Brilliantov Nikolai V, Pöschel Thorsten
Department de Fisica Fonamental, Universitat de Barcelona, Spain.
Philos Trans A Math Phys Eng Sci. 2002 Mar 15;360(1792):415-28. doi: 10.1098/rsta.2001.0940.
Our study examines the long-time behaviour of a force-free granular gas of viscoelastic particles, for which the coefficient of restitution depends on the impact velocity, as it follows from the solution of the impact problem for viscoelastic spheres. Starting from the Boltzmann equation, we derived the hydrodynamic equations and obtained microscopic expressions for the transport coefficients in terms of the elastic and dissipative parameters of the particle material. We performed the stability analysis of the linearized set of equations and found that any inhomogeneities and vortices vanish after a long time and the system approaches the flow-free stage of homogeneous density. This behaviour is in contrast to that of a gas consisting of particles which interact via a (non-realistic) constant coefficient of restitution, for which inhomogeneities (clusters) and vortex patterns have been proven to arise and to continuously develop.
我们的研究考察了由粘弹性颗粒组成的无力颗粒气体的长期行为，其恢复系数取决于碰撞速度，这是由粘弹性球体碰撞问题的解得出的。从玻尔兹曼方程出发，我们推导了流体动力学方程，并根据颗粒材料的弹性和耗散参数得到了输运系数的微观表达式。我们对线性化方程组进行了稳定性分析，发现任何不均匀性和涡旋在长时间后都会消失，系统趋近于均匀密度的无流动阶段。这种行为与由通过（非现实的）恒定恢复系数相互作用的颗粒组成的气体的行为形成对比，对于后者，不均匀性（团簇）和涡旋模式已被证明会出现并持续发展。
