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Vortices, dissipation and flow transition in volatile binary drops

Published online by Cambridge University Press:  22 May 2014

R. Bennacer  and
K. Sefiane
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: [email protected]
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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.

JFM classification

Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 649 - 665
Copyright
© 2014 Cambridge University Press 

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