The difference frequency technique for bubble size and Doppler velocity measurements

Bubbles in liquids are very resonant and nonlinear objects. Since nonlinear responses from a bubble can be easily observed at the resonance frequency in relatively low intensity acoustic fields, that makes possible bubble diagnostics. The present paper describes the feasibility of the difference frequency method. It is considered that the difference frequency signal is generated by a bubble cloud insonified with two primary waves of different frequencies. Incoherent difference frequency scattering from a bubble cloud is described theoretically. The difference frequency amplitude is shown to be proportional to the bubble density having resonance frequency close to the difference frequency. When bubbles move, a specific Doppler frequency shift arises in the nonlinear scattered field. A theory of the nonlinear Doppler effect for moving bubbles is described. It is shown, in particular, that the difference frequency Doppler shift strongly exceeds the linear Doppler shift when primary acoustic waves propagate from different directions relatively to a moving bubble. Experimental verification of the difference frequency bubble sizing and the Doppler velocity measurement are described.