Method In Cylindrical Coordinates Research Articles

Optical TM ⇄ TE mode conversion contribution to the radiation force on a cylinder exhibiting rotary polarization in circularly polarized light

Circularly polarized light can induce additional mode conversion when it interacts with a material that rotates the orientation of the plane of polarization, which is known as “optical rotation” or “rotary polarization”. The effect of this additional mode conversion phenomenon is studied in the framework of the optical radiation force theory. The time-averaged force (per-length) acting on an infinitely long perfect electromagnetic conductor (PEMC) circular cylinder is considered. The multipole modal expansion method in cylindrical coordinates is utilized to derive exact series expansions for the components of the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation) applicable to any range of frequencies. Numerical predictions for the radiation force function (which is the radiation force per unit energy density and cross-sectional surface) and its components clearly demonstrate the contribution of the co-polarized and cross-polarized waves. It is shown that the total radiation force is not the mere sum of the TM and TE mode components in a circularly polarized wave-field. There is an additional cross-interference term describing the contributions of TM ⇄ TE mode conversion to the total force that cannot be neglected. The computations show that the interference term can be positive, null or negative as the dimensionless size parameter ka and admittance M of the cylinder vary (where k is the wavenumber in the medium of wave propagation and a is the radius of the cylinder). The results show that the total force is always positive and acts in the direction of wave propagation (i.e., force of repulsion). The analysis is further extended to compute the energy efficiencies, demonstrating the validity of the results from the standpoint of energy conservation. This work generalizes the radiation force formalism for linearly polarized fields by introducing additional terms corresponding to TM ⇄ TE mode conversions in the series expansion for the longitudinal radiation force on cylindrical materials exhibiting rotary polarization in circularly polarized plane progressive waves.

Optical cross-sections and energy efficiencies of a cylindrical material exhibiting circular dichroism in arbitrary-shaped monochromatic light-sheets

Optical scattering, extinction and absorption cross-sections are derived for a cylindrical material exhibiting rotary polarization. A structured light-sheet of arbitrary shape illuminates the cylindrical particle of arbitrary geometrical cross-section. The partial-wave series expansion method in cylindrical coordinates is used and Poynting’s theorem is applied. Exact mathematical series expansions are obtained without any approximations. They demonstrate that the optical cross-sections are not the mere sum of linearly polarized components. Additional terms contributing to the series arise from the cross-interaction of the linearly polarized modes (known also as mode conversion TM ⇆ TE) in the scattering field. Numerical examples for the scattering or extinction energy efficiencies of a left-handed circularly polarized Airy light sheet illustrate the analysis for a circular perfect electromagnetic conductor cylinder in air. The results clearly demonstrate the contribution of mode conversion for a cylinder exhibiting circular dichroism. Under some specific conditions determined by the incident light-sheet characteristics and cylinder size, mode conversion can be zero, or it can contribute in the enhancement or reduction of the scattering.

Dynamic oscillatory radiation force in optical heterodyning

In contrast with the optical radiation force induced by conventional lasers of continuous mono-frequency wave-fields, a dynamic or oscillatory mode arises when a beating effect caused by intensity changes over time (i.e., amplitude modulation) occurs. The purpose of this analysis is directed toward examining theoretically the dynamic (oscillatory) radiation force in optical heterodyning, caused by interfering/mixing two electromagnetic/optical plane waves driven at slightly different frequencies. The example of a dielectric cylinder material having a circular geometric cross-section is considered. Based on the integration of Maxwell's stress tensor over the surface of the object in the near-field, the modal expansion method in cylindrical coordinates is used in conjunction with the short-term time average to obtain mathematical series for the longitudinal dynamic optical radiation force per-length (i.e. acting along the direction of wave propagation). The cases of incident TM and TE polarized plane progressive waves are considered. Numerical illustrative results for the dimensionless dynamic radiation force function are performed with particular emphasis on changing the size parameter of the cylinder as well as the normalized difference-frequency and time parameters. The results show that the total force is not the mere sum of the components originated by the primary waves. There is an additional cross-term factor related to the dynamic component which cannot be neglected, suggesting that the radiation force phenomenon using beating optical waves is slowly time-varying (oscillatory). Moreover, a resonance splitting effect in the plots of the dynamic radiation force is observed and discussed. The present analysis has the potential to open a novel method in the development of dynamic/oscillatory optical heterodyne tweezers and tractor beams for particle manipulation and characterization.

