Trapping forces by multidimensional fields on particles beyond Rayleigh regimes: From Gorkov potential to Born approximation

The analysis of trapping forces on particles much smaller than the sound wavelength (i.e., in the Rayleigh regime) has been derived from the Gorkov potential, resulting in a gradient force. This leads to the widely used concept of the acoustic contrast factor in trapping with one-dimensional standing waves. The Gorkov potential is also applicable for trapping in the Rayleigh regime using two- or three-dimensional acoustic fields, including both standing and progressive wave fields where compound gradients dominate the gradient force. The contrast factor formula was extended for trapping by two-dimensional standing waves, three-dimensional Bessel beams, and vortex beams [Fan and Zhang, Phys. Rev. Appl. 11(1), 014055 (2019)]. This contrast factor incorporates beam parameters alongside the mass density and compressibility contrast between particles and the surrounding medium. For particles larger than the Rayleigh regime, trapping forces can still be analyzed using the Gorkov potential under the condition of weak scattering, as described by the Born approximation, when the mass density and compressibility contrasts between the particles and the medium are small. This approach offers a simplified framework for examining trapping forces on larger particles [Fan and Zhang, J. Acoust. Soc. Am. 154(5), 3354–3363 (2023)].