Dynamic acoustic tractor beams II: Oscillatory powers, cross sections, and energy efficiencies of a spherical non-viscous liquid droplet

Abstract

A previous work on dynamic acoustic tractor beams [Mitri, J. Appl. Phys. 117, 094903 (2015)] demonstrated the feasibility of pulling a liquid sphere toward a finite circular piezo-disk transducer and vibrating it around an equilibrium position at the beat frequency of two interfering waves driven at slightly different frequencies. The analysis is extended here to investigate the oscillatory phenomenon from the standpoint of energy conservation applied to scattering. Expressions for dynamic scattering, extinction and absorption powers, and their related cross sections and energy efficiencies are formally defined and derived based on the partial-wave series expansion method in spherical coordinates and the short-term time averaging (STTA) procedure. A circular flat piston transducer insonifying a spherical liquid hexane droplet (with arbitrary radius) centered on the axis of wave propagation is considered. Numerical predictions for dynamic extinction and scattering energy efficiencies illustrate the theory. A percentage error criterion related to extinction and scattering energy efficiencies is defined. Computations are also performed to quantify the numerical inaccuracy introduced by the difference-frequency component of the STTA. This criterion must be always utilized as a benchmark tool to validate dynamic radiation force computations. The results show that the percent error (induced by the difference-frequency component of the STTA process) increases as the dimensionless difference-frequency Δka increases. The present analysis is of some importance to validate dynamic radiation force numerical computations from the standpoint of energy conservation, used in the design and optimization of dynamic/oscillatory acoustic tractor beams and single-beam tweezers.