Interaction Mechanisms: Heating

Abstract

When ultrasound of a given frequency is transmitted into a medium (e.g., a liquid, a solid, or biological tissue) a fraction of the acoustic power is converted into heat. If effects of shear viscosity are not important the time-averaged rate Q at which heat is produced per unit volume is given by the following expression (Nyborg, 1981; Cavicchi and O’Brien, Jr., 1984):

$$ Q{\mkern 1mu} = {\mkern 1mu} ({{2}^{\alpha }}/\rho c){\mkern 1mu} < {\mkern 1mu} {{p}^{2}} > , $$

(1)

where α is the absorption coefficient at the specified frequency; p and c are the density and velocity of sound, respectively, for the medium; p is the acoustic pressure (total instantaneous pressure less the mean value) and <p²> denotes the time average of p². If the ultrasound source is driven at frequency f, and if the approximations of linear acoustics hold, the pressure at any point will be given by

$$ p{\mkern 1mu} = {\mkern 1mu} {{p}_{o}}{\mkern 1mu} \cos {\mkern 1mu} (\omega t{\mkern 1mu} + {\mkern 1mu} \beta ),{\mkern 1mu} \omega {\mkern 1mu} = {\mkern 1mu} 2\pi f. $$

(2)