Relationship between frequency and resonant bubble radius

Relationship between frequency and resonant bubble radius 

Obviously, some constraints will exist between the critical bubble radius (Rk, i.e., the radius R of a bubble at which a minimum reduction of the hydrostatic pressure causes a dramatic increase of R ) and the mean radius of the pores of the catalytic particle (rp). If the bubble radius is indicated as Re, then two classes of bubbles satisfy the following conditions  

Pv being the vapor pressure of the liquid inside the bubble. At low temperatures Pv can be neglected with respect to Ph, and therefore by substitution of Eq. 8 in 7 one derives 

For the large and small bubbles considered above at Ph = 1 bar, the values of Rk are 8.6 X 10-5 and 2.7 x 10- m respectively. At Ph = 10 bar, the corresponding values are 8.6 x 10 and 2.7 x 10 m. Galli et have shown that the very simple equation 10 can be used to describe the relation between the ultrasound frequency f (kHz) and the radius of a resonating bubble R (pm) in water under 1 bar. 

By inserting the values of Rk reported at Ph = 1 bar a resonance frequency of = 40 kHz is foimd for the large bubbles and f 15 MHz for the small ones. 

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