Minnaert bubble models

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.