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Vortices, dissipation and flow transition in volatile binary drops

Published online by Cambridge University Press:  22 May 2014

R. Bennacer
Affiliation:
LMT, Ecole Normale Superieure Cachan, F-94235 Cachan, France
K. Sefiane*
Affiliation:
School of Engineering, The University of Edinburgh, Edinburgh EH9 3JL, UK
*
Email address for correspondence: ksefiane@ed.ac.uk

Abstract

Despite its fundamental and practical relevance, flow structure and evolution within volatile mixture drops remains largely unexplored. We study experimentally, using particle image velocimetry (PIV), the evolution of internal flow during the evaporation of ethanol–water mixture drops for different initial concentrations. The investigation revealed the existence of three stages in the evolving flow behaviour within these binary volatile drops. We propose an analysis of the nature of the flow and focus on understanding successive flow stages as well as transition from multiple vortices to a monotonic outward flow. We show that the existence of multiple vortices during the first stage is driven by local concentration gradients along the interface. When the more volatile component (in this case ethanol) is depleted, the intensity of this Marangoni flow abruptly declines. Towards the end of the first stage, ethanol is driven from the bulk of the drop to the interface to sustain weakening concentration gradients. Once these gradients are too weak, the solutal Marangoni number becomes sub-critical and the driving force for the flow switches off. The evolution of flow structure and transition between stages is found to be well correlated with the ratio of Marangoni and Reynolds numbers. Furthermore, we argue that whilst the observed vortices are driven by surface tension shear stress originating at the liquid/vapour interface, the transition in flow and its dynamics is entirely determined by viscous dissipation. The comparison between the analytical expression for vorticity decay based on viscous dissipation and the experimental data shows a very good agreement. The analysis also shows that regardless of the initial concentration, for same sized drops, the transition in flow follows exactly the same trend. This further supports the hypothesis of a viscous dissipation transition of the flow. The last stage is satisfactorily explained based on non-uniform evaporation and continuity-driven flow.

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Type
Papers
Copyright
© 2014 Cambridge University Press 

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References

Cheng, A. K. H., Soolaman, D. M. & Yu, H. 2006 Evaporation of micro droplets of ethanol–water mixtures on gold surfaces modified with self-assembled monolayers. J. Phys. Chem. B 110, 1126711271.CrossRefGoogle Scholar
Christy, J., Hamamoto, Y. & Sefiane, K. 2011 Flow transition within an evaporating binary mixture sessile drop. Phys. Rev. Lett. 106, 205701.CrossRefGoogle ScholarPubMed
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, 827829.CrossRefGoogle Scholar
Erbil, H. Y. 2012 Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170, 6786.CrossRefGoogle ScholarPubMed
Ghasemi, H. & Ward, C. A. 2010 Energy transport by thermocapillary convection during sessile-water-droplet evaporation. Phys. Rev. Lett. 13, 136102.CrossRefGoogle Scholar
Hamamoto, Y., Christy, J. R. E. & Sefiane, K. 2011 Order-of-magnitude increase in flow velocity driven by mass conservation during the evaporation of sessile drops. Phys. Rev. E 83, 051602.CrossRefGoogle ScholarPubMed
Hopkins, R. J. & Reid, J. P. 2006 A comparative study of the mass and heat transfer dynamics of evaporating ethanol/water, methanol/water, and 1-propanol/water aerosol droplets. J. Phys. Chem. B 110, 32393249.CrossRefGoogle ScholarPubMed
Hu, H. & Larson, R. G. 2006 Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110, 70907094.CrossRefGoogle ScholarPubMed
Marin, A. G., Gelderblom, H., Lohse, D. & Snoeijer, J. H. 2011 Rush-hour in evaporating coffee drops. Phys. Fluids 23, 091111.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Rowan, S. M., Newton, M. I., Driewer, F. W. & McHale, G. J. 2000 Evaporation of microdroplets of azeotropic liquids. J. Phys. Chem. B 104, 82178220.CrossRefGoogle Scholar
Sefiane, K. & Bennacer, R. 2011 An expression for droplet evaporation incorporating thermal effects. J. Fluid Mech. 667, 260271.CrossRefGoogle Scholar
Sefiane, K., David, S. & Shanahan, M. E. R. 2008 Wetting and evaporation of binary mixture drops. J. Phys. Chem. B 112, 1131711323.CrossRefGoogle ScholarPubMed
Sefiane, K., Wilson, S. K., David, S., Dunn, G. & Duffy, B. R. 2009 On the effect of the atmosphere on the evaporation of sessile droplets of water. Phys. Fluids 21, 062101.CrossRefGoogle Scholar
Young, T. 1805 An essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. 95, 6587.Google Scholar