Simulation of the Acoustic Radiation Force on a Small Rigid Sphere Generated by an Array of Transducers

The acoustic radiation force generated by an array of transducers can be applied for suspending and manipulating small objects in mid-air. To simulate the radiation force that acts on the levitated object, most authors employ the Gor'kov equation, which assumes the acoustic radiation force is a conser-vative force. However, there are cases where the acoustic radiation force is not conservative, resulting in an incorrect evaluation of the radiation force. In this study, we implement a numerical model for simulating the acoustic radiation force on a small rigid sphere suspended by an array of 40 kHz transducers operating in mid-air. With the purpose of estimating the errors caused by the Gor'kov approach, we compare the results obtained by two versions of the model: A model based on the Gor'kov equation and another model based on the radiation force calculated by Silva (J. Acoust. Soc. Am. 136, 2405, 2014) and rewritten by Abdelazis and Grier (Phys. Rev. E 2, 013172, 2020). Comparison between the acoustic radiation force obtained by the Gor'kov approach and by the Silva/Abdelazis and Grier approach shows that the Gor'kov equation can be accurately used for calculating the radiation force generated by standing wave fields, but the Gor'kov approach can lead to an incorrect evaluation of the force when the sphere is subjected to a focused beam or a vortex beam. For these cases, the model based on Silva/Abdelazis and Grier approach seems more appropriate for simulating the acoustic radiation force that acts on small spheres.