Optical radiation force circular dichroism spectroscopy

This work introduces the method of circular dichroism spectroscopy in the framework of the electromagnetic/optical radiation force theory. This technique is defined here as the difference in radiation force of left-handed and right-handed circularly polarized electromagnetic waves illuminating an object exhibiting rotary polarization. The example of a lossless material, such as the perfect electromagnetic conductor (PEMC) cylinder having a circular geometric cross-section, is considered. The modal expansion method in cylindrical coordinates is used to obtain exact mathematical series expansions for the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation) considering left-handed and right-handed circularly polarized cylindrically diverging waves emanating from a line source. The case of plane progressive waves is recovered when the source is located far from the cylinder. Numerical illustrative results for the dimensionless radiation force functions as well as the scattering, extinction and absorption energy efficiencies and their co-polarized and cross-polarized components are performed with particular emphasis on the size parameter of the cylinder, the dimensionless distance parameter from the line source, and the admittance of the cylinder. The results reveal that the individual radiation force functions for left-handed and right-handed circularly polarized waves can be negative, zero, or positive depending on the cylinder distance from the source. Moreover, the optical radiation force circular dichroism (ORFCD) and the extinction energy efficiency circular dichroism (EEECD) are positive for a negative admittance of the cylinder, while they reverse sign for a positive admittance. While the EEECD shows some form of symmetry versus admittance sign change, the ORFCD does not. The possibility of achieving invisibility cloaking for a small PEMC cylinder is also predicted. The present ORFCD spectroscopy method is applicable to any cylinder material exhibiting rotary polarization such as chiral, topological insulator, plasma, liquid crystal etc.

Radiation force and torque on an elliptical cylinder illuminated by a TE-polarized non-paraxial focused Gaussian light sheet with arbitrary incidence.

Predicting and computing the optical radiation force and torque experienced by an elliptical cylinder illuminated by a structured finite light-sheet beam in two dimensions (2D) remains a challenge from the standpoint of light-matter interactions in electromagnetic (EM) optics, tweezers, laser trapping, and scattering theory. In this work, the partial-wave series expansion method in cylindrical coordinates (which utilizes standard Bessel and Hankel wave functions) is proposed, verified, and validated. Exact expressions for the longitudinal and transverse radiation force components (per length) as well as the axial radiation torque component (per length) are derived analytically without any approximations. The example of a TE-polarized non-paraxial focused Gaussian light sheet illuminating a perfect electrically conducting (PEC) elliptical cylinder is considered. The scattering coefficients of the elliptical cylinder are determined by imposing the Neumann boundary condition and numerically solving a linear system of equations by matrix inversion. The structural functions are determined using a single numerical angular integration procedure to enforce the orthogonality and thus validity of the solution, making the proposed method semi-analytical. Calculations are performed for the non-dimensional longitudinal and transverse radiation force efficiencies (or functions) as well as the axial radiation torque efficiency. Emphases are given to varying the ellipticity of the cylindrical particle, its non-dimensional size, the non-paraxial beam waist (i.e., focusing), and the angle of incidence in the polar plane. Suitable convergence plots confirm the validity of the partial-wave series method to evaluate accurately the radiation force and torque with no limitation to a particular frequency range or particle size. The results are mostly relevant in understanding the fundamentals of the optical/EM radiation force and torque theories for structured focused light sheets and related applications dealing with the interactions of EM waves with elongated tubular particles with elliptical surfaces in particle manipulation and other areas. The analogy with the acoustical counterpart is also noted, which shows the universal character of the radiation force and torque phenomena.

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.

