Gayen Bishakhdatta, Alam Meheboob
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Aug;84(2 Pt 1):021304. doi: 10.1103/PhysRevE.84.021304. Epub 2011 Aug 12.
From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.e., with no sliding contact) of rough particles, decreasing the Coulomb friction is found to reduce the density and spatial velocity correlations which, together with diminished orientational correlation for small enough μ, are responsible for the transition from non-gaussian to gaussian distribution functions in the double limit of small friction (μ→0) and nearly elastic particles (e→1). This double limit in fact corresponds to perfectly smooth particles, and hence the maxwellian (gaussian) is indeed a solution of the Boltzmann equation for a frictional granular gas in the limit of elastic collisions and zero Coulomb friction at any roughness. The high-velocity tails of both distribution functions seem to follow stretched exponentials even in the presence of Coulomb friction, and the related velocity exponents deviate strongly from a gaussian with increasing friction.
通过对剪切摩擦颗粒气体的粒子模拟，我们表明，即使在玻尔兹曼（稀薄）极限下，库仑摩擦对取向关联以及平动和角速度分布函数都能产生显著影响。发现取向关联对摩擦系数（μ）的依赖性是非单调的，并且库仑摩擦根据切向恢复系数的值（其表征颗粒的粗糙度），起着增强或减弱取向关联的双重作用。从粗糙颗粒的粘着极限（即无滑动接触）来看，发现减小库仑摩擦会降低密度和空间速度关联，这与足够小的μ时取向关联的减弱一起，导致在小摩擦（μ→0）和近弹性颗粒（e→1）的双重极限下，分布函数从非高斯分布转变为高斯分布。实际上，这个双重极限对应于完全光滑的颗粒，因此在弹性碰撞极限和任何粗糙度下的零库仑摩擦条件下，麦克斯韦分布（高斯分布）确实是摩擦颗粒气体玻尔兹曼方程的一个解。即使存在库仑摩擦，两个分布函数的高速尾部似乎都遵循拉伸指数分布，并且随着摩擦增加，相关的速度指数与高斯分布有很大偏差。
