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Scaling maximum spreading of droplet impacting on flexible substrates

Published online by Cambridge University Press:  07 March 2023

Yufei Ma Open the ORCID record for Yufei Ma [Opens in a new window]  and
Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window]
Yufei Ma
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Haibo Huang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: huanghb@ustc.edu.cn
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Abstract

We numerically study the impact of a droplet on superhydrophobic flexible plates, aiming to understand how the flexible substrate influences the maximum spreading of the droplet. Compared with the rigid case, the vertical movement of the flexible substrate due to droplet impact reduces the maximum spreading. Besides, the average acceleration $a$ during droplet spreading changes significantly. Arising from energy conservation, we rescale the acceleration $a$ for cases with different bending stiffness $K_B$ and mass ratio $M_r$. Moreover, through theoretical analysis, we propose a scaling for the droplet's maximum spreading diameter ratio $\beta _{max}$. In the scaling, based on the derived $a$, an effective Weber number $We_m$ is well defined, which accounts for the substrate properties without any adjustable parameters. In the ($\beta _{max}, We_m$) plane, the two-dimensional numerical results of different $K_B$, $M_r$ and rigid cases all collapse into a single curve, as do the experimental and three-dimensional (3-D) results. In particular, the collapsed 3-D data can be well represented by the universal rescaling of $\beta _{max}$ proposed by Lee et al. (J. Fluid Mech., vol. 786, 2016, R4). Furthermore, an a posteriori energy analysis confirms the validation of our a priori scaling law.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Contact lines

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 958 , 10 March 2023 , A35
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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