Journal of Fluid Mechanics



Bubble collapse near a solid boundary: a numerical study of the influence of viscosity


STÉPHANE POPINET a1p1 and STÉPHANE ZALESKI a1
a1 Laboratoire de Modélisation en Mécanique, CNRS and Université Pierre et Marie Curie (Paris VI), 8 rue du Capitaine Scott, 75015 Paris, France; s.popinet@niwa.cri.nz; zaleski@lmm.jussieu.fr

Abstract

The effect of viscosity on jet formation for bubbles collapsing near solid boundaries is studied numerically. A numerical technique is presented which allows the Navier–Stokes equations with free-surface boundary conditions to be solved accurately and efficiently. Good agreement is obtained between experimental data and numerical simulations for the collapse of large bubbles. However, the bubble rebound in our simulation is larger than that observed in laboratory experiments. This leads us to conclude that compressible and thermal effects should be taken into account to obtain a correct model of the rebound. A parametric study of the effect of viscosity on jet impact velocity is undertaken. The jet impact velocity is found to decrease as viscosity increases and above a certain threshold jet impact is impossible. We study how this critical Reynolds number depends on the initial radius and the initial distance from the wall. A simple scaling law is found to link this critical Reynolds number to the other non-dimensional parameters of the problem.

(Received January 11 2001)
(Revised January 15 2002)


Correspondence:
p1 Present address: NIWA (National Institute of Water & Atmospheric Research), PO Box 14-901 Kilbirnie, Wellington, New Zealand.


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