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John F Brady - One of the best experts on this subject based on the ideXlab platform.
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suspensions of Prolate Spheroids in stokes flow part 3 hydrodynamic transport properties of crystalline dispersions
Journal of Fluid Mechanics, 1993Co-Authors: Ivan Claeys, John F BradyAbstract:The short-time limit of the hydrodynamic transport properties is calculated for crystalline dispersions of parallel Prolate Spheroids using a moment expansion technique similar in concept to the simulation method known as Stokesian dynamics. The concentration dependence of the sedimentation rate, the hindered diffusivity and the Theological behaviour of face-centred lattices are examined for concentrations up to regular close packing (74% by volume). The influence of the detailed microstructure of the dispersion is also investigated by considering different arrangements of parallel ellipsoids. Useful reference configurations are proposed as standard geometries for regular arrays of Prolate Spheroids.
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Suspensions of Prolate Spheroids in Stokes flow. Part 2. Statistically homogeneous dispersions
Journal of Fluid Mechanics, 1993Co-Authors: Ivan L. Claeys, John F BradyAbstract:The simulation method for Prolate Spheroids in Stokes flow introduced in a companion paper (Claeys & Brady 1993a) is extended to handle statistically homogeneous unbounded dispersions. The convergence difficulties associated with the slow decay of velocity disturbances at zero Reynolds number are overcome by applying O';Brien's renormalization procedure. The Ewald summation technique is employed to accelerate the evaluation of all mobility interactions. As a first application of this new method, the hydrodynamic transport properties of equilibrium hard-ellipsoid structures are calculated for aspect ratios ranging from 3 to 50. Calculated viscosities in the isotropic phase agree reasonably well with published experimental measurements.
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suspensions of Prolate Spheroids in stokes flow part 1 dynamics of a finite number of particles in an unbounded fluid
Journal of Fluid Mechanics, 1993Co-Authors: Ivan Claeys, John F BradyAbstract:A new simulation method is presented for low-Reynolds-number flow problems involving elongated particles in an unbounded fluid. The technique extends the principles of Stokesian dynamics, a multipole moment expansion method, to ellipsoidal particle shapes. The methodology is applied to Prolate Spheroids in particular, and shown to be efficient and accurate by comparison with other numerical methods for Stokes flow. The importance of hydrodynamic interactions is illustrated by examples on sedimenting Spheroids and particles in a simple shear flow.
Nicholas K Spyrou - One of the best experts on this subject based on the ideXlab platform.
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steadily rotating perfect fluid gravitating Prolate Spheroids in weyl gravity
Classical and Quantum Gravity, 1997Co-Authors: Nicholas K Spyrou, Demosthenes Kazanas, E P EstebanAbstract:It is shown that the equations of hydrodynamics do not admit solutions describing gravitating, incompressible, perfect fluid, Prolate Spheroids within the context of Weyl gravity, i.e. a theory whose static, spherically symmetric solution admits, besides the usual 1/r potential, an additional linear one, which has been invoked to solve the galactic rotation curve problem without the introduction of `dark matter'. This extends the similar, recent result obtained by Florides and Spyrou within Newtonian gravity to this alternative gravitational theory.
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steadily rotating perfect fluid gravitating Prolate Spheroids in newtonian theory
The Astrophysical Journal, 1993Co-Authors: P S Florides, Nicholas K SpyrouAbstract:It is proved that the Newtonian equations of hydrodynamics do not admit a solution describing an incompiessible perfect-fluid gravitating Prolate spheroid, which is steadily rotating about its axis of symmetry. The possible dynamical and astrophysical interest or the result is briefly discussed
B. P. Sinha - One of the best experts on this subject based on the ideXlab platform.
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electromagnetic scattering by a system of two parallel uniformly lossy dielectric Prolate Spheroids
IEEE Conference on Electromagnetic Field Computation, 1995Co-Authors: S K Nag, B. P. SinhaAbstract:By means of modal series expansions of electromagnetic fields in terms of Prolate spheroidal vector wave functions, an exact solution is obtained for the electromagnetic plane wave scattering by a system of two parallel uniformly lossy dielectric Prolate Spheroids. The incident excitation is a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Translational Addition Theorems for spheroidal vector wave functions are employed in order to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. Application of appropriate boundary conditions gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known incident field expansion coefficients and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of parallel two-body system of uniformly lossy dielectric Prolate Spheroids and different values of distances of separation. >
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electromagnetic plane wave scattering by a system of two uniformly lossy dielectric Prolate Spheroids in arbitrary orientation
IEEE Transactions on Antennas and Propagation, 1995Co-Authors: Soumya Nag, B. P. SinhaAbstract:By means of modal series expansions of electromagnetic fields in terms of Prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric Prolate Spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric Prolate Spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation. >
Ivan Claeys - One of the best experts on this subject based on the ideXlab platform.
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suspensions of Prolate Spheroids in stokes flow part 3 hydrodynamic transport properties of crystalline dispersions
Journal of Fluid Mechanics, 1993Co-Authors: Ivan Claeys, John F BradyAbstract:The short-time limit of the hydrodynamic transport properties is calculated for crystalline dispersions of parallel Prolate Spheroids using a moment expansion technique similar in concept to the simulation method known as Stokesian dynamics. The concentration dependence of the sedimentation rate, the hindered diffusivity and the Theological behaviour of face-centred lattices are examined for concentrations up to regular close packing (74% by volume). The influence of the detailed microstructure of the dispersion is also investigated by considering different arrangements of parallel ellipsoids. Useful reference configurations are proposed as standard geometries for regular arrays of Prolate Spheroids.
