A Lagrangian formulation for a gravitational analogue of the acoustic radiation force

Abstract

In this letter, we propose an expression for the instantaneous acoustic radiation force acting on a compressible sphere when it is immersed in a sound field with a wavelength much larger than the particle size (Rayleigh scattering regime). By following a Lagrangian approach, we show that the leading term of the radiation force can alternatively be expressed as a fluctuating gravitation-like force. In other words, the effect of the acoustic pressure gradient is to generate a local acceleration field encompassing the sphere, which gives rise to an apparent buoyancy force, making the object move in the incoming field. When averaging over time, we recover the celebrated Gor’kov expression and emphasize that two terms appear, one local and one convective, which identify with the well-known monopolar and dipolar contributions.