Abstract

A second harmonic sound pressure emitted from a micro-bubble, which is used as contrast agent for ultrasound imaging, in an acoustic field is theoretically studied. A thermal damping effect of the bubble oscillation is taken into account. An acoustic pressure amplitude “(ΔPL)” is assumed to be sufficiently smaller than a surrounding pressure “PLO” and a weak non-linearity of the bubble motion is analyzed. Governing equations are perturbed up to O ((ΔPL) 2/P2L0). From O ((ΔPL) /PL0) and O ((ΔPL) 2/P2L0) solutions, algebraic correlation equation of the second harmonic sound is derived. The numerical simulation is also performed. The simulation results show good agreement with the present correlation equation in the case of (ΔPL) /PL0<<1. The limitation of the present theory is discussed at the higher (ΔPL).

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