Radiation force and torque on perfect electrically–conducting (PEC) corrugated circular and elliptical cylinders in TE or TM polarized plane progressive waves with arbitrary incidence

In this work, theoretical modeling and numerical computations for the electromagnetic (EM) radiation force and torque (per-length) on perfect electrically conducting (PEC) cylinders of corrugated circular and elliptical geometrical cross-sections are developed and presented. A TE-polarized or TM-polarized plane progressive wave illumination with arbitrary incidence (in the polar plane) is assumed at normal incidence with respect to the axis of the cylindrical particle. The multipole expansion method in cylindrical coordinates is used and the scattering coefficients of the object of arbitrary shape (in 2D) are determined by imposing appropriate boundary conditions and solving numerically a linear system of equations by matrix inversion. Numerical computations are performed for the non-dimensional longitudinal and transverse radiation force functions as well as the axial radiation torque function. Suitable convergence plots confirm the validity of the multipole expansion approach to evaluate the radiation force and torque with no limitation to a particular frequency range (i.e. Rayleigh, Mie or geometrical optics regimes can be considered using the presented formalism). Particular emphases are given on the shape of the particle (i.e., circular or elliptical), its non-dimensional size, the corrugation/waviness characteristic of its surface, the polarization of the incident plane wave field, and the angle of incidence in the polar plane. The numerical predictions show that the longitudinal and transverse components of the radiation force vector are positive regardless of particle shape, size, corrugation properties, polarization and incidence angle [0 ≤ α ≤ 90°], while the axial torque component reverses sign at particular values of these parameters. The results are predominantly relevant in understanding the fundamentals of the optical/EM radiation force and torque theories and possible applications dealing with the interactions of EM waves with elongated tubular particles with circular or noncircular ribbed surfaces in particle manipulation and other areas. The acoustical analogue is also noted, which shows the universal characteristic of the radiation force and torque phenomena.

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

ABSTRACTExact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.

Electromagnetic radiation force on a perfect electromagnetic conductor (PEMC) circular cylinder

Unlike isotropic dielectric objects, the interaction of incident electromagnetic (EM) or optical waves with a material allowing rotary polarization produces coupled polarized internal and scattered fields. The aim of this investigation is to examine theoretically a novel physical effect, which concerns the contributions of the co-polarized and cross-polarized fields to the radiation force (per-length) experienced by an infinitely long perfect electromagnetic conductor (PEMC) cylinder having a circular cross-section and illuminated by TM-polarized plane progressive waves propagating perpendicularly to its axis. The multipole partial-wave series expansion method in cylindrical coordinates is used to derive exact series expansions for the co-polarized and cross-polarized components of the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation). In contrast with the perfect electric or magnetic conductors (PECs or PMCs), or the dielectric cylinder case, numerical illustrative results for the radiation force function (which is the radiation force per unit energy density and cross-sectional surface) clearly demonstrate the contribution of the cross-polarized component of the radiation force for a PEMC cylinder allowing rotary polarization. The results show that the cross-polarized component of the radiation force function can be positive or negative as the dimensionless frequency parameter ka varies (where k is the wavenumber in the medium of wave propagation and a is the radius of the cylinder). Moreover, it vanishes for ka = 0.67946 regardless of the admittance of the PEMC cylinder. Notice that the total force (i.e. the sum of the co-polarized and cross-polarized components) is always repulsive (i.e., positive). It is also verified that the results are in complete agreement with the law of energy conservation applied to scattering. The present analysis generalizes the classical radiation force investigations by introducing extra new terms in the series expansion for the longitudinal radiation force function for cylindrical materials allowing rotary polarization.

Edge-induced radiation force and torque on a cylindrically-radiating active acoustic source located near a rigid corner-space

This work examines the physical effect of the edge-induced acoustic radiation force and torque on an acoustically radiating infinitely-long circular cylindrical source, located near a rigid corner. Assuming harmonic (linear) radiating waves of the source, vibrating in monopole or dipole radiation modes near a rigid corner-space in a non-viscous fluid, the modal series expansion method in cylindrical coordinates, the classical method of images and the translational addition theorem are applied to obtain the mathematical expressions for the radiation force and torque components in exact partial-wave series. Computational results illustrate the theory, and examine some of the conditions where the radiation force and torque components vanish, which has the potential to achieve total motion suppression (i.e., translation or rotation). Furthermore, depending on the size parameter of the source and the distances from the rigid corner space, these physical observables take positive or negative values, anticipating the prediction of pulling/pushing motions toward the corner space, and possible spinning of the source clockwise or counter-clockwise. The present analysis and its results may be useful in some applications related to underwater acoustical oceanographic engineering of submerged objects, cloaking and stealth technology development and the experimental design of elongated unmanned autonomous vehicles or submarines, as well as the manipulation of an active carrier or ultrasound contrast agents of elongated cylindrical shapes near a corner space or chamber walls at a right angle.

