Effective equations for wave propagation in bubbly liquids

Caflisch, Russel E.; Miksis, Michael J.; Papanicolaou, George; Ting, Lu

doi:10.1017/s0022112085001252

Cited by 286 publications

(167 citation statements)

References 16 publications

Supporting

Mentioning

160

Contrasting

Unclassified

Order By: Relevance

“…The equation of conservation of mass and momentum for a mixture containing bubbles and liquid are given by [18] 1…”

Section: Theorymentioning

confidence: 99%

“…The volumetric pulsations of bubbles is formulated with a damped-oscillator equation; though this may be violated when the driving pressure amplitude is high as the bubbles experience 1-2 orders of magnitude increment in their volumes. Servant and co-workers [22,23,24] performed computational fluid dynamics simulations solving for the coupled Caflisch equations [18]. They were able to predict the pressure distribution and verify their results by comparison with the erosion of an aluminium foil by cavitation bubbles [23], though this comparison indicated qualitative agreement rather than quantitative.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Louisnard [17] has published a wave propagation model, recasting the time domain Caflisch equations [18] into a nonlinear Helmholtz equation using an elegant mathematical approach. In addition, a conservation of energy formula is given for the bubbly medium which allows an explicit definition of dissipation mechanisms upon performing cycle averaging.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

Doğan

Popov²

2016

Ultrasonics Sonochemistry

View full text Add to dashboard Cite

show abstract

“…The equation of conservation of mass and momentum for a mixture containing bubbles and liquid are given by [18] 1…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

Doğan

Popov²

2016

Ultrasonics Sonochemistry

View full text Add to dashboard Cite

show abstract

“…At first sight, it might sound doubtful, since high-amplitude waves are subject to nonlinear phenomena, even in homogeneous liquids. Moreover, the presence of cavitation bubbles modifies the acoustic properties of the effective medium, decreasing the effective sound velocity, and introducing dispersion and nonlinear phenomena [5,6,7]. However, in most cases, the bubbles are concentrated in relatively small regions of the liquid, and one could expect that linear acoustics may at least give a qualitative idea of the acoustic field and the approximate location of the various resonance frequencies, in the first step of the design of a sono-reactor.…”

Section: Introductionmentioning

confidence: 99%

FEM simulation of a sono-reactor accounting for vibrations of the boundaries

Louisnard

González-Garcı́a

Tudela

et al. 2009

Ultrasonics Sonochemistry

View full text Add to dashboard Cite

The chemical effects of acoustic cavitation are obtained in sono-reactors built-up from a vessel and an ultrasonic source. In this paper, simulations of an existing sono-reactor are carried out, using a linear acoustics model, accounting for the vibrations of the solid walls. The available frequency range of the generator (19 kHz-21 kHz) is systematically scanned. Global quantities are plotted as a function of frequency in order to obtain response curves, exhibiting several resonance peaks. The attenuation coefficient of the wave is taken as a variable parameter, in absence of the precise knowledge of the bubble size distribution, and its influence is studied. The concepts of acoustic energy, intensity and active power are recalled, along with the general balance equation for acoustic energy. The latter is used as a convergence check of the simulations. Finally, it is shown that the interface between the liquid and the solid walls cannot be correctly represented by the simple approximations of either infinitely soft, or infinitely hard boundaries. Moreover, the liquid-solid coupling allows the cooling jacket to receive a noticeable part of the input power, although it is not in direct contact with the sonotrode. It may therefore undergo cavitation and this feature opens the perspective to design sono-reactors which avoid direct contact between the working liquid and the sonotrode.

show abstract

“…With minor variations, this mixture-averaged model for bubbly flow was derived by earlier investigators [3][4][5] and has been used to investigate linear and nonlinear wave propagations in bubbly liquids. 6 For example, Commander and Prosperetti 7 provided a detailed comparison of the dispersion relation for small amplitude pressure waves with experimental data.…”

Section: Introductionmentioning

confidence: 99%

Statistical equilibrium of bubble oscillations in dilute bubbly flows

et al. 2008

View full text Add to dashboard Cite

The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid ͑impulsive or step change͒ change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one. For sufficiently broad distributions of bubble equilibrium ͑or initial͒ radius, it is demonstrated that bubble statistics reach equilibrium on a time scale that is fast compared to physical damping of bubble oscillations due to viscosity, heat transfer, and liquid compressibility. The period-averaged bubble radius may then be used to predict the slow changes in the moments caused by the damping. A benefit is that period averaging gives a much smoother integrand, and accurate statistics can be obtained by tracking as few as five bubbles from the broad distribution. The period-averaged formula may therefore prove useful in reducing computational effort in models of dilute bubbly flow wherein bubbles are forced by shock waves or other rapid pressure changes, for which, at present, the strong effects caused by a distribution in bubble size can only be accurately predicted by tracking thousands of bubbles. Some challenges associated with extending the results to more general ͑nonimpulsive͒ forcing and strong two-way coupled bubbly flows are briefly discussed.

show abstract

Effective equations for wave propagation in bubbly liquids

Cited by 286 publications

References 16 publications

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

FEM simulation of a sono-reactor accounting for vibrations of the boundaries

Statistical equilibrium of bubble oscillations in dilute bubbly flows

Contact Info

Product

Resources

About