Journal of Engineering Mathematics

, Volume 102, Issue 1, pp 35–64 | Cite as

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

  • 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 under-heating 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 impacts 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 works and with practical findings to the extent that the explicit predictions here for ice-accretion rates are found to agree with the experimental range.


Droplets Ice accretion Multistructure Supercooled  



Thanks are due to the UK Icing Group, especially Roger Gent and David Hammond, for their insights, and to the referees for their helpful comments.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Physics and MathematicsUniversity of HullHullUK
  2. 2.Department of MathematicsUCLLondonUK

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