Ultrahigh sensitivity with different taper geometries of thin-core fiber modal interferometer for refractive index sensing

A highly sensitive refractive index sensor based on a fiber in-line Mach–Zehnder interferometer sensor based on single-mode–tapered thin-core–single-mode fiber is proposed. We developed a theoretical model using wide-angle beam propagation method in cylindrical coordinates to simulate light propagation performance of such fiber devices. Tapered structures using different taper geometries (linear, exponential, and parabolic taper) with waist diameters as low as 30 μm are presented. The proposed sensor has an ultrahigh sensitivity of 996.4 nm/refractive index unit in glycerin solution with different concentrations in water using the linear taper geometry. The designed structure presents the merits of high sensitivity, which is 6 times higher than that of the thin-core fiber modal interferometer and makes it an excellent candidate for biochemical sensing applications.

Optical radiation force (per–length) on an electrically conducting elliptical cylinder having a smooth or ribbed surface

The aim of this work is to develop a formal semi-analytical model using the modal expansion method in cylindrical coordinates to calculate the optical/electromagnetic (EM) radiation force-per-length experienced by an infinitely long electrically-conducting elliptical cylinder having a smooth or wavy/corrugated surface in EM plane progressive waves with different polarizations. One of the semi-axes of the elliptical cylinder coincides with the direction of the incident field. The modal matching method is used to determine the scattering coefficients by matrix inversion. Standard cylindrical (Bessel and Hankel) wave functions are used. Simplified expressions leading to exact series expansions for the optical/EM radiation forces assuming either electric (TM) of magnetic (TE) plane wave incidences are provided without any approximations, in addition to integral equations demonstrating the direct relationship of the radiation force with the square of the scattered field magnitude. Numerical computations for the non-dimensional radiation force function are performed for electrically conducting elliptic and circular cylinders having a smooth or ribbed/corrugated surface. Adequate convergence plots confirm the validity and correctness of the method to evaluate the radiation force with no limitation to a particular frequency range (i.e. Rayleigh, Mie or geometrical optics regimes). Emphases are given on the aspect ratio, the non-dimensional size of the cylinder, the corrugation characteristic of its surface, and the polarization of the incident field. The results are particularly relevant in optical tweezers and other related applications in fluid dynamics, where the shape and stability of a cylindrical drop stressed by a uniform external electric/magnetic field are altered. Furthermore, a direct analogy with the acoustical counterpart is discussed.

The involvement of vaginal microbiome in threatened premature delivery

This investigation shows that an active emitting electromagnetic (EM) Dirichlet source (i.e., with axial polarization of the electric field) in a homogeneous non-dissipative/non-absorptive medium placed near a perfectly conducting boundary can render total invisibility (i.e. zero extinction cross-section or efficiency) in addition to a radiation force cancellation on its surface. Based upon the Poynting theorem, the mathematical expression for the extinction, radiation and amplification cross-sections (or efficiencies) are derived using the partial-wave series expansion method in cylindrical coordinates. Moreover, the analysis is extended to compute the self-induced EM radiation force on the active source, resulting from the waves reflected by the boundary. The numerical results predict the generation of a zero extinction efficiency, achieving total invisibility, in addition to a radiation force cancellation which depend on the source size, the distance from the boundary and the associated EM mode order of the active source. Furthermore, an attractive EM pushing force on the active source directed toward the boundary or a repulsive pulling one pointing away from it can arise accordingly. The numerical predictions and computational results find potential applications in the design and development of EM cloaking devices, invisibility and stealth technologies.

