Water entry of small hydrophobic spheres
Name
Bush_Water Entry.pdf
Size
1.6 MB
Format
Adobe PDF
Checksum (MD5)
8f93b21901919e5f5c0601c4963c1837
Author(s)
Bush, John W. M.
Aristoff, Jeffrey M.
Date Issued
December 2008
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
Citation
Aristoff, Jeffery M., John W.M. Bush. "Water entry of small hydrophobic spheres". Journal of Fluid Mechanics, (2009) 619, pp 45-78 © 2009 Cambridge University Press.
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1017/S0022112008004382
