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Impact dynamics of compound drops of fluids with density contrast

Published online by Cambridge University Press:  02 June 2023

Zhen Zhang ,
Chun-Yu Zhang Open the ORCID record for Chun-Yu Zhang [Opens in a new window] ,
Hao-Ran Liu Open the ORCID record for Hao-Ran Liu [Opens in a new window]  and
Hang Ding Open the ORCID record for Hang Ding [Opens in a new window]
Zhen Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Chun-Yu Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Hao-Ran Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Hang Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: hding@ustc.edu.cn
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Abstract

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$. In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$, volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 964 , 10 June 2023 , A34
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Zhang et al. Supplementary Movie 1

Impact dynamics of a compound drop at λ=0.1, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 1(Video)
Video 4.6 MB

Zhang et al. Supplementary Movie 2

Impact dynamics of a compound drop at λ=1, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 2(Video)
Video 4.7 MB

Zhang et al. Supplementary Movie 3

Impact dynamics of a compound drop at λ=4, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 3(Video)
Video 4.8 MB