Parametric Amplification of the Dynamic Radiation Force of Acoustic Waves in Fluids

Abstract

We report on parametric amplification in dynamic radiation force produced by a bichromatic acoustic beam in a fluid. To explain this effect we develop a theory taking into account the nonlinearity of the fluid. The theory is validated through an experiment to measure the dynamic radiation force on an acrylic sphere. Results exhibit an amplification of 66 dB in water and 80 dB in alcohol as the difference of the frequencies is increased from 10 Hz to 240 kHz.

Dynamic radiation force of acoustic waves on solid elastic spheres

“…This is experimentally supported by Ref. [21]. Further, the force is proportional to the nonlinear parameter of the fluid γ.…”

“…To simplify our analysis we consider k 21 z 0 ≫ 1 and a ≪ z 0 . Let us denote the complex amplitudes of the potential functions (incident plus scattered) at the frequencies ω 1 , ω 2 , and ω 21 by, respectively,φ 1 ,φ 2 , andφ 21 . The total potential for scattering problem can be found using the Mie scattering theory.…”

“…The total potential for scattering problem can be found using the Mie scattering theory. Accordingly, the velocity potentials in terms of spherical waves in the spherical coordinates (r, θ, ϕ) is given by [21] …”

“…This suggests that dynamic radiation force itself should achieve a regime of parametric amplification. Silva et al [21] verified that the dynamic radiation force on an acrylic sphere can be greatly amplified as the difference frequency is increased.…”

Dynamic radiation force of acoustic waves on absorbing spheres

“…This effect is know as parametric amplification of acoustic waves [11]. It is also observed in the dynamic radiation force exerted on objects [12]. A study on dynamic radiation force acting on non-absorptive spheres taking into account parametric amplification can be found in [13].…”