Acoustic radiation force of attraction, cancellation and repulsion on a circular cylinder near a rigid corner space

• The acoustic radiation force on a cylindrical particle near a corner space is determined. • Plane progressive waves with an arbitrary incidence angle are considered. • Depending on the distances, incidence angle and particle size, particle neutrality is yielded. • Attraction or repulsion forces to the corner space can also arise. • Potential applications are in acoustofluidics applications and related areas of research. The purpose of this study is to derive exact partial wave series expansions for the longitudinal and transverse radiation force components, for a circular cylinder in the proximity of a rigid corner space, and illuminated by incident plane waves with arbitrary orientation in the polar plane. Based on the multipole expansion method in cylindrical coordinates , the method of images as well as the translational addition theorem , an effective incident field (resulting from the primary waves as well as the multiple scattered fields from the image sources) is determined first, and used subsequently with the scattered field to derive the mathematical expressions for the radiation force components, stemming from the integration of the radiation stress in a non-viscous fluid. Numerical computations illustrate the analysis for rigid and soft cylinders with particular emphasis on the distances from the particle edges to the neighbouring walls, the size of the cylinder and the angle of incidence. Depending on the choice of these parameters, the radiation force components can vanish, rendering complete “invisibility”; i.e., the cylinder becomes unresponsive to the transfer of linear momentum carried by the incident effective field. Moreover, the radiation force components alternate between positive and negative values, suggesting a force of repulsion or attraction. The results find potential applications in acoustofluidics design and optimization as they shed light on the anechoic radiation force effect on a particle nearby a rigid corner. Other applications in noise and vibration control could also benefit from the results of the present investigation along with further related topics.

Scattering cross-section of a cylindrical conducting particle illuminated by electromagnetic plane waves near a conducting quarter-space

The study of the electromagnetic scattering by a particle located near a perfectly conducting corner is a fundamental topic in radar imaging, communications, remote sensing and other applications. In earlier works, the analytical modeling considered the linear field and its scattering properties. Nonetheless, energy efficiencies (or cross-sections) are meaningful fundamental physical observables connected with quadratic quantities of the linear field, which reveal additional properties of the scatterer not obtained from the linear scattered field. The aim of this work is therefore directed toward developing an improved analytical formalism for the energy efficiency factors (or cross-sections) of a cylindrical conducting particle, illuminated by electromagnetic plane waves, and located near a perfectly conducting corner-space. Incident plane progressive waves with an arbitrary angle of incidence are considered in a homogeneous, non-dissipative and non-magnetic fluid. The multiple scattering effects occurring between the electrically-conducting cylindrical particle and corner are described rigorously using the modal expansion method in cylindrical coordinates, the classical method of images and the translational addition theorem. Exact closed-form series expansions are derived and numerical examples illustrate the analysis with particular emphases on the distances from the corner-space, particle size and polarization of the incident field. The results are useful to predict the energetic scattering for various applications, and can serve to validate the results of purely numerical methods in experimental design. Some analogies with the acoustical cross-section theory are also noted.

Computation of Tensor Green’s Functions in Uniaxial Planar-Stratified Media With a Rescaled Equivalent Boundary Approach

An equivalent boundary approach is developed to compute electric- and magnetic-type tensor Green’s functions in general anisotropic media. With this approach, a succinct and robust representation is provided of the tensor Green’s functions for planar-stratified media with uniaxial anisotropic layers based on the propagator matrix method in cylindrical coordinates. In deriving the tensor Green’s functions in the spectral domain, the point electric- or magnetic-current source is replaced by appropriate boundary conditions. In the cylindrical coordinate system, a cylindrical Hankel integral transformation is adopted to expedite the integration of the tensor Green’s functions from the spectral domain to the spatial domain. A Levin-type collocation method for the fast integration of rapidly oscillatory functions is applied to effectively compute the spectral integrals with oscillatory and slowly decaying behavior along the contour integral path.

Implementation of the FDTD method in cylindrical coordinates for dispersive materials: Modal study of C-shaped nano-waveguides

The objective of this work is to develop a code based on the finite difference time domain method in cylindrical coordinates (CC-FDTD) that integrates the Drude Critical Points model (DCP) and to apply it in the study of a metallic C-shaped waveguide (CSWG). The integrated dispersion model allows an accurate description of noble metals in the optical range and working in cylindrical coordinates is necessary to bypass the staircase effect induced by a Cartesian mesh especially in the case of curved geometrical forms. The CC-FDTD code developed as a part of this work is more general than the Body-Of-Revolution-FDTD algorithm that can only handle structures exhibiting a complete cylindrical symmetry. A N-order CC-FDTD code is then derived and used to perform a parametric study of an infinitly-long CSWG for nano-optic applications. Propagation losses and dispersion diagrams are given for different geometrical parameters.

