Journal of Fluid Mechanics



Pyramidal and toroidal water drops after impact on a solid surface


Y. RENARDY a1, S. POPINET a2, L. DUCHEMIN a3, M. RENARDY a1, S. ZALESKI a3, C. JOSSERAND a3, M. A. DRUMRIGHT-CLARKE a1, D. RICHARD a4, C. CLANET a5 and D. QUÉRÉ a6
a1 Department of Mathematics and ICAM, 460 McBryde Hall, Virginia Tech, Blacksburg, VA 24061-0123, USA
a2 National Institute for Water and Atmospheric Research, PO Box 14 901, Kilbirnie, Wellington, New Zealand
a3 Laboratoire de Modélisation en Mécanique, CNRS-UMR 7607, Université Pierre et Marie Curie, 8 rue du Capitaine Scott, 75015 Paris Cedex 05, France
a4 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
a5 Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594 du CNRS, BP 146, 13384 Marseille Cedex, France
a6 Laboratoire de Physique de la Matire Condense, URA 792 du CNRS, Collège de France, 75231 Paris Cedex 05, France

Abstract

Superhydrophobic surfaces generate very high contact angles as a result of their microstructure. The impact of a water drop on such a surface shows unusual features, such as total rebound at low impact speed. We report experimental and numerical investigations of the impact of approximately spherical water drops. The axisymmetric free surface problem, governed by the Navier–Stokes equations, is solved numerically with a front-tracking marker-chain method on a square grid. Experimental observations at moderate velocities and capillary wavelength much less than the initial drop radius show that the drop evolves to a staircase pyramid and eventually to a torus. Our numerical simulations reproduce this effect. The maximal radius obtained in numerical simulations precisely matches the experimental value. However, the large velocity limit has not been reached experimentally or numerically. We discuss several complications that arise at large velocity: swirling motions observed in the cross-section of the toroidal drop and the appearance of a thin film in the centre of the toroidal drop. The numerical results predict the dry-out of this film for sufficiently high Reynolds and Weber numbers. When the drop rebounds, it has a top-heavy shape. In this final stage, the kinetic energy is a small fraction of its initial value.

(Received July 23 2002)
(Revised December 26 2002)



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