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 AirBubbles 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.