Active electromagnetic invisibility cloaking and radiation force cancellation

This investigation shows that an active emitting electromagnetic (EM) Dirichlet source (i.e., with axial polarization of the electric field) in a homogeneous non-dissipative/non-absorptive medium placed near a perfectly conducting boundary can render total invisibility (i.e. zero extinction cross-section or efficiency) in addition to a radiation force cancellation on its surface. Based upon the Poynting theorem, the mathematical expression for the extinction, radiation and amplification cross-sections (or efficiencies) are derived using the partial-wave series expansion method in cylindrical coordinates. Moreover, the analysis is extended to compute the self-induced EM radiation force on the active source, resulting from the waves reflected by the boundary. The numerical results predict the generation of a zero extinction efficiency, achieving total invisibility, in addition to a radiation force cancellation which depend on the source size, the distance from the boundary and the associated EM mode order of the active source. Furthermore, an attractive EM pushing force on the active source directed toward the boundary or a repulsive pulling one pointing away from it can arise accordingly. The numerical predictions and computational results find potential applications in the design and development of EM cloaking devices, invisibility and stealth technologies.

Extinction cross-section cancellation of a cylindrical radiating active source near a rigid corner and acoustic invisibility

Active cloaking in its basic form requires that the extinction cross-section (or energy efficiency) from a radiating body vanishes. In this analysis, this physical effect is demonstrated for an active cylindrically radiating acoustic source in a non-viscous fluid, undergoing periodic axisymmetric harmonic vibrations near a rigid corner (i.e., quarter-space). The rigorous multipole expansion method in cylindrical coordinates, the method of images, and the addition theorem of cylindrical wave functions are used to derive closed-form mathematical expressions for the radiating, amplification, and extinction cross-sections of the active source. Numerical computations are performed assuming monopole and dipole modal oscillations of the circular source. The results reveal some of the situations where the extinction energy efficiency factor of the active source vanishes depending on its size and location with respect to the rigid corner, thus, achieving total invisibility. Moreover, the extinction energy efficiency factor varies between positive or negative values. These effects also occur for higher-order modal oscillations of the active source. The results find potential applications in the development of acoustic cloaking devices and invisibility in underwater acoustics or other areas.

Acoustic radiation torques on a pair of fluid viscous cylindrical particles with arbitrary cross-sections: Circular cylinders example

The numerical prediction of the radiation torques in acoustofluidics and fluid dynamics applications is essential for the design and the understanding of the underlying physics as it allows quantitative analyses. In this work, closed-form analytical expressions for the acoustic radiation torques arising from multiple scattering effects between a pair of fluid viscous cylindrical particles of arbitrary cross-sections are derived. Plane progressive waves with an arbitrary incidence angle are considered. The multipole expansion method in cylindrical coordinates is used to describe the multiple scattering effects as well as the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined and used with the scattered field to derive the analytical expressions for the torques. The mathematical expressions for the radiation torque on each particle are formulated using partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the radiation torque expressions depend on the coupled expansion coefficients of both scatterers in addition to an interference factor coupled to the interparticle distance. Numerical examples illustrate the analysis for two fluid viscous circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation torque functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the circular particles. Depending on the interparticle distance and incidence angle, the particles can yield rotational neutrality; they become unresponsive (i.e., “invisible”) to the angular momentum transfer caused by multiple scattering and cancellation effects. Moreover, the radiation torque functions can be positive implying a direction of rotation in the counter-clockwise direction, and under some conditions determined by the interparticle distance, angle of incident and particle size, they reserve sign, indicating an opposite spinning in the clockwise direction. This study provides a complete analytical method and computations of the acoustic radiation torques in multiple acoustic scattering by a pair of fluid viscous scatterers. The results can be used as a priori information in the design of acoustofluidic devices and other applications involving particle rotation and handling.