What is the exact formula for calculating bubble resonance frequencies?

In summary, the conversation discusses the dependency for the resonance frequencies of bubbles and the calculation of sound wave frequencies that cause resonance. The Landau formula for droplets and an approximation formula are mentioned, as well as the differences between gas and liquid in terms of compressibility. The conversation also mentions the need for an exact formula and references an article on Cavitation and Bubble Dynamics for more information. The speaker also asks for help in determining the relationship between bubble characteristics and sound frequency, specifically the dependence on size and diameter. The conversation ends with the mention of an article on forced oscillations and the speaker's search for information on induced bubble frequencies.
  • #1
Regger
3
0
This is very important. Can someone tell the dependency for the resonance frequencies of bubbles? i.e if know a bubble's diameter, the surface tension, the liquid and the gas' densities how do I calculate the sound wave frequencies that causes a resonance in a bubble. I have Landau's formula for droplets. But since gas is compressible and liquids aren't I guess there sould be some differences.
I have also found another formula in the net which is an aproximation for vey small bubbles, but gives radical deviation for bigger quantities. In this formula the raduis of the bubbles raised to the power of -1. While in Landau's formula it in -3/2 (i.e. the resonance frequency is reversly proportional to square root of the 3-rd power of the raduis).
If I'ld be very gratefull if someone gave me the exact formula.
 
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  • #2
Admittedly this has been on my to-read list. I haven't had a chance to digest this at all. Hopefully it helps you out. It does appear that resonance does depend on radius.

http://caltechbook.library.caltech.edu/1/04/chap4.htm#L2 [Broken]

This is taken from "Cavitation and Bubble Dynamics" by Christopher Brennen.
http://caltechbook.library.caltech.edu/1/04/content.htm [Broken]
 
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  • #3
Thank you very much.
I would have tor read through the article some time soon. But I think this wouldn't be very usefull for me. See what I need is the frequency of a sound wave that causes a resonance. The article talks about pressure for instance, which I can use because I can't measure it. If could tell me what how does a sound frequency causing resonace in the bubble depend only on the bubble's characteristics. Because you know that bubbles soak up the intensity of a sound wave with a frequency matching their own resonating frequency.

Here is the set up. I have made two experiments. I the first I propagated white noise trough foam recorded it and compared it to one the same noise not passing through foam. The idea is that by the lowering in sound intensity for each frequency I could make a judgement for size distribution of the bubbles (because the resonance frequency depends on the size of the bubble).

In the second experiment I produced foam consisting of same-sized bubbles. Again I propagated white sounf through the foam and recorded it. I noticed that for the intensity for two frequencies was notebly lower than for the rest. Of cource those two frequencies should be the first two resonance of the bubbles.
Using Landau formula for droplets, I mentioned, I calculted what resonance frequencies should the bubbles I produced have. But it deviated severly from the actual frequencies.

If someone could help me.
 
  • #4
I am going to ask again 'cause I really, really need it - and need it soon. I'll try putting it this way. How do the characteristics of a bubble affect its resanating frequency. And I'm talking about sound - resonance aroused by sound. I'm more specifincally interested in the dependency between a bubbles' size - its diameter (assuming it's spherical) and the sound frequency that causes it to resonate.

If someone please knows somethink abou it, if he could share it. My ass is on the line.
 
  • #5
Regger said:
(i.e. the resonance frequency is reversly proportional to square root of the 3-rd power of the raduis).

That's curious, because doing only dimensional analysis:

[tex] \omega\sim \phi\left(\sqrt{\frac{\rho R^3}{\sigma}}\right)[/tex]

where [tex]\sigma[/tex], [tex]\rho[/tex] and [tex]R[/tex] are the surface tension, density, and bubble radius. It seems to me this is only for asymptotically large Reynolds Numbers.

Bubbles are not my area of expertise, but you should take a look at on line journals such as Journal of Fluid Mechanics or Physics of Fluids about this subject.
 
  • #6
Article on "forced oscillations"

Regger,
Did you find information on induced bubble frequencies? I found you posting while Googling the subject. Not a lot out there. I also found this article, which may be close to what you were looking for(?). Good luck. This is a new topic for me.

Nigmatulin, Akhatov, and Vakhitova (1999). "FORCED OSCILLATIONS OF A GAS BUBBLE IN A SPHERICAL VOLUME OF A COMPRESSIBLE LIQUID," Journal of Applied Mechanics and Technical Physics, 40(2):285-291
ABSTRACT: A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed."
 

1. What is a bubble resonance frequency?

A bubble resonance frequency is the natural frequency at which a bubble will vibrate or oscillate in a liquid medium. It is determined by the size, shape, and physical properties of the bubble and the surrounding liquid.

2. How is the bubble resonance frequency calculated?

The bubble resonance frequency can be calculated using the formula f = (3.0/4.0) * sqrt((2.0 * sigma)/(density * radius)), where f is the frequency in Hertz, sigma is the surface tension of the liquid, density is the density of the liquid, and radius is the radius of the bubble.

3. What factors affect the bubble resonance frequency?

The bubble resonance frequency can be affected by the size and shape of the bubble, the surface tension and density of the liquid, and the presence of any external forces such as sound waves or pressure changes.

4. How is bubble resonance frequency used in research and engineering?

Bubble resonance frequency is used in various fields such as acoustics, fluid dynamics, and materials science for studying and manipulating bubbles. It can also be utilized in technologies like ultrasonic cleaning and medical imaging.

5. Can bubble resonance frequencies be manipulated?

Yes, bubble resonance frequencies can be manipulated by changing the size and shape of the bubble, adjusting the properties of the surrounding liquid, or using external forces to alter the frequency. This is useful in applications where precise control of bubble behavior is required.

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