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Asymptotic analysis of the evaporation dynamics of partially wetting droplets

Published online by Cambridge University Press:  06 July 2017

Nikos Savva Open the ORCID record for Nikos Savva [Opens in a new window] ,
Alexey Rednikov  and
Pierre Colinet
Nikos Savva*
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Alexey Rednikov
Affiliation:
Université Libre de Bruxelles, TIPs-Fluid Physics Unit, CP 165/67, 1050 Brussels, Belgium
Pierre Colinet
Affiliation:
Université Libre de Bruxelles, TIPs-Fluid Physics Unit, CP 165/67, 1050 Brussels, Belgium
*
†Email address for correspondence: savvan@cf.ac.uk
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Abstract

We consider the dynamics of an axisymmetric, partially wetting droplet of a one-component volatile liquid. The droplet is supported on a smooth superheated substrate and evaporates into a pure vapour atmosphere. In this process, we take the liquid properties to be constant and assume that the vapour phase has poor thermal conductivity and small dynamic viscosity so that we may decouple its dynamics from the dynamics of the liquid phase. This leads to a so-called ‘one-sided’ lubrication-type model for the evolution of the droplet thickness, which accounts for the effects of evaporation, capillarity, gravity, slip and kinetic resistance to evaporation. By asymptotically matching the flow near the contact line region and the bulk of the droplet in the limit of a small slip length and commensurably small evaporation and kinetic resistance effects, we obtain coupled evolution equations for the droplet radius and volume. The predictions of our asymptotic analysis, which also include an estimate of the evaporation time, are found to be in excellent agreement with numerical simulations of the governing lubrication model for a broad range of parameter regimes.

JFM classification

Phase change: Condensation/evaporation Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 574 - 623
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© 2017 Cambridge University Press 

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