Absorption, scattering, and radiation force efficiencies in the longitudinal wave scattering by a small viscoelastic particle in an isotropic solid.

Analytical expressions of the absorption, scattering, and elastic radiation force efficiency factors are derived for the longitudinal plane wave scattering by a small viscoelastic particle in a lossless solid matrix. The particle is assumed to be much smaller than the incident wavelength, i.e., the so-called long-wavelength (Rayleigh) approximation. The efficiencies are dimensionless quantities that represent the absorbed and scattering powers and the elastic radiation force on the particle. In the quadrupole approximation, they are expressed in terms of contrast functions (bulk and shear moduli, and density) between the particle and solid matrix. The results for a high-density polyethylene particle embedded in an aluminum matrix agree with those obtained with the partial wave expansion method. Additionally, the connection between the elastic radiation force and forward scattering function is established through the optical theorem. The present results should be useful for ultrasound characterization of particulate composites, and the development of implanted devices activated by radiation force.

Scattering of a longitudinal Bessel beam by a sphere embedded in an isotropic elastic solid.

The scattering of a longitudinal Bessel beam of arbitrary order by a sphere embedded in an isotropic solid matrix is theoretically analyzed. The spherical inclusion can be made of a viscoelastic, elastic, or fluid-filled isotropic material. In the analysis, the absorbing, scattering, and extinction efficiency factors are obtained, e.g., the corresponding power per characteristic beam intensity per sphere's cross-section area. Furthermore, the extended optical theorem, which expresses the extinction efficiency in terms of an integral of the longitudinal scattering function is derived. Several features of zeroth- and first-order Bessel beams scattering in solids are illustrated considering a polymer adhesive (cured) sphere embedded in a stainless steel matrix. For instance, omnidirectional scattering can be achieved by choosing specific values of the half-cone angle of the Bessel beam, which is the beam's geometrical parameter. Additionally, it is demonstrated that mode suppression leads to lower absorption inside the inclusion when compared to plane wave scattering results.

Acoustic radiation force and torque exerted on a small viscoelastic particle in an ideal fluid.

We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (i.e. the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin-Voigt model. Simple analytical expressions for the radiation force and torque are obtained. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) in the MHz-range with polymeric particles, namely lexan, low-density (LDPE) and high-density (HDPE) polyethylene. We found that particle absorption is chiefly the cause of the radiation force due to a traveling plane wave and zero-order Bessel beam when the frequency is smaller than 5MHz (HDPE), 3.9MHz (LDPE), and 0.9MHz (lexan). Whereas in a standing wave field, the radiation force is mildly changed due to dispersion inside the particle. We also show that the radiation torque caused by a first-order Bessel beam varies nearly quadratic with frequency. These findings may enable new possibilities of particle handling in acoustophoretic techniques.