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Water droplet freezing on cold surfaces with distinct wetabilities

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Abstract

This paper investigates the total freezing time of droplets on surfaces with various wettabilities with horizontal and inclined orientations. A two-dimensional Volume of Fluid (VOF) method was applied to capture the liquid-air interface, and an automatic localized grid treatment technique was applied to increase the accuracy, especially near the impact and spreading areas. The Kistler and Shikhumurzaev dynamic contact angle models were implemented to impose the dynamic contact angles on different surfaces. An enthalpy-porosity technique was used to predict the phase change of droplets after impact with the surface. The results of the nondimensional droplet diameter ratios and total freezing times for both dynamic contact angle models have been presented and verified with experimental data. The effects of both wetting properties and the surface inclination on the freezing time have been analyzed. The results indicate that a lower surface temperature, a decrease in static contact angle and a higher inclination will result in more rapid freezing of droplets.

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Abbreviations

\(\rho\) :

Density

\(\overrightarrow{v}\) :

two-dimensional velocity field

\({x}_{i}\) :

two-dimensional space

\(t\) :

time

\(\overrightarrow{g}\) :

gravitational acceleration

\(\overrightarrow{{\uptau }}\) :

tress tensor

\(\nu\) :

kinematic viscosity

\(I\) :

unit tensor

\(\mu\) :

Viscosity

\(S\) :

source term

\(\beta\) :

liquid fraction

\({v}_{p}\) :

pull velocity

\({A}_{mush}\) :

mushy zone constant

\({a}_{p}\) :

Volume fraction in the cell

\({p}^{th}\) :

Phase name

\(\phi\) :

Level set function

\(Ca\) :

Capillary number

\(\sigma\) :

Surface tension

\(u\) :

contact line velocity

\({f}_{H}\) :

Hoffman’s function

\({\theta }_{eq}\) :

equilibrium contact angle

\({\theta }_{dyn}\) :

Dynamic contact angle

\(H\) :

enthalpy per unit volume

\(\lambda\) :

thermal conductivity

\(h\) :

sensible enthalpy

\({h}_{ref}\) :

sensible enthalpy at a reference temperature

\(c\) :

specific heat

\(\Delta H\) :

modified latent heat equation

\({\alpha }_{l}\) :

liquid volume fraction

\(L\) :

latent heat of the phase change

\(\gamma\) :

liquid volume fraction of a numerical cell occupied by solid and liquid

\(T\) :

Temperature

\(\alpha\) :

Inclined surface angle

\(\theta\) :

Static contact Angle

\({\theta }_{A}\) :

Advancing contact angle

\({\theta }_{R}\) :

Receding contact angle

\(We\) :

Droplet Weber number

\(Re\) :

Droplet Reynolds number

\({V}_{0}\) :

Droplet initial velocity

\({D}_{0}\) :

Droplet initial diameter

\(D/{D}_{0}\) :

droplet diameter ratio

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Acknowledgements

The authors acknowledge the financial support from a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2015-03940).

Funding

This research is financially supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2015-03940).

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Authors and Affiliations

  1. Faculty of Sustainable Design Engineering, University of Prince Edward Island (UPEI), Charlottetown, PEI, Canada

    Armin Bodaghkhani

  2. Department of Mechanical Engineering, Memorial University of Newfoundland (MUN), St. John’s, NL, Canada

    Xili Duan

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  1. Armin Bodaghkhani
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Correspondence to Armin Bodaghkhani.

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Bodaghkhani, A., Duan, X. Water droplet freezing on cold surfaces with distinct wetabilities. Heat Mass Transfer 57, 1–10 (2021). https://doi.org/10.1007/s00231-020-02984-w

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