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Journal of Applied Mathematics and Statistical Applications | Volume: 1
August 23-24, 2018 | London, UK
Applied Physics
3
rd
International Conference on
Microbubble dynamics in a viscous compressible liquid subject to ultrasound
Qianxi Wang
University of Birmingham, UK
T
his talk is concerned with microbubble dynamics in a
viscous compressible liquid subject to ultrasound. The
topic is associated with important applications in medical
ultrasonics and ultrasound cleaning. The compressible
effects are modelled using the weakly compressible theory
of Wang & Blake (J. Fluid Mech. 730, 245-272, 2010 and 679,
559-581, 2011), since the Mach number associated is small.
The viscous effects are approximated using the viscous
potential flow theory of Joseph & Wang (J. Fluid Mech., 505,
365-377, 2004), because the flow field is characterized as
being an irrotational flow in the bulk volume but with a thin
viscous boundary layer at the bubble surface. Consequently,
the phenomenon is modelled using the boundary integral
method, in which the compressible and viscous effects are
incorporated into the model through including additional
terms in the dynamic boundary condition at the bubble
surface. The numerical results are shown in good agreement
with the experiments of Versluis et al. (Phys. Rev. E 2010,
82, 026321), for the development of shape modes after
dozens cycles of oscillation. The model is accurate, highly
efficient, stable for many cycles of oscillation and grid-free
in the flow domain. Our computations show that when
subject to an acoustic wave a microbubble initially oscillates
spherically. Beyond a critical threshold of the acoustic
pressure amplitude, nonspherical surface modes generate
after several cycles of oscillation. The threshold decreases
as the acoustic frequency is equal to the natural frequency
of the bubble. As the pressure amplitude increases, non-
spherical shape modes develop earlier. A shape mode can
be activated if the driving acoustic frequency is equal to the
natural frequency of the shape mode.
e:
q.x.wang@bham.ac.uk