Linear pressure waves in mono- and poly-disperse bubbly liquids: Attenuation and propagation speed in slow and fast and evanescent modes.

Using volumetric averaged equations from a two-fluid model, this study theoretically investigates linear pressure wave propagation in a quiescent liquid with many spherical gas bubbles. The speed and attenuation of sound are evaluated using the derived linear dispersion. Mono- and poly-disperse bubbly liquids are treated.

Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles.

To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller-Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles.

Weakly nonlinear propagation of focused ultrasound in bubbly liquids with a thermal effect: Derivation of two cases of Khokolov-Zabolotskaya-Kuznetsoz equations.

A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived.

Oscillation of a rotating levitated droplet: Analysis with a mechanical model.

A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010).