Farid G. Mitri

Radiation torque produced by an arbitrary acoustic wave

Acoustic waves may force a suspended object in the wavepath to spin by exerting a radiation torque. Generally, this torque depends on how the incident wave is scattered and absorbed by the object. We derive a general formula for the Cartesian components of the acoustic radiation torque produced by an arbitrary incident beam on an object of any geometrical shape in a nonviscous fluid. To illustrate the method, we calculate the acoustic radiation torque produced by a zero- and a first-order Bessel beam on an absorbing sphere in the off-axis configuration. Unexpectedly, the results show that some radiation torque components reverse their directions depending on the beam offset and the sphere size factor.

Application of the Biot model to ultrasound in bone: Inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimentally measured signals. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The ultrasonic propagation in cancellous bone is modelled using the Biot theory modified by the Johnson-Koplik-Dashen model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow waveforms. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

Electromagnetic Wave Scattering of a High-Order Bessel Vortex Beam by a Dielectric Sphere

This study investigates the arbitrary scattering of an unpolarized electromagnetic (EM) high-order Bessel vortex (helicoidal) beam (HOBVB) by a homogeneous water sphere in air. The radial components of the electric and magnetic scattering fields are expressed using partial wave series involving the beam-shape coefficients and the scattering coefficients of the sphere. The magnitude of the 3D electric and magnetic scattering directivity plots in the far-field region are evaluated using a numerical integration procedure for cases where the sphere is centered on the beams axis and shifted off-axially with particular emphasis on the half-conical angle of the wave number components and the order (or helicity) of the beam. Some properties of the EM scattering of an HOBVB by the water sphere are discussed. The results are of some the scattering of importance in applications involving EM HOBVBs by a spherical object.

Off-axial acoustic radiation force of repulsor and tractor bessel beams on a sphere

Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beams direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beams axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beams axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the spheres size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beams axis are found, depending on ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.

Single Bessel tractor-beam tweezers

The tractor behavior of a zero-order Bessel acoustic beam acting on a fluid sphere, and emanating from a finite circular aperture (as opposed to waves of infinite extent) is demonstrated theoretically. Conditions for an attractive force acting in opposite direction of the radiating waves, determined by the choice of the beams half-cone angle, the size of the radiator, and its distance from a fluid sphere, are established and discussed. Numerical predictions for the radiation force function, which is the radiation force per unit energy density and cross-sectional surface, are provided using a partial-wave expansion method stemming from the acoustic scattering. The results suggest a simple and reliable analysis for the design of Bessel beam acoustical tweezers and tractor beam devices.

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams

The theoretical formalism for acoustical Bessel vortex (helicoidal) tractor beams and results presented here are the first to demonstrate the emergence of a pulling force of attraction on non-spherical oblate and prolate rigid spheroidal particles centered on the beams axis of wave propagation. Numerical predictions for the axial acoustic radiation force illustrate the theory with particular emphasis on the aspect ratio of the spheroid, the half-cone angle and order of the beam, as well as the dimensionless size parameter. It is demonstrated here that the Bessel vortex beam parameters may be tailored in such a way that the spheroid is pulled against the forward linear momentum density flux associated with the incoming waves. Those results potentially suggest the use of Bessel vortex beams in the development of emergent technologies for non-contact remote sampling and particle characterization.

Near-field acoustic resonance scattering of a finite bessel beam by an elastic sphere

The near-field acoustic scattering from a sphere centered on the axis of a finite Bessel acoustic beam is derived stemming from the Rayleigh-Sommerfeld diffraction surface integral and the addition theorems for the spherical wave and Legendre functions. The beam emerges from a finite circular disk vibrating according to one of its radial modes corresponding to the fundamental solution of a Bessel beam J0. The incident pressure fields expression is derived analytically as a partial-wave series expansion, taking into account the finite size and the distance from the center of the disk transducer. Initially, the scattered pressure by a rigid sphere is evaluated, and backscattering pressure moduli plots as well as 3-D directivity patterns for an elastic PMMA sphere centered on a finite Bessel beam with appropriate tuning of its half-cone angle reveal possible resonance suppression of the sphere only in the zone near the Bessel transducer. Moreover, the analysis is extended to derive the mean spatial incident and scattered pressures at the surface of a rigid circular receiver of infinitesimal thickness. The transducer, sphere, and receiver are assumed to be coaxial. Some applications can result from the present analysis because all physically realizable Bessel beam sources radiate finite sound beams as opposed to waves of infinite extent.

Airy acoustical–sheet spinner tweezers

The Airy acoustical beam exhibits parabolic propagation and spatial acceleration, meaning that the propagation bending angle continuously increases before the beam trajectory reaches a critical angle where it decays after a propagation distance, without applying any external bending force. As such, it is of particular importance to investigate its properties from the standpoint of acoustical radiation force, spin torque, and particle dynamics theories, in the development of novel particle sorting techniques and acoustically mediated clearing systems. This work investigates these effects on a two-dimensional (2D) circular absorptive structure placed in the field of a nonparaxial Airy “acoustical-sheet” (i.e., finite beam in 2D), for potential applications in surface acoustic waves and acousto-fluidics. Based on the characteristics of the acoustic field, the beam is capable of manipulating the circular cylindrical fluid cross-section and guides it along a transverse or parabolic trajectory. This feature of ...

Partial-wave series expansions in spherical coordinates for the acoustic field of vortex beams generated from a finite circular aperture.

A method based on the Rayleigh-Sommerfeld surface integral is provided, which makes it feasible to rigorously model, evaluate and compute the acoustic scattering and other mechanical effects of finite-aperture vortex beams such as the acoustic radiation force and torque on a viscoelastic sphere in various applications in acoustic tweezers and microfluidics, particle entrapment, manipulation and rotation. Partial-wave series expansions are derived for the incident field of acoustic spiraling (vortex) beams, comprising high-order Bessel and Bessel-Gauss beams.Stemming from the Rayleigh-Sommerfeld surface integral, the addition theorems for the spherical wave and Legendre functions, and a weighting function describing the behavior of the radial component vp1 of the normal velocity at the surface of a finite circular radiating source, partial-wave series expansions are derived for the incident field of acoustic spiraling (vortex) beams in a spherical coordinate system centered on the axis of wave propagation. Examples for vortex beams, comprising ρ-vortex, zeroth-order and higher order Bessel-Gauss and Bessel, truncated Neumann-Gauss and Hankel- Gauss, Laguerre-Gauss, and other Gaussian-type vortex beams are considered. The mathematical expressions are exact solutions of the Helmholtz equation. The results presented here are particularly useful to accurately evaluate analytically and compute numerically the acoustic scattering and other mechanical effects of finite vortex beams, such as the axial and 3-D acoustic radiation force and torque components on a sphere of any (isotropic, anisotropic, etc.) material (fluid, elastic, viscoelastic, etc.), either centered on the beams axis of wave propagation, or placed off-axially. Numerical predictions allow optimal design of parameters in applications including but not limited to acoustical tweezers, acousto-fluidics, beamforming design, and imaging, to name a few.