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1

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An alternative expression for the addition theorems of spherical wave solutions of the Helmholtz equation (1993)

Clercx, H. J. H. ; Schram, P. P. J. M.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 34 (1993), S. 5292-5302

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: An alternative formulation of the addition theorem for spherical wave solutions of the Helmholtz equation is presented. The 3-j symbols of Wigner, or more precisely the Gaunt coefficient (complete solid angle integral of a triple product of spherical harmonics), which appear in the formerly introduced expressions of these addition theorems are replaced by an explicit matrix expression relating the spherical wave solutions defined with respect to the different origins. The generalized Gaunt coefficients, which are complete solid angle integrals of a multiple product of spherical harmonics, can then be written in terms of a matrix product of basic matrices representing the Gaunt coefficient.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530305

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2

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Three particle hydrodynamic interactions in suspensions (1992)

Clercx, H. J. H. ; Schram, P. P. J. M.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 96 (1992), S. 3137-3151

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: We present an outline of a method to determine the components of the grand mobility matrix of a system of three hydrodynamically interacting spherical particles with arbitrary particle configuration. We present the results of a study of some components of the grand mobility matrix in the case of two special configurations. The results derived for one configuration, with the three particles on a line, are compared with some results from the literature. In the other configuration, we have put the particles on the corners of an equilateral triangle. Besides the study of the mobility matrix, we have derived virial expansions for the translational and rotational self-diffusion coefficients up to quadratic order in cursive-phi, the volume fraction. Three particle contributions are incorporated in these expressions. We also present virial expansions, where three particle hydrodynamic interactions are included, for the translational and rotational sedimentation velocities. There are some results available in the literature in the case of the translational self-diffusion coefficient and the translational sedimentation velocity, which are different from our results. We discuss these differences. As far as we know, the results of the three particle contribution to the virial expansions of the rotational self-diffusion coefficient and the rotational sedimentation velocity are new. All the virial expansions mentioned above are compared with experimental results and simulation data from the literature.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.462843

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3

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Electrostatic interactions in slabs of polarizable particles (1993)

Clercx, H. J. H. ; Bossis, G.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 98 (1993), S. 8284-8293

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: We present results of a study of electrostatic interactions in slabs consisting of L layers with polarizable spheres on a two-dimensional Bravais lattice in an externally applied electric field. A multipole expansion to describe N-particle electrostatic interactions, introduced by the authors in a simultaneously published paper, has been used to calculate the induced dipoles on particles in the respective layers of the slab. The conclusion is that the induced dipoles differ from their bulk values if situated near the surface, and these differences depend strongly on the internal structure of the slabs. With these results the surface energy has been calculated. Moreover, the local electric field has been studied as a function of the distance from the surface of the slab. These results are compared with a mean field approximation where each particle is considered to be surrounded by a homogeneous polarization. The differences between both models are striking.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.464534

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4

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Self-organization of quasi-two-dimensional turbulence in stratified fluids in square and circular containers (2002)

Maassen, S. R. ; Clercx, H. J. H. ; van Heijst, G. J. F.

[S.l.] : American Institute of Physics (AIP)

Physics of Fluids 14 (2002), S. 2150-2169

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ISSN: 1089-7666

Source: AIP Digital Archive

Topics: Physics

Notes: Laboratory experiments on decaying quasi-2D (two-dimensional) turbulence have been performed in stratified fluids in both square and circular containers. The turbulence was generated by towing an array of vertical cylinders through the container, which was filled with either a two-layer or a linearly stratified fluid. By varying the grid configuration a different amount of angular momentum could be added to the initial flow. The evolution of the flow was visualized by 2D particle tracking velocimetry. The observed decay scenario has been investigated with emphasis on the evolution of the kinetic energy and the enstrophy of the horizontal flow, vortex statistics and the angular momentum of the flow. In particular it is shown that the experiments in both the square and the circular container support the observations from numerical simulations of decaying 2D turbulence in bounded domains with no-slip walls. Two striking examples are the experimental observation of the spontaneous spin-up phenomenon (in the square-container experiments) and the confirmation that the angular momentum of the flow in the circular-container experiment is better conserved than the total kinetic energy of the flow. The role of the initial nonzero net angular momentum on the decay of quasi-2D turbulence is investigated for both geometries and indications for an acceleration of the self-organization process are presented. © 2002 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.1480263

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5

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Dipole formation by two interacting shielded monopoles in a stratified fluid (2002)

Beckers, M. ; Clercx, H. J. H. ; van Heijst, G. J. F.

