Quantitative Analysis of Secondary Bjerknes Forces in Various Liquids

Abstract

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 βs 0 and βa 0 = βu 0 + βth 0 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, R 0 = ⎡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 fa ∈ (10−3 −1). For superfluid helium, the forces change direction, oscillating, and the ratio of the forces is much less than one, |fa | 1.