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Role of natural convection in the dissolution of sessile droplets

Published online by Cambridge University Press:  30 March 2016

Erik Dietrich ,
Sander Wildeman ,
Claas Willem Visser ,
Kevin Hofhuis ,
E. Stefan Kooij ,
Harold J. W. Zandvliet  and
Detlef Lohse
Erik Dietrich
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Center for Fluid Dynamics, and Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Physics of Interfaces and Nanomaterials, Department of Science and Technology, Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Sander Wildeman
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Center for Fluid Dynamics, and Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Claas Willem Visser
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Center for Fluid Dynamics, and Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Kevin Hofhuis
Affiliation:
Physics of Interfaces and Nanomaterials, Department of Science and Technology, Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
E. Stefan Kooij
Affiliation:
Physics of Interfaces and Nanomaterials, Department of Science and Technology, Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Harold J. W. Zandvliet
Affiliation:
Physics of Interfaces and Nanomaterials, Department of Science and Technology, Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Detlef Lohse*
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Center for Fluid Dynamics, and Mesa+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Goettingen, Germany
*
†Email address for correspondence: d.lohse@utwente.nl
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Abstract

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.

JFM classification

Convection: Convection Drops and Bubbles: Drops and Bubbles Convection: Plumes/thermals

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Papers
Information
Journal of Fluid Mechanics , Volume 794 , 10 May 2016 , pp. 45 - 67
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© 2016 Cambridge University Press 

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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.

Download Dietrich et al. supplementary movie(Video)
Video 3.1 MB

Dietrich et al. supplementary movie

Short outtake of a μPIV measurement, visualizing the convective flow around a dissolving 1-pentanol droplet.

Download Dietrich et al. supplementary movie(Video)
Video 9.9 MB