[S.l.] : American Institute of Physics (AIP)

Physics of Fluids 14 (2002), S. 704-720

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ISSN: 1089-7666

Source: AIP Digital Archive

Topics: Physics

Notes: The interaction between two shielded monopolar vortices has been investigated experimentally in a nonrotating linearly stratified fluid and by full three-dimensional (3D) numerical simulations. The characteristic Reynolds and Froude numbers in the experiments are approximately Re(approximate)500–1000 and F(approximate)0.2–0.4. In a first set of numerical simulations the flow is initialized with the experimentally obtained two-dimensional horizontal velocity field, which is measured in the horizontal symmetry plane of the vortices, and the lacking initial data such as the density perturbation and the full 3D vorticity field are provided by the so-called diffusion model [Beckers et al., J. Fluid Mech. 433, 1 (2001)]. A comparison of the experimental and numerical data shows that using the diffusion model to supply the full 3D initial data is reliable for the Reynolds and Froude numbers considered in present experiments. Conjecturing a wider range of applicability, a second set of numerical simulations has been performed using initial conditions for the flow field and the density perturbation entirely based on the diffusion model. These numerical simulations enable an investigation of the role of Reynolds numbers (up to Re=10 000) and Froude numbers (F=0.30, 0.65, and 1.0) which are outside the experimentally accessible range. These simulations provide a better understanding of the dipole formation process, the influence of the vortex shields and the density perturbation in this process, and of the 3D structure of the dipoles. Compactness of the dipole, entrainment of irrotational fluid from the rear, and tail formation behind the dipole have been discussed. Additionally, experimental and numerical results are reported on the interaction between two shielded monopoles of the same sign in a linearly stratified fluid. It is found that for the full range of Reynolds and Froude numbers mentioned above the presence of the vortex shields prevents the merging of these monopoles. © 2002 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.1431242

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6

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Erratum: "Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries" [Phys. Fluids 11, 611 (1999)] (1999)

Clercx, H. J. H. ; Maassen, S. R. ; van Heijst, G. J. F.

[S.l.] : American Institute of Physics (AIP)

Physics of Fluids 11 (1999), S. 1963-1963

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ISSN: 1089-7666

Source: AIP Digital Archive

Topics: Physics

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.870060

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7

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Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries (1999)

Clercx, H. J. H. ; Maassen, S. R. ; van Heijst, G. J. F.

[S.l.] : American Institute of Physics (AIP)

Physics of Fluids 11 (1999), S. 611-626

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ISSN: 1089-7666

Source: AIP Digital Archive

Topics: Physics

Notes: We report results of direct numerical simulations of decaying two-dimensional (2D) turbulence inside a square container with rigid boundaries. It is shown that the type of boundary condition (no-slip or stress-free) determines the flow evolution essentially. During the initial (0≤t≤0.2Re) and intermediate (0.2Re≤t≤3Re) stages of decaying 2D turbulence (t≅1 is comparable with an eddy turnover time, Re is the Reynolds number of the flow), the decay scenario for simulations with no-slip boundary conditions can be understood from turbulent spectral transfer and selective decay. A third mechanism can be recognized for t≥3Re: A decay stage where diffusion dominates over nonlinear advection, i.e., spectral transfer is then absent in favor of self-similar decay. The present results show that at presently accessible Reynolds numbers and computation times, laboratory experiments cannot be accurately compared with quasi-stationary states from ideal maximum-entropy theories or with computed solutions of flows in containers with stress-free boundaries. The decay which results in rectangular containers with no-slip boundaries does not yet yield anything that is meaningfully comparable with these formulations. The evolution of the number of vortices V, the average vortex radius a, the ratio of enstrophy Ω over energy E, and the extremum of vorticity (normalized by E) have been computed based on ensemble averaging of the no-slip runs. An algebraic regime has been observed with V(t)∼t−0.90, a(t)∼t0.31, Ω(t)/E(t)∼t−0.63, and ωext(t)/E(t)∼t−0.30. Finally, quantities such as a measure of the viscous stresses near the boundaries have been computed in order to analyze the decay of 2D turbulence in containers with rigid boundaries. © 1999 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.869933

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8

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Static yield stresses and shear moduli in electrorheological fluids (1995)

Clercx, H. J. H. ; Bossis, G.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 103 (1995), S. 9426-9437

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: A previously introduced method to study many-body electrostatic interactions among spherical particles [H. J. H. Clercx and G. Bossis, Phys. Rev. E 48, 2721 (1993)] has been used to study yield stresses and shear moduli for simple cubic (SC), simple hexagonal (SH), and body-centered tetragonal (BCT) structures, with polarizable spheres on the lattice sites, to gain insight in the electrostatic response of these structures to externally applied stresses. The shear modulus G and the static yield stress τs have been calculated for several ratios of particle to fluid dielectric constant. It turned out that interchain interactions are very weak in SC and SH structures which is confirmed by the nearly linear cursive-phi dependence of G and τs (even no weak maximum appears in these curves). The results reported for the BCT structure are rather unexpected, because both G and τs suddenly decrease to zero at large volume fractions. We discuss the data for G and τs and compare some of these results with data obtained by employing the dipolar approximation and the Laplacian relaxation technique to calculate the electrostatics. This comparison shows that in general a multipolar approach is indispensable in obtaining correct values for G and τ; especially the dipolar approximation underestimates these quantities. As an example the strength of single vs double chains has been compared for both the dipolar approach and a multipolar calculation. In the dipolar approximation the double chain structure seems strongest. However, multipolar calculations show that the single chain structure is stronger than the double chain structure. © 1995 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.470004

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