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Ratchet mechanism of drops climbing a vibrated oblique plate

  • Hang Ding (a1), Xi Zhu (a1), Peng Gao (a1) and Xi-Yun Lu (a1)

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.

Copyright

Corresponding author

Email address for correspondence: hding@ustc.edu.cn

References

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Benilov, E. S. & Billingham, J. 2011 Drops climbing uphill on an oscillating substrate. J. Fluid Mech. 674, 93119.
Bradshaw, J. & Billingham, J. 2016 Thin three-dimensional droplets on an oscillating substrate with contact angle hysteresis. Phys. Rev. E 93, 013123.
Brunet, P., Eggers, J. & Deegan, R. D. 2007 Vibration-induced climbing of drops. Phys. Rev. Lett. 99, 144501.
Celestini, F. & Kofman, R. 2006 Vibration of submillimeter-size supported droplets. Phys. Rev. E 73, 041602.
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, 393415.
Daniel, S., Sircar, S., Gliem, J. & Chaudhury, M. K. 2004 Ratcheting motion of liquid drops on gradient surfaces. Langmuir 20, 40854092.
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, 217244.
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, 287296.
Ding, H. & Spelt, P. D. M. 2007b Wetting condition in diffuse interface simulations of contact line motion. Phys. Rev. E 75, 046708.
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, 341362.
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, 20782095.
John, K. & Thiele, U. 2010 Self-ratcheting Stokes drops driven by oblique vibrations. Phys. Rev. Lett. 104, 107801.
Marsh, J. A., Garoff, S. & Dussan, V. E. B. 1993 Dynamic contact angles and hydrodynamics near a moving contact line. Phys. Rev. Lett. 70, 27782781.
Noblin, X., Kofman, R. & Celestini, F. 2009 Ratchet-like motion of a shaken drop. Phys. Rev. Lett. 102, 194504.
Podgorski, T., Flesselles, J. M. & Limat, L. 2001 Corners, cusps, and pearls in running drops. Phys. Rev. Lett. 87, 036102.
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.
Savva, N. & Kalliadasis, S. 2014 Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates. J. Fluid Mech. 754, 515549.
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