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Scaling laws of the maximum spreading factor for impact of nanodroplets on solid surfaces

Published online by Cambridge University Press:  22 February 2022

Yi-Feng Wang ,
Yi-Bo Wang ,
Xin He ,
Ben-Xi Zhang ,
Yan-Ru Yang ,
Xiao-Dong Wang Open the ORCID record for Xiao-Dong Wang [Opens in a new window]  and
Duu-Jong Lee
Yi-Feng Wang
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Yi-Bo Wang
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Xin He
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Ben-Xi Zhang
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Yan-Ru Yang
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Xiao-Dong Wang*
Affiliation:
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, PR China
Duu-Jong Lee*
Affiliation:
Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan Department of Mechanical Engineering, City University of Hong Kong, Kowloon Tang 999077, Hong Kong
*
†Email addresses for correspondence: wangxd99@gmail.com, djlee@ntu.edu.tw
†Email addresses for correspondence: wangxd99@gmail.com, djlee@ntu.edu.tw
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Abstract

This study investigates the dynamics of low-viscosity nanodroplets impacting surfaces with static contact angles from θ = 73° to 180° via molecular dynamics (MD) simulations. Two typical morphologies of impacting nanodroplets are observed at the maximum spreading state, a Hertz-ball-like in a low-Weber-number range and a thin-film-like in a high-Weber-number range. Only inertial and capillary forces dominate the impact for the former, whereas viscous force also becomes dominant for the latter. Regardless of morphologies at the maximum spreading state, the ratio of spreading time to contact time always remains constant on an ideal superhydrophobic surface with θ = 180°. With the help of different kinematic approximations of the spreading time and scaling laws of the contact time, scaling laws of the maximum spreading factor ${\beta _{max}}\sim W{e^{1/5}}$ in the low-Weber-number range (capillary regime) and ${\beta _{max}}\sim W{e^{2/3}}R{e^{ - 1/3}}$ (or ${\beta _{max}}\sim W{e^{1/2}}O{h^{1/3}}$) in the high-Weber-number range (cross-over regime) are obtained. Here, We, Re, and Oh are the Weber number, Reynolds number, and Ohnesorge number, respectively. Although the scaling laws are proposed only for the ideal superhydrophobic surface, they are tested valid for θ over 73° owing to the ignorable zero-velocity spreading effect. Furthermore, combining the two scaling laws leads to an impact number, $W{e^{3/10}}O{h^{1/3}} = 2.1$. This impact number can be used to determine whether viscous force is ignorable for impacting nanodroplets, thereby distinguishing the capillary regime from the cross-over regime.

JFM classification

Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A12
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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