Rectified Diffusion under Adiabatic Conditions

The theoretically predicted bubble growth rate for rectified diffusion under isothermal conditions is much lower than the rate found experimentally by Eller [J. Acoust. Soc. Amer. 46, 1246 (1969)]. The assumption of isothermal condition can only be justified for infinite thermal diffusivity. For real gas bubbles, however, the thermal condition lies between the isothermal and adiabatic limits. Our analysis was undertaken to establish the adiabatic limit. Contrary to the case of isothermal collapse, wherein the increased pressure (hence the surface concentration) can only result in an outwards diffusional flux, the solubility inversion effect for gases can cause first inwards and then outwards diffusional flux during the same phase of adiabatic collapse. In particular, when the heat of solution, ΔH0, of the gas is less than −(νBT0)/(ν − 1), where ν = Cν/Cr, and B is the gas constant, the diffusional flux changes direction as mentioned above at RR0=[(νν − 1)(BT0−ΔH0)]13(ν − 1). This flux reversal can cause the bubble to grow much faster than in the isothermal case.