Goldhirsch I, Noskowicz S H, Bar-Lev O
Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978 Israel.
J Phys Chem B. 2005 Nov 17;109(45):21449-70. doi: 10.1021/jp0532667.
Hydrodynamic equations of motion for a monodisperse collection of nearly smooth homogeneous spheres have been derived from the corresponding Boltzmann equation, using a Chapman-Enskog expansion around the elastic smooth spheres limit. Because in the smooth limit the rotational degrees of freedom are uncoupled from the translational ones, it turns out that the required hydrodynamic fields include (in addition to the standard density, velocity, and translational granular temperature fields) the (infinite) set of number densities, n(s,r, t), corresponding to the continuum of values of the angular velocities. The Chapman-Enskog expansion was carried out to high (up to 10th) order in a Sonine polynomial expansion by using a novel computer-aided method. One of the consequences of these equations is that the asymptotic spin distribution in the homogeneous cooling state for nearly smooth, nearly elastic spheres, is highly non-Maxwellian. The simple sheared flow possesses a highly non-Maxwellian distribution as well. In the case of wall-bounded shear, it is shown that the angular velocity injected at the boundaries has a finite penetration length.
对于近乎光滑的均匀球体的单分散集合，其流体动力学运动方程已从相应的玻尔兹曼方程导出，采用了围绕弹性光滑球体极限的查普曼 - 恩斯科格展开。由于在光滑极限下，转动自由度与平动自由度解耦，结果表明所需的流体动力学场包括（除了标准的密度、速度和平动颗粒温度场之外）对应于角速度连续值的（无限）数密度集(n(s, r, t))。通过使用一种新颖的计算机辅助方法，在索宁多项式展开中，查普曼 - 恩斯科格展开进行到了高阶（高达第十阶）。这些方程的一个结果是，对于近乎光滑、近乎弹性的球体，在均匀冷却状态下的渐近自旋分布高度非麦克斯韦分布。简单剪切流也具有高度非麦克斯韦分布。在有壁面限制的剪切情况下，表明在边界处注入的角速度具有有限的穿透长度。
