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Minnaert bubble models

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Minnaert bubble models


Chad Greene (view profile)


Functions to calculate the radius, volume, or acoustic oscillation frequency of a gas bubble.

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Bundle of three functions:

[fo] = minnaert_freq(r_m,P_Pa,rho_l,nu,Z)
[bub_rad] = minnaert_rad(fo,P_Pa,rho_l,nu,Z)
[bub_vol] = minnaert_vol(fo,P_Pa,rho_l,nu,Z)

r_m = radius of bubble (m)
fo = natural frequency of the bubble in (Hz)
P_Pa = average hydrostatic pressure on the bubble (Pa)
rho_l = density of the liquid surrounding the bubble (kg/m3)
nu = polytropic exponent of the gas bubble (optional input)
Z = compressibility factor of the gas (optional input)

The function minnaert_freq calculates the approximate natural oscillation frequency (sometimes mistakenly referred to as the Minnaert resonance) of a gas bubble. The other functions, minnaert_rad and minnaert_vol return the radius or volume of a bubble given its natural resonance frequency.

The model neglects surface tension (assumes clean bubble of radius > 0.1 mm). For a detailed treatment of the development of these formulas, see

M. Minnaert. On Musical Air-Bubbles and the Sounds of Running Water. Philosophical Magazine, 1933.

C.A. Greene and P.S. Wilson. Laboratory investigation of a passive acoustic method for measurement of underwater gas seep ebullition. JASA Express Letters, Dec. 2011.
K. Commander and A. Prosperetti. Linear pressure waves in bubbly liquids: Comparison between theory and experiments. J. Acoust. Soc. Am. 1989.


Compressibility Factor Calculator and Water Sound Speed Calculator inspired this file.

This file inspired Two Phase Medium Sound Speed Calculator and Prosperetti's Phi Calculator.

Required Products MATLAB
MATLAB release MATLAB 7.12 (R2011a)
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