2000/02/29 by Andres Santos
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.62.6597
published as Phys. Rev. E 62, 6597-6607 (2000) · 18 pages (Revtex), including 5 figures (eps). Analysis of the heat flux plus other minor changes added. Revised version accepted for publication in PRE
arxiv created 2000/08/18 · arxiv updated 2009/11/30
A compressible flow characterized by a velocity field ux(x,t)=ax/(1+at) is analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook kinetic model. The sign of the control parameter (the longitudinal deformation rate a) distinguishes between an expansion (a>0) and a condensation (a<0) phenomenon. The temperature is a decreasing function of time in the former case, while it is an increasing function in the latter. The non-Newtonian behavior of the gas is described by a dimensionless nonlinear viscosity η^*(a^*), that depends on the dimensionless longitudinal rate a^*. The Chapman-Enskog expansion of η^* in powers of a^* is seen to be only asymptotic (except in the case of Maxwell molecules). The velocity distribution function is also studied. At any value of a^*, it exhibits an algebraic high-velocity tail that is responsible for the divergence of velocity moments. For sufficiently negative a^*, moments of degree four and higher may diverge, while for positive a^* the divergence occurs in moments of degree equal to or larger than eight.