A Spheroidal Model of Light Scattering by Nonspherical Particles

Optics and Spectroscopy - We have constructed a spheroidal model to solve the problem of light scattering by nonspherical particles. The semiaxes of the model spheroid are determined based on the...     

Acoustic scattering on spheroidal shapes near boundaries

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an “ultimate” singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.     

The energy of a prolate spheroidal shell in a uniform magnetic field

The problem of the energy of a spheroidal magnetic shell, solved by methods of classical electrodynamics, arises, in particular, upon the study of thin-wall biocompatible microcapsules in connection with a pressing issue of targeted drug delivery. The drug inside a microcapsule should be released from the shell at a required instant of time by destroying the capsule’s shell. The placement inside a shell of magnetic nanoparticles sensitive to an external magnetic field theoretically makes it possible to solve both problems: to transport a capsule to the required place and to destroy its shell. In particular, the shell can be destroyed under the action of internal stress when the shape of a capsule is changed. In this paper, the analysis of the model of a magnetic microcapsule in the form of a prolate spheroidal shell is performed and formulas for the magnetostatic and magnetic free energy when the magnetic field is directed along the major axis of the spheroid are derived.     

Acoustic radiation impedance of rectangular pistons on prolate spheroids

The self and mutual radiation impedances for rectangular piston(s) arbitrarily located on a rigid prolate spheroidal baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution is expressed in terms of a modal series representation in spheroidal eigenfunctions. The prolate spheroidal wave functions are obtained using computer programs that have been recently developed to provide accurate values of the wave functions at high frequencies. Results for the normalized self and mutual radiation resistance and reactance are presented over a wide frequency range for different piston sizes and spheroid shapes.     

Application of Mie theory to determine the structure of spheroidal scatterers in biological materials

We present here the results of a numerical study on light scattering from nonspherical particles with relevance to detecting precancerous states in epithelial tissues. In previous studies of epithelial cell nuclei, the experimental light scattering data have been analyzed by comparison with Mie theory. However, given the spheroidal shape of many cell nuclei, the validity of this assumption demands a thorough investigation. We investigate this assumption by using the T-matrix method to model light scattered from spheroids with parameters relevant to epithelial cell nuclei. In our previous studies, we have developed a data analysis procedure that extracts the oscillatory component of the angular-scattering distribution for an ensemble of epithelial cell nuclei for comparison with Mie theory. We demonstrate that application of our analysis procedure to the predictions of the T-matrix method for spheroids, oriented such that their axis of symmetry is aligned with the incident light propagation direction, generally yields the spheroid dimension that is transverse to the incident light propagation direction with subwavelength accuracy.     

Study of the scattering of nonlinearly interacting plane acoustic waves by an elongated spheroid

The scattering of nonlinearly interacting plane acoustic waves on a rigid elongated spheroid is considered. The foci of the spheroid coincide with foci of the spheroidal coordinate system. The method of successive approximations is used to obtain the solutions to the inhomogeneous wave equation in the first and second approximations. Asymptotic expressions are offered for the components of the total acoustic pressure of the difference frequency wave, and the scattering diagrams for these components are presented.     

Extended boundary condition method in combination with field expansions in terms of spheroidal functions

The problem of light scattering by nonspherical particles, which arises in many applications, is nowadays most frequently solved by the method of extended boundary conditions in combination with the expansion of the fields in terms of spherical wave functions. However, such an approach encounters difficulties if the shape of particles is far from spherically symmetric, even in the simplest case of spheroids with the semiaxis ratio a/b > 5?10. A new approach to solving this problem is proposed, which also applies the extended boundary condition method but involves the expansion of the fields in terms of spheroidal functions. In this case, to obtain effective solutions for strongly prolate and oblate particles, the fields are divided in two parts with known properties and specific scalar potentials are used for each part. The basic relations of the approach are presented and some results of calculations of the optical properties of spheroids and spheroidal Chebyshev particles that are performed using computer codes realizing this approach are given. The convergence of the results for different cases and the domain of applicability of the method are discussed.     

Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field

A general spheroidal coordinate separation-of-variables solution is developed for the determination of the acoustic pressure distribution near the surface of a rigid spheroid for a monofrequency incident acoustic field of arbitrary character. Calculations are presented, for both the prolate and oblate geometries, demonstrating the effects of incident field orientation and character (plane-wave, spherical wave, cylindrical wave, and focused beam) on the resultant acoustic pressure distribution.     

Achieving sub-wavelength resonant structures and transparency by a conducting spheroid with metamaterial coatings

The possibility of using metamaterial covers to dramatically enhance the total scattering cross-sections (SCS) or drastically reduce total SCSs of spheroidal objects is presented. The scattering problem by a conducting spheroid with metamaterial coating at axial incidence is studied using an analytic solution by expanding the incident and scattered waves in terms of spheroidal vector wave functions and imposing the appropriate boundary conditions at each spheroidal surface. Numerical results show that the total SCSs of a conducting spheroid with different metamaterial coatings can be dramatically enhanced to achieve 'sub-wavelength resonant structures' or drastically reduced to achieve 'transparency' of objects. The results with different parameters, such as relative permittivity, the spheroidal geometry, and the ratio of semimajor axes of two layers, are provided and discussed.     

随机取向非球形沙尘气溶胶粒子的光学特性

利用离散偶极子近似法分析了一种随机取向旋转椭球体沙尘气溶胶粒子模型在尺度参数变化范围为0.1~23时(波长0.55!m对应有效半径为0.01~2!m)的光学特性,研究了沙尘粒子非球形性程度对其光学特性的影响,并考察了非球形粒子的随机取向能否用等体积球体来代替。就随机取向单分散和多分散旋转椭球体沙尘气溶胶而言,粒子非球形特征越明显,消光效率因子、不对称因子和单次散射反照率基本上偏离其等体积球体越大;对于相同的非球形,不对称因子偏离其等体积球体的相对偏差要比消光效率因子和单次散射反照率要大。非球形粒子的随机取向并不能使其光学特性严格等效为其等体积球体的光学特性。如果粒子形状偏离球体较小,则非球形粒子的随机取向的平均效果能使其消光效率因子、不对称因子和单次散射反照率近似用等体积球体的对应光学参量来等效;而如果粒子形状偏离球形较大,仅有单次散射反照率可以近似用等体积球体的单次散射反照率来等效,例如,轴半径比为16的旋转椭球体沙尘粒子的单次散射反照率偏离其等体积球体仅在3%以内。     

Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other nonspherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry, and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition as the shear rate decreases. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.     

Uniform asymptotic formulae for the spheroidal angular function

The problem of wave scattering by a spheroid is treated. Special interest is paid to the solution of the differential wave equation related to the angular spheroidal functions. A solution is obtained using uniform asymptotic formulae along with semiclassical methods. The developed method shows that it is possible to interpolate uniformly the spheroidal angular function with Weber's parabolic cylindric functions and Legendre's functions.     

Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method

An improved penalty immersed boundary method (pIBM) has been proposed for simulation of flow-induced deformation of three-dimensional (3D) elastic capsules. The motion of the capsule membrane is described in the Lagrangian coordinates. The membrane deformation takes account of the bending and twisting effects as well as the stretching and shearing effects. The method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C¹ continuous. The membrane motion is then solved by the subdivision-surface based finite element method on the triangular unstructured mesh. On the other hand, the fluid motion is defined on the Eulerian domain, and is advanced by the fractional step method on a staggered Cartesian grid. Coupling of the fluid motion and the membrane motion is realized in the framework of the pIBM. Using the proposed method, deformation of 3D elastic capsules in a linear shear flow is studied in detail, and validations are examined by comparing with previous studies. Both the neo-Hookean membrane and the Skalak membrane are tested. For an initially spherical capsule the tank-treading motion is formed under various dimensionless shear rates and reduced bending moduli. It is found that buckling occurs near the equator of the capsule for small shear rates but near the tips for large shear rates, which is suppressed by including the bending rigidity of the membrane. Effects of the Reynolds number and the membrane density are investigated for an initially spherical capsule. For a non-spherical capsule, with the initial shape of the oblate spheroid or the biconcave circular disk as a model of the red blood cell, the swinging motion is observed due to the shape memory effect. By decreasing the dimensionless shear rate or increasing the reduced bending modulus, the swinging motion is transited into the tumbling motion.     

