Axial time-averaged acoustic radiation force on a cylinder in a nonviscous fluid revisited

Longitudinal and transverse optical scattering asymmetry parameters for a dielectric cylinder in light-sheets of arbitrary wavefronts and polarization

The asymmetry parameter is an important quantity used in radiative transfer modeling and scattering. This parameter specifies the amount of energy scattered by the particle along the direction of the incident illuminating field. However, a rigorous and complete analysis of the energetic scattering requires determining the energy scattered in the lateral direction as well. As such, the present work introduces generalized expressions for the scattering asymmetry parameters for a dielectric cylinder in arbitrary-shaped light-sheets, both along and perpendicular to the direction of the incident radiation. Both longitudinal and transverse scattering asymmetry parameters are defined, and their generalized expressions are obtained based on the (spatial) average cosine and sine of the scattering angle θ and the expression of the scattering cross section (or energy efficiency). The partial-wave series expansion method in cylindrical coordinates is used, and the resulting mathematical expressions depend on the beam-shaped coefficients and the scattering coefficients of the dielectric cylinder. Numerical results for arbitrary-shaped light-sheets illuminating a dielectric cylinder cross section located arbitrarily in space are presented and discussed. The longitudinal and transverse scattering asymmetry parameters defined here offer additional quantitative (quadratic) observables for the analysis of the energetic scattering in applications in electromagnetic scattering, optical light-sheet tweezers, radiative transfer computations, and remote sensing, to name a few examples.

Induced radiation force of an optical line source on a cylinder material exhibiting circular dichroism

The optical radiation force experienced by a cylinder material of circular cross section exhibiting circular dichroism (known also as rotary polarization) in an electric line source illumination is considered. An exact analytical expression for the radiation force (per length) valid for any frequency range is derived assuming an electric line source radiating cylindrically diverging TM-polarized waves without any approximations. The partial-wave series expansion method in cylindrical coordinates utilizing standard Bessel and Hankel functions is used to derive the electric and magnetic field expressions and a dimensionless radiation force function (or efficiency), which depends on the scattering coefficient of the cylinder as well as the distance from the radiating source. To illustrate the analysis, numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force. The numerical predictions demonstrate the possibility to pull a circular-shaped cylinder material with rotary polarization toward the illuminating electric line source with TM-polarized waves using a curved wavefront depending on the PEMC material admittance, distance to the source, and size of the cylinder.

Revised model for the radiation force exerted by standing surface acoustic waves on a rigid cylinder

In this paper, a model for the radiation force exerted by standing surface acoustic waves (SSAWs) on a rigid cylinder in inviscid fluids is extended to account for the dependence on the Rayleigh angle. The conventional model for the radiation force used in the SSAW-based applications is developed in plane standing waves, which fails to predict the movement of the cylinder in the SSAW. Our revised model reveals that, in the direction normal to the piezoelectric substrate on which the SSAW is generated, acoustic radiation force can be large enough to drive the cylinder even in the long-wavelength limit. Furthermore, the force in this direction can not only push the cylinder away, but also pull it back toward the substrate. In the direction parallel to the substrate, the equilibrium positions for particles can be actively tuned by changing Rayleigh angle. As an example considered in the paper, with the reduction of Rayleigh angle the equilibrium positions for steel cylinders in water change from pressure nodes to pressure antinodes. The model can thus be used in the design of SSAWs for particle manipulations.

Physical constraints on the non-dimensional absorption coefficients of compressional and shear waves for viscoelastic cylinders

BACKGROUND

Normalized absorption coefficients for the longitudinal and shear waves in viscoelastic (polymer-type) materials, extracted from non-fictional experimental data showed anomalous effects, such as the generation of a negative radiation force (NRF) in plane progressive waves, negative energy absorption and extinction efficiencies and a scattering enhancement, not in agreement with energy conservation.

OBJECTIVE

The objective of this work is directed towards analyzing those anomalies from the standpoint of energy conservation. Physical conditions which demonstrate that the ratio of the normalized absorption coefficients cannot be of arbitrary value but depends on the ratio of the square of the compressional and shear wave speeds, are established and discussed.

METHOD

The necessary physical condition for the validity of the linear viscoelastic (VE) model for any passive (i.e. that does not generate energy) polymeric cylinder with an ultrasonic absorption of hysteresis-type submerged in a non-viscous fluid requires that the absorption efficiency be positive (Q_abs>0) since there are no active radiating sources inside the core material. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce anomalous/unphysical NRF, negative absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency using plane progressive waves, not in agreement with energy conservation.

RESULTS

Based on the partial wave series expansion method in cylindrical coordinates, numerical results for the radiation force, extinction, absorption and scattering energy efficiencies assuming plane progressive wave incidence are performed for three VE polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient, the dimensionless size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the partial-wave mode number n. Physical and mathematical conditions are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. the 2D case) in terms of the sound velocities in the VE material. The physical condition for the spherical 3D case is also noted.

CONCLUSION

For passive materials, the physical conditions must be always satisfied to allow accurate computations of the acoustic radiation force, torque, and energy absorption, extinction and scattering efficiencies for VE cylinders having a hysteresis type of absorption (such as polymers and plastics), and submerged in a non-viscous fluid. The physical conditions must be always satisfied regardless of the shape of the incident field. They also serve to validate and verify experimental data for VE materials and test the accuracy of related numerical computations.

Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves

This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque.

