scholarly journals Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

2011 ◽  
Vol 130 (5) ◽  
pp. 3357-3369 ◽  
Author(s):  
Eru Kurihara ◽  
Todd A. Hay ◽  
Yurii A. Ilinskii ◽  
Evgenia A. Zabolotskaya ◽  
Mark F. Hamilton
Keyword(s):  
Spherical Bubbles ◽  
Shape Oscillations

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

1995 ◽  
Vol 300 ◽  
pp. 149-167 ◽  
Author(s):  
Thomas J. Asaki ◽  
Philip L. Marston
Keyword(s):  
Nonlinear Response ◽  
Sea Water ◽  
Clean Water ◽  
Asymptotic Results ◽  
Two Fluids ◽  
Free Decay ◽  
Higher Order Terms ◽  
Liquid Systems ◽  
Spherical Bubbles ◽  
Shape Oscillations

Asymptotic results for the free decay of shape oscillations of viscous liquid spheres have been extended to include higher-order terms in the ratios of the inner and outer viscous penetration lengths to the radius. The new expressions are shown to be important for studies in which the two fluids have dissimilar densities and viscosities such as air/liquid systems. The analysis also includes an expansion for the frequency of maximum response of driven oscillations. The calculations are supported by measurements of the small-amplitude quadrupole mode free decay of nearly spherical bubbles acoustically levitated in clean water. The bubble radii ranged from 400 μm to 1400 μm. The results are interpreted in light of the initial-value problem. The lack of excess damping suggests that the interface behaves ideally for times up to two hours after bubble injection. Measurements were also carried out on bubbles in 0.5 m NaCl solution and in sea water. Larger bubbles (radius > 800 μm) in clean water exhibit damping two to four times larger than predicted by theory. The transition from this anomalous damping to theoretical damping is a very abrupt function of radius. All observations were carried out with similar acoustic fields for counteracting buoyancy. The excess damping appears to be associated with some nonlinear response of the bubble.

SHAPE OSCILLATIONS OF A BOILING BUBBLE

2010 ◽  
Vol 22 (2) ◽  
pp. 157-175 ◽  
Author(s):  
Cees W. M. van der Geld
Keyword(s):  
Shape Oscillations

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Shape Oscillations Mark Crystal Growth

Science News ◽  
1993 ◽  
Vol 143 (10) ◽  
pp. 150
Author(s):  
I. Peterson
Keyword(s):  
Crystal Growth ◽  
Shape Oscillations

Coalescence and shape oscillations of Au nanoparticles in CO2 hydrogenation for methanol reaction

Nanoscale ◽  
2021 ◽  
Author(s):  
Shengnan Yue ◽  
Yongli Shen ◽  
Ziliang Deng ◽  
Wenjuan Yuan ◽  
Wei Xi
Keyword(s):  
Au Nanoparticles ◽  
High Selectivity ◽  
Co2 Hydrogenation ◽  
Au Nanoparticle ◽  
Limited Knowledge ◽  
Shape Oscillations

Recently, there has been renewed interest in Au nanoparticle (Au NP) catalysts owing to their high selectivity for CO2 hydrogenation to methanol. However, there is still limited knowledge on the...

scholarly journals Growing bubbles rising in line

2001 ◽  
Vol 5 (2) ◽  
pp. 65-73 ◽  
Author(s):  
John F. Harper
Keyword(s):  
Reynolds Numbers ◽  
Dissipation Function ◽  
Supersaturated Solution ◽  
Liquid Theory ◽  
High Reynolds Numbers ◽  
Lagrange’S Equations ◽  
Spherical Bubbles ◽  
High Reynolds ◽  
Lagrange's Equations

Over many years the author and others have given theories for bubbles rising in line in a liquid. Theory has usually suggested that the bubbles will tend towards a stable distance apart, but experiments have often showed them pairing off and sometimes coalescing. However, existing theory seems not to deal adequately with the case of bubbles growing as they rise, which they do if the liquid is boiling, or is a supersaturated solution of a gas, or simply because the pressure decreases with height. That omission is now addressed, for spherical bubbles rising at high Reynolds numbers. As the flow is then nearly irrotational, Lagrange's equations can be used with Rayleigh's dissipation function. The theory also works for bubbles shrinking as they rise because they dissolve.

Sign in / Sign up

Export Citation Format

Share Document