New expressions for the radiation force function of spherical targets in stationary and quasi-stationary waves

A new expression for the radiation force function – which is the radiation force per unit energy density and unit cross-sectional surface area – for spheres in a stationary (or standing) and quasi-stationary wave is obtained based on the far-field acoustic scattering field. The radiation force function formulation has been simplified mathematically and improved into a more general form. Numerical results are presented for rigid and elastic spheres, air bubbles in water as well as liquid drops in air to illustrate the theory. It is demonstrated that expressions for the radiation force functions obtained from the far-field derivation approach are equivalent to those obtained from the near-field-based derivation.