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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: hding@ustc.edu.cn
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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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References

Benilov, E. S. & Billingham, J. 2011 Drops climbing uphill on an oscillating substrate. J. Fluid Mech. 674, 93–119.Google Scholar
Bradshaw, J. & Billingham, J. 2016 Thin three-dimensional droplets on an oscillating substrate with contact angle hysteresis. Phys. Rev. E 93, 013123.Google Scholar
Brunet, P., Eggers, J. & Deegan, R. D. 2007 Vibration-induced climbing of drops. Phys. Rev. Lett. 99, 144501.CrossRefGoogle ScholarPubMed
Celestini, F. & Kofman, R. 2006 Vibration of submillimeter-size supported droplets. Phys. Rev. E 73, 041602.Google ScholarPubMed
Curie, P. 1894 Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique. J. Phys. Theor. Appl. 3, 393–415.CrossRefGoogle Scholar
Daniel, S., Sircar, S., Gliem, J. & Chaudhury, M. K. 2004 Ratcheting motion of liquid drops on gradient surfaces. Langmuir 20, 4085–4092.Google Scholar
Ding, H., Gilani, M. N. H. & Spelt, P. D. M. 2010 Sliding, pinch-off and detachment of a droplet on a wall in shear flow. J. Fluid Mech. 644, 217–244.Google Scholar
Ding, H. & Spelt, P. D. M. 2007a Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations. J. Fluid Mech. 576, 287–296.Google Scholar
Ding, H. & Spelt, P. D. M. 2007b Wetting condition in diffuse interface simulations of contact line motion. Phys. Rev. E 75, 046708.Google ScholarPubMed
Ding, H. & Spelt, P. D. M. 2008 Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers. J. Fluid Mech. 599, 341–362.Google Scholar
Ding, H., Spelt, P. D. M. & Shu, C. 2007 Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226, 2078–2095.Google Scholar
John, K. & Thiele, U. 2010 Self-ratcheting Stokes drops driven by oblique vibrations. Phys. Rev. Lett. 104, 107801.Google Scholar
Marsh, J. A., Garoff, S. & Dussan, V. E. B. 1993 Dynamic contact angles and hydrodynamics near a moving contact line. Phys. Rev. Lett. 70, 2778–2781.Google Scholar
Noblin, X., Kofman, R. & Celestini, F. 2009 Ratchet-like motion of a shaken drop. Phys. Rev. Lett. 102, 194504.Google Scholar
Podgorski, T., Flesselles, J. M. & Limat, L. 2001 Corners, cusps, and pearls in running drops. Phys. Rev. Lett. 87, 036102.CrossRefGoogle ScholarPubMed
Sartori, P., Quagliati, D., Varagnolo, S., Pierno, M., Mistura, G., Magaletti, F. & Casciola, C. M. 2015 Drop motion induced by vertical vibrations. New J. Phys. 17, 113017.CrossRefGoogle Scholar
Savva, N. & Kalliadasis, S. 2014 Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates. J. Fluid Mech. 754, 515–549.Google Scholar