Under consideration for publication in J. Fluid Mech.
1
Bubble cloud dynamics in an ultrasound field
Kazuki Maeda
†
, Tim Colonius
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA
91125, USA
(Received xx; revised xx; accepted xx)
The dynamics of bubble clouds induced by high-intensity focused ultrasound are investi-
gated in a regime where the cloud size is similar to the ultrasound wavelength. High-speed
images show that the cloud is asymmetrical; the bubbles nearest the source grow to a
larger radius than the distal ones. Similar structures of bubble clouds are observed in
numerical simulations that mimic the laboratory experiment. To elucidate the structure,
a parametric study is conducted for plane ultrasound waves with various amplitudes and
diffuse clouds with different initial void fractions. Based on an analysis of the kinetic
energy of liquid induced by bubble oscillations, a new scaling parameter is introduced
to characterize the dynamics. The new parameter generalizes the cloud interaction pa-
rameter originally introduced by d’Agostino & Brennen (1989). The dynamic interaction
parameter controls the energy localization and consequent anisoptropy of the cloud.
Moreover, the amplitude of the far-field, bubble-scattered acoustics is likewise correlated
with the proposed parameter. Findings of the present study not only shed light on the
physics of cloud cavitation, but may also be of use to quantification of the effects of
cavitation on outcomes of ultrasound therapies including HIFU-based lithotripsy.
1. Introduction
The dynamics of cavitation bubble clouds excited in an intense ultrasound field are of
critical importance for the safety and efficacy of lithotripsy and high-intensity focused
ultrasound (HIFU). In such therapy, cavitation bubbles can be formed in the human
body during the passage of the tensile part of ultrasound pulses. Bubbles can scatter and
absorb subsequent pulses, and the violent collapse of bubbles can cause cavitation damage
(Coleman
et al.
1987; Pishchalnikov
et al.
2003; Matsumoto
et al.
2005; McAteer
et al.
2005; Ikeda
et al.
2006; Bailey
et al.
2006; Stride & Coussios 2010; Miller
et al.
2012).
Due to the short time scale and three-dimensional nature of cloud cavitation, precise
measurement of individual bubbles has been challenging. Numerical simulations using
mixture-averaging approaches (vanWijngaarden 1968; Biesheuvel & vanWijngaarden
1984) have remained central tools for quantification of the dynamics of bubble clouds.
Early studies of bubble cloud dynamics focused on assessment of cavitation noise and
erosion on materials. Mørch (1980, 1982) theoretically modeled the inward-propagating
collapse of spherical bubble clusters and quantified the resulting collapse pressure. Omta
(1987) studied acoustic emission from the spherical bubble cloud excited by step change
of the pressure in the surrounding liquid. d’Agostino & Brennen (1989) formulated
the linearized dynamics of monodisperse, spherical bubble clouds under weak, long
wavelength pressure excitation and identified that the cloud interaction parameter,
B
=
βR
2
c
/R
2
b
0
, dictates the linear dynamics of the cloud, where
β
is the void fraction,
R
c
and
R
b
0
are the initial radius of the cloud and the bubbles, respectively. Wang &
Brennen (1994, 1999) extended the study to the nonlinear regime, further characterizing
†
Email address for correspondence: maeda@caltech.edu
arXiv:1805.00129v1 [physics.flu-dyn] 30 Apr 2018