The Permeability of a Random Array of Identical Rigid-Spheres

Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler–Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.

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THE ABSORPTION OF HIGH-ENERGY RADIATION, A MONTE CARLO STUDY: II. SPHERICAL GEOMETRY

Canadian Journal of Physics ◽

10.1139/p63-066 ◽

1963 ◽

Vol 41 (4) ◽

pp. 651-663

Author(s):

N. R. Steenberg

Keyword(s):

Cross Section ◽

Spherical Geometry ◽

Monte Carlo Study ◽

Nuclear Data ◽

High Energy ◽

Rare Gas ◽

Nuclear Radius ◽

Rigid Spheres ◽

High Energy Radiation ◽

The Individual

The absorption of radiation in a spherical obstacle composed of rigid spheres has been studied. The result is the absorption cross section of such an obstacle as a function of the free cross section and the number A of the individual spheres and of packing density. It is found that the usual rare-gas formula represents the cross section adequately. The analysis is applied to nuclear data for the absorption of 25-Bev/c protons by nuclei. It is found that for a nuclear radius R = r0A1/3 + δ, where δ is the radius of the nucleon, r0 = 1.17 fermi, δ = 1.05 fermi, and an average nucleon transparency a2 = 0.30 is consistent with the data.

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Structural and electrical transport properties of superconductingAu0.7In0.3films: A random array of superconductor–normal-metal–superconductor Josephson junctions

Physical Review B ◽

10.1103/physrevb.66.054512 ◽

2002 ◽

Vol 66 (5) ◽

Cited By ~ 6

Author(s):

Yu. Zadorozhny ◽

Y. Liu

Keyword(s):

Transport Properties ◽

Electrical Transport ◽

Josephson Junctions ◽

Normal Metal ◽

Electrical Transport Properties ◽

Random Array

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Inertial migration of rigid spheres in two-dimensional unidirectional flows

Journal of Fluid Mechanics ◽

10.1017/s0022112074001431 ◽

1974 ◽

Vol 65 (2) ◽

pp. 365-400 ◽

Cited By ~ 507

Author(s):

B. P. Ho ◽

L. G. Leal

Keyword(s):

Shear Flow ◽

Simple Shear ◽

Poiseuille Flow ◽

Initial Position ◽

Rigid Sphere ◽

Simple Shear Flow ◽

Two Dimensional ◽

Lateral Migration ◽

Rigid Spheres ◽

Inertial Migration

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

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