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  • 1
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper reports a numerical method for the solution of Stokes flows of a system of rigid particles in a container. The method is an application of the completed double layer boundary integral method (CDL-BIEM) by Kim and Karrila (1991). It uses an iterative solver and therefore can handle a large-number of particles with complex geometries. Particles' trajectories for a few typical problems are presented to illustrate the feasibility of the method. Experimental data are obtained with a two-camera system for the cases of two and eight spheres sedimenting in a container. A comparison with the numerical prediction in these cases shows a good agreement, to within the bounds of the experimental error.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 1 (1986), S. 259-268 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We report an implementation of the Boundary Element Method (BEM) for half-space elasticity or Stokes problems with a plane interface (the boundary of the half space). With a proper choice of the singularity solution this plane interface, on which the displacement or velocity vector is zero, does not need to be discretized. For a large class of problems involving translating or rotating bodies a simplification of the boundary element formulation is possible, with a resulting improvement in the accuracy of the numerical results. The three-dimensional boundary element program was tested with the moving sphere problem and was found to be satisfactory in all cases.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 3442-3448 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: As an extension of the previous paper, we derive a similar theory for the plane Poiseuille flow of a dilute polymer solution. The strict enforcement of reflective boundary conditions allows an approximate solution to the Fokker–Planck–Kolmogorov equation to be obtained which is found to be consistent with solutions obtained by Galerkin methods and Monte Carlo simulation. The approximate theory also allows us to derive analytical expressions for the slip velocity and the effective viscosity which are again consistent with the plane Couette flow results derived in the previous paper. The theory is also extended to the nonlinear Warner spring model via Monte Carlo simulation.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 988-995 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Existing experimental data have suggested that the flow of a dilute polymer solution near a wall exhibits a slip effect. In the case of a plane shear flow, the suspension of macromolecules contributes a nonuniform stress field profile across the channel which causes the velocity field to deviate from its otherwise linear profile. The apparent slip velocity can be calculated from such deviation. In this paper, we consider the flow problem of a suspension of bead-spring molecules in the presence of solid reflective boundary. Analytical and simulation solutions to the problem are obtained which do not require any small shear rate assumption. The added stresses contributed by the molecules are used to derive the slip velocity and the effective viscosity. Extension to nonlinear Warner spring model is also attempted by the simulation and the results give rise to some qualitative features which cannot be accounted for by the linear model.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 453-461 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A boundary element method (BEM) is developed and used to compute the arbitrary Stokes flow of a system of N particles of arbitrary shape and size embedded in a Newtonian fluid. The particles can be assumed to have a specified deformation (this feature is included here in anticipation of some applications in biophysics). Hydrodynamic and nonhydrodynamic forces are assumed to act in general; Brownian forces are neglected; and the Stokes flow field is assumed to be arbitrary. The method is benchmarked against the exact solution of two equal spheres in free settling motion by Goldman, Cox, and Brenner [Chem. Eng. Sci. 21, 1151 (1966)]. The handling of a finite bounding surface (i.e., arbitrary flow field, container walls) is tested with the calculation of the effective shear viscosity of a dilute suspension of monosized rigid spheres. The benchmarks show that the method performs satisfactorily. Also reported are the results for three spheres, arranged either in equispaced linear or triangular configuration (fixed or free settling under gravity). The effect of the hydrodynamic interaction with a rigid plane boundary (half-space problem) is automatically treated by the use of the special image of the Kelvin state [N. Phan-Thien, J. Elasticity 13, 231 (1983)]. This is illustrated by considering the problem of free settling of particles near a rigid no-slip planar boundary; specifically, some results for two equal spheres are reported. It is shown that the particle motion near the solid plane is fundamentally different from its motion in the far field, and thus the relative divergence of particles and the reversal of their angular velocity is observed.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 666-673 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A boundary element method is developed and used to compute the volume-average rheological properties of layered suspensions in a mean simple shearing flow up to a volume concentration of 0.5. The suspension is made up of a periodic array of neutrally buoyant, monosized spheroids in the x and y directions suspended in a Newtonian fluid that is subjected to a mean shear flow in the xz plane. The results for a monolayered suspension of spheres agree well with other simulations and some experimental results. Some new results for prolate and oblate spheroids are also given. Both the volume-average first and second normal stress differences are found to be zero in the simulation in all the cases considered.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3818-3822 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A recursive relation for the unit isotropic tensor of an arbitrary even order is derived from a rotational Brownian motion of the unit vector. An expression for the eighth-order velocity gradient correlation function is derived from the eighth-order isotropic tensors, after preserving the solenoidal property of the velocity field. This correlation function is compared with measurements in a turbulent wake. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of the Mechanics and Physics of Solids 42 (1994), S. 1177-1197 
    ISSN: 0022-5096
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of the Mechanics and Physics of Solids 41 (1993), S. 1067-1086 
    ISSN: 0022-5096
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 16 (1981), S. 13-18 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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