Nonlinear Wave Propagation in Bubbly Liquids

Yano, Takeru; Kanagawa, Tetsuya; Watanabe, Masao; Fujikawa, Shigeo

doi:10.1007/978-3-642-34297-4_4

Cited by 12 publications

(15 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We proceed without explicitly showing these values to ensure that the contribution of each term on the right-hand side of Eq. (11) is visible in the final result; b 3 does not appear in the final results for any of the problems studied by our group (Yano et al, 2006;Kanagawa et al, 2010Kanagawa et al, , 2011aYano et al, 2013) including the present analysis.…”

Section: Basic Equationsmentioning

confidence: 46%

“…Drew, 1983) and should ideally not be ignored, but because the propagation of acoustic waves in an almost quiescent bubbly liquid causes small amplitude oscillations of the fluid particles, small bubbles move together with the surrounding liquid. Hence, only the virtual mass force is taken into account as a representative force because it has a strongly influence on both unsteady fluid flow and the bubbles (see also Yano et al, 2013).…”

Section: B Assumptionsmentioning

confidence: 99%

“…Liquids containing gas bubbles exhibit fairly complex acoustic properties due to the complexity of gas-liquid twophase flow and a variety of wave properties (e.g., Nigmatulin, 1991;Nakoryakov et al, 1993;Yano et al, 2013). Weakly nonlinear analysis (e.g., Nayfeh, 1973;Jeffrey and Kawahara, 1982) is effective for evaluating the phenomena observed in such liquids because nonlinear (i.e., finite amplitude) effects appear during long-range propagation processes and can significantly alter the wave behavior, even for small wave amplitudes.…”

Section: Introductionmentioning

confidence: 98%

“…Electronic mail: kanagawa@kz.tsukuba.ac.jp are based on the basic equations for gas-liquid two-phase flows, and which incorporate the diffraction effect as quasiplane waves and the nonuniformity of the bubble distribution, will progress the predictions for various problems on acoustics in bubbly liquids. Kanagawa et al (2010) (or Yano et al, 2013 proposed a unified method to derive nonlinear wave equations for plane wave propagation in uniform bubbly liquids. This method is based on a set of scaling relations among the physical parameters that are appropriate to a specific wave phenomenon, and parameter scaling is the measurement of the nondimensional magnitudes of physical quantities in terms of a typical nondimensional amplitude of the wave under consideration.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we extend our method to encompass a sound beam in a nonuniform bubbly liquid without these restrictions. The method is extended by the following two steps (Kanagawa et al, 2011a;Yano et al, 2013):…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Kanagawa

2015

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

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). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

show abstract

Section: Basic Equationsmentioning

confidence: 46%

Section: B Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Kanagawa

2015

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

Nguyen

Kanagawa

2023

Nonlinear Dyn

View full text Add to dashboard Cite

With promising applications in medical diagnosis and therapy, the behavior of shell-encapsula-ted ultrasound contrast agents (UCAs) has attracted considerable attention. Currently, second-generation contrast agents stabilized by a phospholipid membrane are widely used and studies have focused on the dynamics of single phospholipid shell-encapsulated microbubbles. To improve the safety and the efficiency of the methods using the propagation or targeted ultrasound, a better understanding of the propagation of ultrasound in liquids containing multiple encapsulated microbubbles is required. By incorporating the Marmottant–Gompertz model into the multiple scale analysis of two-phase model, this study derived a Korteweg–de Vries–Burgers equation as a weakly nonlinear wave equation for one-dimensional ultrasound in bubbly liquids. It was found that the wave propagation characteristics changed with the initial surface tension, highlighting two notable features of the phospholipid shell: buckling and rupture. These results may provide insights into the suitable state of microbubbles, and better control of ultrasound for medical applications, particularly those that require high precision.

show abstract

Physico-mathematical model for multiple ultrasound-contrast-agent microbubbles encapsulated by a visco-elastic shell: Effect of shell compressibility on ultrasound attenuation

Kikuchi

Kanagawa

Ayukai

2023

Chemical Engineering Science

View full text Add to dashboard Cite

Nonlinear Wave Propagation in Bubbly Liquids

Cited by 12 publications

References 30 publications

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

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

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

Physico-mathematical model for multiple ultrasound-contrast-agent microbubbles encapsulated by a visco-elastic shell: Effect of shell compressibility on ultrasound attenuation

Contact Info

Product

Resources

About