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Ice formation on a smooth or rough cold surface due to the impact of a supercooled water droplet

Elliott, J. W.; Smith, F. T.


J. W. Elliott

F. T. Smith


Ice accretion is considered in the impact of a supercooled water droplet on a smooth or rough solid surface, the roughness accounting for earlier icing. In this theoretical investigation the emphasis and novelty lie in the full nonlinear interplay of the droplet motion and the growth of the ice surface being addressed for relatively small times, over a realistic range of Reynolds numbers, Froude numbers, Weber numbers, Stefan numbers and capillary underheating parameters. The Prandtl number and the kinetic under-heating parameter are taken to be order unity. The ice accretion brings inner layers into play forcibly, affecting the outer flow. (The work includes viscous effects in an isothermal impact without phase change, as a special case, and the differences between impact with and without freezing.) There are four main findings. First, the icing dynamically can accelerate or decelerate the spreading of the droplet whereas roughness on its own tends to decelerate spreading. The interaction between the two and the implications for successive freezings are found to be subtle. Second, a focus on the dominant physical effects reveals a multi-structure within which restricted regions of turbulence are implied. The third main finding is an essentially parabolic shape for a single droplet freezing under certain conditions. Fourth is a connection with a body of experimental and engineering work and with practical findings to the extent that the explicit predictions here for ice-accretion rates are found to agree with the experimental range. .


Elliott, J. W., & Smith, F. T. (2017). Ice formation on a smooth or rough cold surface due to the impact of a supercooled water droplet. Journal of engineering mathematics, 102(1), 35-64 .

Acceptance Date Jan 12, 2015
Online Publication Date Mar 24, 2015
Publication Date Feb 1, 2017
Deposit Date Jun 24, 2015
Publicly Available Date Jun 24, 2015
Journal Journal of engineering mathematics
Print ISSN 0022-0833
Electronic ISSN 1573-2703
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 102
Issue 1
Pages 35-64
Keywords Ice accretion, Droplets, Supercooled, Multi-structure
Public URL
Publisher URL
Additional Information Author's accepted manuscript of an article which has been published in: Journal of engineering mathematics, 2017, v.102, issue 1. The final publication is available at Springer via


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