I would like to calculate the ultrasound (20MHz) absorption of particles (polystyrene of size 15 microns) in water. I tried to search in the internet, but couldn't find any simple analytical expressions. Can anyone please help me? Thanks in advance.
It should work with a focused US-Sensor - practical.
Search for:
"Werkstoffpruefung mit Ultraschall" (Krautkraemer) a very good book. It is in german language, but you should understand the diagrams and calculations.
An alternative is: "Wave motion in elastic solids" (Graff)
Yes, ultrasound can be absorbed by particles in a liquid. Naturally it is a function of the elastic properties of the particles but when the frequency of the incident ultrasound is tuned to one of the elastic resonance frequencies of the particles, you get a large response from the particles. This is called "resonance scattering", where the energy dissipation by the particles will be maximized. Note that this can occur with an un-focused ultrasonic beam. Contact me if you need more details.
You might start with the following papers :
Epstein, P. S., & Carhart, R. R. (1953). The absorption of sound in suspensions and emulsions. I. Water fog in air. The Journal of the Acoustical Society of America, 25(3), 553-565.
Allegra, J. R., & Hawley, S. A. (1972). Attenuation of sound in suspensions and emulsions: theory and experiments. The Journal of the Acoustical Society of America, 51(5B), 1545-1564.
However I doubt that you will find "simple" analytic expression, the mechanisms are somewhat involved... Such theories yield "not so simple" analytical results, and are currently implemented on commercial acoustic granulometers.
Hope this helps.
I would like to refer you to a paper that was published recently in Materials Evaluation, Vol 72, No 12, Dec 2014, pp. 1519-1529, by Govind Sharma et al.
It investigates ultrasonic attenuation in autentic steel. The nice thing about it is that it provides a very nice summary on the effect of microstructure on attenuation. Plenty of references are given. It describes two attenuation mechanisms
1) Due to material damping (absorption due to thermo-elastic losses),
alpha1 = a*f^0.5 + b*f^2
2) Due to scatter (grain scatter in metals would be similar to particle scatter in water)
alpha2 = S*d^3*f^4
where
a= constant for thermo-elastic losses
b= constant for dislocation damping (absent in water or different mechanism would apply)
S=Scattering factor depends on material property
d= grain size (particle size in water)
f= frequency
I hope this gets you close to your answer
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