Linear Velocity-Gradient Term in Time-Dependent Pair Distribution Function
A Chapman-Enskog-type perturbation solution, in gradients of energy, velocity, and density, is proposed for the hierarchy of intergo-differential equations obeyed by the time-dependent Ursell-Mayer functions. The hierarchy is then terminated by an ansatz relating the three-particle Ursell functions to those of lower order, which yields a closed system for the perturbations to the singlet and pair distribution functions (it is assumed the equilibrium functions are known). Attention is focused on the equation for the two-particle functions, and on the term therein proportional to the divergence of fluid velocity, from which the bulk viscosity may be calculated. An expansion for this term is assumed in powers of scalar products of particle separations and velocities, in which the coefficients in turn are expanded in Sonine polynomials in the velocities. The functions which multiply these polynomials satisfy a system of integral equations, for which a first approximation is written down and the solution discussed. Finally, it is shown that substitution of the solution for the pair distribution function into the hierarchy equation for the singlet distribution yields an infinite number of conditions which may be used to evaluate a corresponding number of parameters in the ansatz employed to close the hierarchy.
- Research Organization:
- National Bureau of Standards, Washington, D.C.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-031655
- OSTI ID:
- 4676407
- Journal Information:
- Journal of Chemical Physics, Vol. 38, Issue 8; Other Information: Orig. Receipt Date: 31-DEC-63; ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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