Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

Details Nonlinear viscosity and velocity distribution function in a simple longitudinal flow Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

2000-02-16

arxiv.org/abs/cond-mat/0002240v2

Phys. Rev. E 62, 6597-6607 (2000)

Physics

Condensed Matter

Statistical Mechanics

18 pages (Revtex), including 5 figures (eps). Analysis of the heat flux plus other minor changes added. Revised version accept

Scientific paper

10.1103/PhysRevE.62.6597

A compressible flow characterized by a velocity field $u_x(x,t)=ax/(1+at)$ 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 $\eta^*(a^*)$, that depends on the dimensionless longitudinal rate $a^*$. The Chapman-Enskog expansion of $\eta^*$ 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.

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