Quantitative Analysis of Secondary Bjerknes Forces in Various Liquids

Evaluating numerically the interaction forces between two free bubbles, under the action of a background of random acoustic radiation, we highlight the contributions of coefficients β_s0 and β_a0 = β_u0 + β_th0 to the magnitude of these forces. The quantitative study of the forces is done for several fluids, as different as possible in terms of properties: water, mercury, liquid helium, and superfluid helium. These forces are evaluated, for different radii of the oscillating bubbles, R₀ = ⎡10⁻¹ − 10⁻¹⁰⏋ m, that the scattering–absorption forces and the scattering–scattering forces are close in magnitude. For water, mercury and liquid helium, the force ratio is in the range f_a ∈ (10⁻³ −1). For superfluid helium, the forces change direction, oscillating, and the ratio of the forces is much less than one, |f_a| 1.