Kinetic Theory of Moderately Dense, Rigid‐Sphere Gases (English)

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In: Physics of Fluids (1958-1988)   ;  4 ,  7  ;  816-833  ;  1961

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By successive partial integrations of the Liouville equation, the hierarchy of BBGKY equations are obtained. The series is terminated at the second equation by the introduction of a superposition approximation. A specialization to rigid spheres is made early in the treatment. Then, after defining a nonequilibrium pair correlation function, the first BBGKY equation is identified as an Enskog equation modified by the inclusion of a momentum‐dependent correlation function in the collision integral. This equation and the second BBGKY equation completely determine the singlet distribution and pair correlation functions. An approximate solution to this pair of equations follows from the usual linearized perturbation expansion of the singlet distribution and pair correlation functions for the system near equilibrium. A set of five equations in the coefficients of the gradients are obtained, and the coupling between them is resolved by expanding these coefficients in powers of the number density. Because of the limitations imposed by the superposition approximation, only the first few terms in the density expansions are considered explicitly. The solutions to these equations and the resulting modifications of the transport coefficients are discussed.

Table of contents – Volume 4, Issue 7

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Internal Waves in the Ocean
Eckart, Carl | 1961
Wakes in Liquid‐Liquid Systems
Magarvey, R. H. / Bishop, Roy L. | 1961
Dual Role of Viscosity in the Instability of Revolving Fluids of Variable Density
Yih, Chia‐Shun | 1961
Shock‐Wave Curvature at Low Initial Pressure
Duff, Russell E. / Young, James L. | 1961
Kinetic Theory of Moderately Dense, Rigid‐Sphere Gases
Livingston, P. M. / Curtiss, C. F. | 1961
Transport Phenomena in a Fully Ionized Gas Confined in a Strong Magnetic Field
Koga, Toyoki | 1961
Persistence of Stability in Lagrangian Systems
Low, F. E. | 1961
Stability of a Plasma Boundary in a Magnetic Field
Lehnert, B. | 1961
Interaction of a Streaming Plasma with the Magnetic Field of a Two‐Dimensional Dipole
Hurley, James | 1961
Plasma as a Microwave Amplifier
Rand, S. | 1961
Radiation by a Large‐Amplitude Plasma Oscillation
Tidman, D. A. / Weiss, George H. | 1961
On Landau Damping
Dawson, John | 1961
Determination of Hydromagnetic Equilibria
Greene, John M. / Johnson, John L. | 1961
Hydromagnetic Stability of a Toroidal Gas Discharge
Lu¨st, R. / Suydam, B. R. / Richtmyer, R. D. / Rotenberg, A. / Levy, D. | 1961
Equilibrium Ambipolar Potentials in a Mirror Machine
Post, Richard F. | 1961
Injection and Trapping of a β = 1 Plasma into a Cusped Magnetic Field
Hagerman, D. C. / Osher, J. E. | 1961
On the Mechanism of Exploding Wires
Nash, C. P. / McMillan, W. G. | 1961
Mach Reflection of Detonation Waves in Condensed High Explosives
Dunne, B. B. | 1961
Semi‐Isotropic Turbulence and Helicoidal Flows
Betchov, Robert | 1961
Interpretation of Linear Approximations for the Viscosity of Gas Mixtures
Hansen, C. Frederick | 1961
Magnetically Driven Cylindrical Shock Waves
Liepmann, H. W. / Vlases, G. | 1961
Asymmetric Collapse Accelerators for Counter‐Helmholtz Geometries with Internal Injection
Waniek, Ralph W. / Fischer, Heinz / Lee, Sang W. | 1961
A new mechanism of period doubling in free shear flows
Tomboulides, A. G. / Triantafyllou, G. S. / Karniadakis, G. E. | 1992
Convection‐induced shears for general planforms
Massaguer, J. M. / Spiegel, E. A. / Zahn, J.‐P. | 1992
Anomalous diffusion of momentum in a dilute gas–solid suspension
Koch, Donald L. | 1992
The deformation and breakup of liquid drops in low Reynolds number flow through a capillary
Olbricht, W. L. / Kung, D. M. | 1992
Large departures from Boussinesq approximation in the Rayleigh–Be´nard problem
Fro¨hlich, J. / Laure, P. / Peyret, R. | 1992
Oscillating flows over periodic ripples of finite slope
Hara, Tetsu / Mei, Chiang C. / Shum, K. T. | 1992
Instabilities in two‐dimensional spatially periodic flows. Part I: Kolmogorov flow
Thess, Andre´ | 1992
Instabilities in two‐dimensional spatially periodic flows. Part II: Square eddy lattice
Thess, Andre´ | 1992
Localized receptivity of boundary layers
Crouch, J. D. | 1992
Analysis of viscous dissipation in disk storage systems and similar flow configurations
Humphrey, J. A. C. / Schuler, C. A. / Iglesias, I. | 1992
Scaling and multifractal properties of mixing in chaotic flows
Muzzio, F. J. / Meneveau, C. / Swanson, P. D. / Ottino, J. M. | 1992
Head‐on collision of a large vortex ring with a free surface
Song, Museok / Bernal, Luis P. / Tryggvason, Gre´tar | 1992
Vorticity amplification and annihilation in a potential vortex
Williams, Marc H. | 1992
Development of singular solutions to the axisymmetric Euler equations
Pumir, Alain / Siggia, Eric D. | 1992
The decay of homogeneous isotropic turbulence
George, William K. | 1992
Development of turbulence models for shear flows by a double expansion technique
Yakhot, V. / Orszag, S. A. / Thangam, S. / Gatski, T. B. / Speziale, C. G. | 1992
Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow
Lee, Sangsan / Lele, Sanjiva K. / Moin, Parviz | 1992
Vorticity generation and evolution in shock‐accelerated density‐stratified interfaces
Yang, Xiaolong / Chern, I‐Liang / Zabusky, Norman J. / Samtaney, Ravi / Hawley, John F. | 1992
The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies
Shaw, Stephen J. / Duck, Peter W. | 1992
Nonsteady detonation driven by a hypervelocity jet in a homogeneous explosive
Asay, Blaine W. / McAfee, John M. / Ferm, Eric N. | 1992
Structure of partly dispersed normal shock waves in vapor‐droplet flows
Guha, A. | 1992
A novel way of computing the Basset term in unsteady multiphase flow computations
Michaelides, Efstathios E. | 1992
A two‐dimensional instability in a mixed convection flow with spatially periodic temperature boundary conditions
Tangborn, Andrew | 1992
Comment on ‘‘Is intermittent motion of outer flow in the turbulent boundary layer deterministic chaos?’’ [Phys. Fluids A 3, 1941 (1991)]
Meneveau, Charles | 1992