Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-03-05
Cont. Mech. Thermodyn. 21, 361-387 (2009)
Physics
Condensed Matter
Statistical Mechanics
26 pages, 7 figures, 6 tables; v2: Change of notation of some variables, new section and two new figures added; published in a
Scientific paper
10.1007/s00161-009-0113-5
In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In general, however, the drift term of the Boltzmann equation couples moments of a given order to moments of a higher order, thus preventing the solvability of the moment hierarchy, unless approximate closures are introduced. On the other hand, there exist a number of states where the moment hierarchy can be recursively solved, the solution generally exposing non-Newtonian properties. The aim of this paper is to present an overview of results pertaining to some of those states, namely the planar Fourier flow (without and with a constant gravity field), the planar Couette flow, the force-driven Poiseuille flow, and the uniform shear flow.
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