Instantaneous axial force of a high-order Bessel vortex beam of acoustic waves incident upon a rigid movable sphere

The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere’s radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m, n) = (0, 1) (where n is the partial-wave number), and vanishes for m > 0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches.

Theoretical magnitude and phase profiles (0.3 mm × 0.3 mm) of Bessel beams of orders m = 0–3, respectively, for β = 25°. Note that the zero-order Bessel beam (displayed in (a)) is of non-vortex nature and possesses a maximum in amplitude (or intensity) at its center. When m ⩾ 1, the beam’s amplitude (or intensity) vanishes at its center, resulting in the birth of a hollow region for which the inner radius in the magnitude profile increases with the order. The vortex nature of the beam manifests itself in the phase profiles.Figure optionsDownload as PowerPoint slideHighlights
► The difference between the terminologies of the “instantaneous force” and “radiation force” is highlighted.
► The instantaneous force of a high-order Bessel vortex beam vanishes for m > 0.
► Only the dipole scattering term contributes to the instantaneous force.
► For the zero-order Bessel beam, the force linearly increases versus ka.
► When ka > 1, the linear relation breaks down.