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Ratchet mechanism of drops climbing a vibrated oblique plate

Published online by Cambridge University Press:  01 December 2017

Hang Ding Open the ORCID record for Hang Ding [Opens in a new window] ,
Xi Zhu ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Hang Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
Xi Zhu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
Peng Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we investigate the ratchet mechanism of drops climbing a vibrated oblique plate based on three-dimensional direct numerical simulations, which for the first time reproduce the existing experiment (Brunet et al., Phys. Rev. Lett., vol. 99, 2007, 144501). With the help of numerical simulations, we identify an interesting and important wetting behaviour of the climbing drop; that is, the breaking of symmetry due to the inclination of the plate with respect to the acceleration leads to a hysteresis of the wetted area in one period of harmonic vibration. In particular, the average wetted area in the downhill stage is larger than that in the uphill stage, which is found to be responsible for the uphill net motion of the drop. A new hydrodynamic model is proposed to interpret the ratchet mechanism, taking account of the effects of the acceleration and contact angle hysteresis. The predictions of the theoretical analysis are in good agreement with the numerical results.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , R1
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Copyright
© 2017 Cambridge University Press 

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