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Water entry of small hydrophobic spheres

Published online by Cambridge University Press:  25 January 2009

JEFFREY M. ARISTOFF  and
JOHN W. M. BUSH
JEFFREY M. ARISTOFF
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
JOHN W. M. BUSH*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: bush@math.mit.edu
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Abstract

We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the low Bond number limit, where cavity collapse is driven principally by surface tension rather than gravity. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description based on the solution to the Rayleigh–Besant problem is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time in the zero Bond number limit. The sphere's depth at cavity pinch-off is also computed in the low Weber number, quasi-static limit. Theoretical predictions compare favourably with our experimental observations in the low Bond number regime, and also yield new insight into the high Bond number regime considered by previous investigators. Discrepancies are rationalized in terms of the assumed form of the velocity field and neglect of the longitudinal component of curvature, which together preclude an accurate description of the cavity for depths less than the capillary length. Finally, we present a theoretical model for the evolution of the splash curtain formed at high Weber number and couple it with the underlying cavity dynamics.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 619 , 25 January 2009 , pp. 45 - 78
Copyright
Copyright © Cambridge University Press 2008

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