On the calculation of radiation force on spheres due to arbitrary spatially distributed acoustic beams

This work presents a theory for the acoustic radiation force exerted on a solid sphere by an arbitrary spatially distributed beam. The theory is developed for an sphere suspended in an ideal fluid. We assume that the acoustic beam can be decomposed in a set of plane waves with same frequency, propagating in different directions. The sphere radius is considered to be much smaller than the wavelength of the beam. Bulk properties of the sphere such as shear and compressional sound speed are taken into account. The radiation force is obtained by solving the linear acoustic scattering problem for the sphere. Theoretically, the radiation force depends on the sphere cross section area, the radiation force function, and the vector energy flux upon the sphere. The radiation force function is related to the sphere scattering properties. We apply the developed theory to study the radiation force produced by an spherical concave transducer. The generated radiation force can be decomposed into two components, namely, axial and transverse with respect to the wave propagation direction. The ratio between the transverse and axial components of the force depends on the transducer F-number and wave frequency. Results show that this ratio for a 2 MHz transducer with 3.5 F-number on the focal plane is less than 5%.