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Drops climbing uphill on an oscillating substrate

  • E. S. BENILOV (a1) and J. BILLINGHAM (a2)
Abstract

Recent experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, p. 144501 and Eur. Phys. J., vol. 166, 2009, p. 11) have demonstrated that drops of liquid placed on an inclined plane oscillating vertically are able to climb uphill. In the present paper, we show that a two-dimensional shallow-water model incorporating surface tension and inertia can reproduce qualitatively the main features of these experiments. We find that the motion of the drop is controlled by the interaction of a ‘swaying’ (odd) mode driven by the in-plane acceleration and a ‘spreading’ (even) mode driven by the cross-plane acceleration. Both modes need to be present to make the drop climb uphill, and the effect is strongest when they are in phase with each other.

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Corresponding author
Email address for correspondence: eugene.benilov@ul.ie
References
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Benilov E. S. 2010 Drops climbing uphill on a slowly oscillating substrate. Phys. Rev. E 82, 026320.
Brunet P., Eggers J. & Deegan R. D. 2007 Vibration-induced climbing of drops. Phys. Rev. Lett. 99, 144501.
Brunet P., Eggers J. & Deegan R. D. 2009 Motion of a drop driven by substrate vibrations. Eur. Phys. J. Special Topics 166, 1114.
Ceniceros H. D. & Hou T. Y. 1998 Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Math. Comput. 67, 137182.
Daniel S., Chaudhury M. K. & de Gennes P.-G. 2005 Vibration-actuated drop motion on surfaces for batch microfluidic processes. Langmuir 21, 42404248.
Davis S. H. 2002 Interfacial fluid dynamics. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor G. K., Moffatt H. K. & Worster M. G.), pp. 151. Cambridge University Press.
Dold J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90115.
Hocking L. M. 1987 The damping of capillary gravity-waves at a rigid boundary. J. Fluid Mech. 179, 253266.
Hocking L. M. & Davis S. H. 2002 Inertial effects in time-dependent motion of thin films and drops. J. Fluid Mech. 467, 117.
King A. C. 1991 Moving contact lines in slender fluid wedges. Q. J. Mech. Appl. Maths 44, 173192.
Noblin X., Kofman R. & Celestini F. 2009 Ratchetlike motion of a shaken drop. Phys. Rev. Lett. 102, 194504.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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