, M. A. & Rodríguez-Rodríguez, J. 2015 Dissolution of a spherical cap bubble adhered to a flat surface in air-saturated water. J. Fluid Mech. 775, 5376.
Picknett, R. G. & Bexon, R. 1977 The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci. 61, 336350.
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71, 036313.
Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry. Springer.
Romero, C. M., Suárez, A. F. & Jiménez, E. 2007 Effect of temperature on the volumetric properties of aliphatic alcohols in dilute aqueous solutions. Rev. Colomb. Quím. 36, 377386.
Settles, G. S. 2001 Schlieren and Shadowgraph Techniques. Springer.
Shahidzadeh-Bonn, N., Rafaï, S., Azouni, A. & Bonn, D. 2006 Evaporating droplets. J. Fluid Mech. 549, 307313.
Somasundaram, S., Anand, T. N. C. & Bakshi, S. 2015 Evaporation-induced flow around a pendant droplet and its influence on evaporation. Phys. Fluids 27, 112105.
Stauber, J. M., Wilson, S. K. & Duffy, B. R. 2015a Evaporation of droplets on strongly hydrophobic substrates. Langmuir 31, 36533660.
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2015b On the lifetimes of evaporating droplets with related initial and receding contact angles. Phys. Fluids 27, 122101.
Stephenson, R., Stuart, J. & Tabak, M. 1984 Mutual solubility of water and aliphatic alcohols. J. Chem. Engng Data 29, 287290.
Vázquez, P. A., Pérez, A. T. & Castellanos, A. 1996 Thermal and electrohydrodynamic plumes: a comparative study. Phys. Fluids 8, 20912096.
Yalkowsky, S. H., He, Y. & Jain, P. 2010 Handbook of Aqueous Solubility Data, 2nd edn. Taylor & Francis.
Zhang, X., Wang, J., Bao, L., Dietrich, E., van der Veen, R. C. A., Peng, S., Friend, J., Zandvliet, H. J. W., Yeo, L. & Lohse, D. 2015 Mixed mode of dissolving immersed nanodroplets at a solid–water interface. Soft Matt. 11, 18891900.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO
Type Description Title

Dietrich et al. supplementary movie
Movie of a 1-hexanol droplet (initial equivalent radius 0.7 mm) dissolving in clean water. The droplet dissolves in the so called stick-jump mode.

 Video (3.1 MB)
3.1 MB

Dietrich et al. supplementary movie
Short outtake of a μPIV measurement, visualizing the convective flow around a dissolving 1-pentanol droplet.

 Video (9.9 MB)
9.9 MB

Role of natural convection in the dissolution of sessile droplets

  • Erik Dietrich (a1) (a2), Sander Wildeman (a1), Claas Willem Visser (a1), Kevin Hofhuis (a2), E. Stefan Kooij (a2), Harold J. W. Zandvliet (a2) and Detlef Lohse (a1) (a3)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.