Ultrasonic Scattering by a Viscoelastic Fiber of Elliptic Cross‐Section Suspended in a Viscous Fluid Medium

Hasheminejad, Seyyed M.; Sanaei, R.

doi:10.1080/01932690600859937

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…The aim of this work is therefore directed toward developing a semi-analytical formalism based on the partial wave series expansion method in cylindrical coordinates [10] without any approximations. Another method may consider a wave-basis using infinite series expansions in elliptical Mathieu functions [15][16][17][18][19][20][21], however, the generation and computation of the elliptical functions may not be a straightforward task in numerical implementation.…”

Section: Introductionmentioning

confidence: 99%

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

Mitri¹

2019

OSA Continuum

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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. In this analysis, one of the semi-axes of the elliptical cylinder coincides with the direction of the incident field. Initially, the modal matching method is used to determine the scattering coefficients by imposing appropriate boundary conditions and solving numerically a linear system of equations by matrix inversion. In this method, standard cylindrical (Bessel and Hankel) wave functions are used. Subsequently, 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. An important application of these integral equations concerns the accurate determination of the radiation force from the measurement of the scattered field by any 2D non-absorptive object of arbitrary shape in plane waves. 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). Particular 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 noted and discussed.

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Section: Introductionmentioning

confidence: 99%

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

Mitri¹

2019

OSA Continuum

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

Mitri

2016

Ultrasonics

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Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

Mitri

2015

Journal of Applied Physics

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Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θi, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.

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Ultrasonic Scattering by a Viscoelastic Fiber of Elliptic Cross‐Section Suspended in a Viscous Fluid Medium

Cited by 3 publications

References 30 publications

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

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

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

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

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