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A comprehensive model for predicting droplet freezing features on a cold substrate

Published online by Cambridge University Press:  21 November 2018

Moussa Tembely Open the ORCID record for Moussa Tembely [Opens in a new window]  and
Ali Dolatabadi
Moussa Tembely*
Affiliation:
Department of Mechanical, Industrial, and Aerospace Engineering, Concordia University, 1515 Ste-Catherine Street West, H3G 1M8, Montreal, Quebec, Canada
Ali Dolatabadi*
Affiliation:
Department of Mechanical, Industrial, and Aerospace Engineering, Concordia University, 1515 Ste-Catherine Street West, H3G 1M8, Montreal, Quebec, Canada
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Water droplet freezing affects many aspects of our daily lives, although there is no comprehensive model which retrieves all of the experimentally observed features when a liquid water droplet deposited on a cold substrate turns to ice. In this paper, we present general governing equations to describe water droplet freezing on a solid substrate by accounting for the physical properties of each phase present, namely the liquid and ice, in addition to the solid substrate. The approach, which takes advantage of the full mean curvature expression of both the droplet–air and liquid–ice interfaces, disjoining pressure, the Gibbs–Thomson effect, natural convection and the substrate thermal and physico-chemical properties, enables us to model a more realistic frozen droplet shape, without a prior assumption for the freezing growth angle. In addition to correctly predicting the freezing time, we capture both qualitatively and quantitatively the key experimentally observed features during water droplet freezing such as volume expansion, concave ice front and the cusp singularity. Furthermore, the proposed equation for the tip angle seems to explain its experimentally observed variability.

JFM classification

Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Multiphase flow Phase change: Icing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 566 - 585
Copyright
© 2018 Cambridge University Press 

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