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suspensions of Prolate Spheroids in stokes flow part 1 dynamics of a finite number of particles in an unbounded fluid
Journal of Fluid Mechanics, 1993Co-Authors: Ivan Claeys, John F BradyAbstract:A new simulation method is presented for low-Reynolds-number flow problems involving elongated particles in an unbounded fluid. The technique extends the principles of Stokesian dynamics, a multipole moment expansion method, to ellipsoidal particle shapes. The methodology is applied to Prolate Spheroids in particular, and shown to be efficient and accurate by comparison with other numerical methods for Stokes flow. The importance of hydrodynamic interactions is illustrated by examples on sedimenting Spheroids and particles in a simple shear flow.
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hydrodynamic transport properties of suspensions of non brownian Prolate Spheroids
1991Co-Authors: Ivan ClaeysAbstract:The methodology of "Stokesian dynamics," an efficient and accurate simulation technique for suspensions of spheres, is extended to non-spherical particles. The model system consists of rigid, non-Brownian Prolate Spheroids suspended in an incompressible Newtonian fluid at zero Reynolds number. The method is applied to calculate the hydrodynamic transport properties of unbounded dispersions of ellipsoids. Both "random" configurations and very orderly arrangements of particles are considered in order to probe the relation between the microstructure of the suspension and its macroscopically observable properties. The simulation method is based on a microstructurally detailed description of the two-phase system and explicitly takes into account hydrodynamic interactions between the particles. Non-local singularity solutions for ellipsoids in Stokes flow are combined with Faxen laws using pair-wise additivity of velocities to construct a far-field approximation to the mobility tensor. The convergence problems associated with the long-ranged nature of viscous interactions at zero Reynolds number are handled using O'Brien's renormalization procedure. The Ewald summation technique is applied to accelerate the evaluation of the lattice sums generated by the periodic boundary conditions. Lubrication stresses between almost touching Spheroids are added in a pair-wise manner to the mobility inverse. All the two-body resistance functions which diverge as the surface separation vanishes are computed to O(e0), with e the gap width, so that the singular behavior of the lubrication interactions is captured correctly for arbitrary relative orientations and relative motions of the particles. The method is first illustrated for a finite number of particles in an unbounded fluid domain, and shown to be accurate and efficient. It is then applied to crystalline geometries of Spheroids over the full concentration range from 0 to closest packing (74% by volume). The dependence of the hydrodynamic transport properties (sedimentation rate, diffusion coefficient, stress/rate-of-strain relation, permeability and hindered diffusivity) on the density of the dispersion, the aspect ratio of the particles and the lattice type is investigated. Equilibrium structures of hard ellipsoids generated by a Monte Carlo procedure are also considered. The high frequency limit of the hydrodynamic transport properties is computed and compared to the results for crystalline configurations, and to available experimental measurements. A discontinuous jump in some suspension properties is observed at the isotropic to nematic transition. As a prelude to dynamic simulations, the compatibility of unit cells with pure straining flows is examined. It is demonstrated that no self-reproducing lattices exist in axisymmetric extensional flows, but a set of compatible basis vectors is derived. Planar straining fields on the other hand possess an infinite number of strain-periodic lattices.
F G Mitri - One of the best experts on this subject based on the ideXlab platform.
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axial acoustic radiation force on rigid oblate and Prolate Spheroids in bessel vortex beams of progressive standing and quasi standing waves
Ultrasonics, 2017Co-Authors: F G MitriAbstract:The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and Prolate Spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation.
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acoustic radiation force on oblate and Prolate Spheroids in bessel beams
Wave Motion, 2015Co-Authors: F G MitriAbstract:Abstract A formal theoretical analysis is developed using the partial-wave series expansion (PWSE) method in spherical coordinates, which allows accurate evaluation of the acoustic radiation force (ARF) of a Bessel beam incident upon a rigid oblate or Prolate spheroid, centered on its axis of wave propagation. The scattering coefficients for either the oblate or the Prolate spheroid are determined based on Neumann’s boundary condition for a rigid immovable surface, and used to compute the ARF function, which is the radiation force per unit characteristic energy density and surface cross-section of the spheroid. Numerical results are performed with particular emphasis on the waves’ amplitude ratio describing the evolution from progressive (traveling), quasi-standing and pure Bessel standing waves, the half-cone angle β of the beam, and the aspect ratio (i.e. the distance from the center to pole along the symmetry axis a divided by the equatorial radius b ) of the spheroid. Unlike the results obtained in the Rayleigh limit (i.e., k a ≪ 1 , where k is the wavenumber of the incident illuminating waves), calculations for the ARF functions for progressive, quasi-standing and standing Bessel waves for k a > 1 , generally reveal larger amplitudes for an oblate rather than a Prolate spheroid having the same surface cross-section. Exceptions are also noted for Bessel beams with a large half-cone angle. Potential applications are in acoustic levitation of dense Spheroids in air, particle dynamics, and other related research.
