2007/06/30 by Andrés Santos, Andres Santos, Vicente Garzó +1 · 20 citations
Engineering · Mathematics · Physics and Astronomy · #Boltzmann equation #Coefficient of restitution #Gas Dynamics and Kinetic Theory #Limit (mathematics) #Nonlinear Partial Differential Equations #Shear (geology) #Shear flow #Shear rate #Simple (philosophy) #Simple shear #Thermoelastic and Magnetoelastic Phenomena #Velocity Moments #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2007/08/p08021
published in Journal of Statistical Mechanics Theory and Experiment 2007(08), P08021 (Institute of Physics) · 18 pages, 7 figures; v2: minor changes
arxiv created 2007/07/17 · openalex publication_date 2007/08/10 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through the fourth degree in the simple shear flow state. First, the rheological properties (which are related to the second-degree velocity moments) are exactly evaluated in terms of the coefficient of restitution α and the (reduced) shear rate a * . For a given value of α, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third-degree and the asymmetric fourth-degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, our results show that, for a given value of α, the scaled symmetric fourth-degree moments diverge in time for shear rates larger than a certain critical value a c * (α) which decreases with increasing dissipation. The explicit shear-rate dependence of the fourth-degree moments below this critical value is also obtained.