Interaction of an acoustical 2D-beam with an elastic cylinder with arbitrary location in a non-viscous fluid

The classical Resonance Scattering Theory (RST) for plane waves in acoustics is generalized for the case of a 2D arbitrarily-shaped beam incident upon an elastic cylinder with arbitrary location that is immersed in a nonviscous fluid. The formulation is valid for an elastic (or viscoelastic) cylinder (or a cylindrical shell, a layered cylinder/shell, or a multilayered cylindrical shell, etc.) of any size and material. Partial-wave series expansions (PWSEs) for the incident, internal and scattered fields are derived, and numerical examples illustrate the theory. The wave-fields are expressed using a generalized PWSE involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. When the beam is shifted off the center of the cylinder, the off-axial BSCs are evaluated by performing standard numerical integration. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. The properties related to the arbitrary scattering of a zeroth-order quasi-Gaussian cylindrical beam (chosen as an example) by an elastic brass cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed. Moreover, the total and resonance backscattering form function moduli are numerically computed, and the results discussed with emphasis on the contribution of the surface waves circumnavigating the cylinder circular surface to the resonance backscattering. Furthermore, the analysis is extended to derive general expressions for the axial and transverse acoustic radiation force functions for the cylinder in any 2D beam of arbitrary shape. Examples are provided for a zeroth-order quasi Gaussian cylindrical beam with different waist. Potential applications are in underwater and physical acoustics, however, ongoing research in biomedical ultrasound, non-destructive evaluation, imaging, manufacturing, instrumentation, and acoustic holography to name a few, would benefit from the results of this analysis.

Finite series expansion of a Gaussian beam for the acoustic radiation force calculation of cylindrical particles in water

This paper focuses on studying the interaction between an acoustical Gaussian beam and cylindrical particles. Based on the finite series method, the Gaussian beam is expanded as cylindrical functions and the beam coefficient of a Gaussian beam is obtained. An expression for the acoustic radiation force function that is the radiation force per unit energy density and unit cross-sectional surface area for a cylinder in a Gaussian beam is presented. Numerical results for the radiation force function of a Gaussian beam are presented for rigid cylinders, liquid cylinders, elastic cylinders, and viscoelastic cylinders to illustrate the theory. The radiation force function versus the dimensionless frequency ka (where k is the wave number and a is the radius of the cylinder) are discussed for different beam waists. The simulation results show the differences from those of a plane wave when the beam waist w0≤5λ (where λ is the wave length). The beam waist has no effects on the radiation force function when ka<1, while the beam waist has greater effects when ka>1. The radiation force function reaches the plane wave limit when w0>5λ. The acoustic radiation force function is also determined by the parameters of the particles.

An exploration in acoustic radiation force experienced by cylindrical shells via resonance scattering theory

In nonlinear acoustic regime, a body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force (RF). This force is a second-order quantity of the velocity potential function of the ambient medium. Exploiting the sufficiency of linear solution representation of potential function in RF formulation, and following the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of the resonant field and a background (non-resonant) component, we will show that the radiation force is a composition of three components: background part, resonant part and their interaction. Due to the nonlinearity effects, each part contains the contribution of pure partial waves in addition to their mutual interaction. The numerical results propose the residue component (i.e., subtraction of the background component from the RF) as a good indicator of the contribution of circumferential surface waves in RF. Defining the modal series of radiation force function and its components, it will be shown that within each partial wave, the resonance contribution can be synthesized as the Breit-Wigner form for adequately none-close resonant frequencies. The proposed formulation may be helpful essentially due to its inherent value as a canonical subject in physical acoustics. Furthermore, it may make a tunnel through the circumferential resonance reducing effects on radiation forces.

Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.

Axial acoustic radiation force of progressive cylindrical diverging waves on a rigid and a soft cylinder immersed in an ideal compressible fluid

BACKGROUND AND MOTIVATION

Previous works investigating the radiation force of diverging spherical progressive waves incident upon spherical particles have demonstrated the direction of reversal of the force when the particle is subjected to a curved wave-front. In this communication, the analysis is extended to the case of diverging cylindrical progressive waves incident upon a rigid or a soft cylinder in a non-viscous fluid with explicit calculations for the radiation force function (which is the radiation force per unit energy density and unit cross-sectional surface) not shown in [F.G. Mitri, Ultrasonics 50 (2010) 620-627].

METHOD

A closed-form solution presented previously in [F.G. Mitri, Ultrasonics 50 (2010) 620-627] is used to plot the radiation force function with particular emphasis on the difference from the results of incident plane progressive waves versus the size parameter ka (k is the wave number and a is the cylinder's radius) and the distance of the cylinder from the acoustic source r(0).

RESULTS

Radiation force function calculations for the rigid cylinder unexpectedly reveal that under specific conditions determined by the frequency of the acoustic field, the radius of the cylinder, as well as the distance to the acoustic source, the force becomes attractive (negative force). In addition, the numerical results show that the radiation force on a rigid cylinder does not generally obey the inverse-distance law with respect to the distance from the source.

CONCLUSION AND POTENTIAL APPLICATIONS

These results suggest that it may be possible, under specific conditions, to pull a cylindrical structure back toward the acoustic source using progressive cylindrical diverging waves. They may also provide a means to predict the radiation force required to manipulate non-destructively a single cylindrical structure. Potential applications include the design of a new generation of acoustic tweezers operating using a single beam of progressive waves (in contrast to the traditional version of acoustical tweezers in which an acoustic standing wave field is produced using two counter-propagating acoustic fields) for investigations in the field of flow cytometry, particle manipulation and entrapment.