Application of spheroidal functions in theory of light scattering by nonspherical particles: Separation of variables method

The separation of variables method (SVM), which uses a spheroidal basis, is proposed. According to this method, fields are presented in the form of expansion in terms of spheroidal functions. The previously conducted analysis of various methods using a spherical basis showed that the SVM is applicable in a broader area for numerical calculations, while the proposed approach using a spheroidal basis yields reliable results in the case of spheroids with a high degree of asphericity where other methods and approaches cannot be used. Importantly, the method includes an SVM that uses a spherical basis as the limiting case. Thus, the proposed method has all chances of being highly efficient for calculation of optical characteristics of various nonspherical particles in a wide range of parameters of the formulated problem.     

A theoretical study of the spheroidal droplet evaporation in forced convection

In many applications, the shape of a droplet may be assumed to be an oblate spheroid. A theoretical study is conducted on the evaporation of an oblate spheroidal droplet under forced convection conditions. Closed-form analytical expressions of the mass evaporation rate for an oblate spheroid are derived, in the regime of controlled mass-transfer and heat-transfer, respectively. The variation of droplet size during the evaporation process is presented in the regime of shrinking dynamic model. Comparing with the droplets having the same surface area, an increase in the aspect ratio enhances the mass evaporation rate and prolongs the burnout time.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.     

利用近前向散射图样识别单粒子形状的理论研究

近前向光学散射图样可以用来表征颗粒物的形状.基于球形芽孢杆菌、枯草芽孢杆菌、类鼻疽伯克氏菌的回转长椭球模型, 采用离散偶极子近似方法, 通过模拟3个不同方位探测器接收的散射光强响应信号, 讨论了非球形生物气溶胶颗粒的形状对前向角分辨光强的影响.结合球形指数反演算法, 在一定取向条件下, 前向5°–20° 内角分辨散射光强具有识别长形颗粒物和非长形颗粒物的能力.该研究可以为颗粒物形态测量仪器设计以及快速检测有害生物气溶胶提供依据.     

含核椭球粒子后向散射特性研究

基于T矩阵方法,给出了随机取向、轴对称、含核椭球粒子的散射计算方法,散射体的核和外壳均可为非球形粒子,内层粒子和外层粒子可以为同心也可为不同心,整个粒子具有轴对称性.以含核椭球粒子为模型,计算了含有吸收性内核的水凝物气溶胶的散射特性,分析了核的大小、形状以及位置对后向散射的影响.计算结果表明,后向散射对内核的形状、大小...     

Proof of expansion of the reciprocal distance in spheroidal coordinates

A concise proof is given for the expansion of the reciprocal distance between two points in spheroidal harmonics. The proof is given for an oblate and a prolate spheroid.     

Scattering of on-axis polarized Gaussian light beam by spheroidal water coating aerosol particle

Small particle light scattering can produce light with polarization characteristics different from those of the incident beam. An analytical solution to the scattering by a spheroid with inclusion for an on-axis polarized Gaussian beam incidence is provided within the generalized Lorenz-Mie theory framework. The shapes of the inclusion can be spherical, confocal spheroid, or non-confocal spheroid. The Muller scattering matrix elements are computed for plane wave incidence or Gaussian light beam incidence. The effect of the size and shape of the inclusion or the coating on the polarized Oaussian light scattering characteristics by a spheroidal water coating aerosol Darticle are commlted and a,nalvzed.