Kolvin Itamar, Livne Eli, Meerson Baruch
Racah Institute of Physics, Hebrew University of Jerusalem, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Aug;82(2 Pt 1):021302. doi: 10.1103/PhysRevE.82.021302. Epub 2010 Aug 13.
We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.
我们表明，在高于一维的维度中，即使在没有重力的情况下，热扩散和粘性也无法阻止自由演化的稀薄颗粒气体中的热坍缩。热坍缩涉及气体密度的有限时间爆炸。它早在无重力情况下稀薄颗粒气体的理想欧拉流体动力学以及有重力情况下的非理想纳维 - 斯托克斯颗粒流体动力学中就已被预测。我们通过解析和数值方法确定了表征接近坍缩时气流的动态标度律。我们还研究了自由演化的稀薄颗粒气体在圆形和楔形容器中的分岔情况。我们的结果表明，一般来说，只有当气体密度与颗粒的密堆积密度相当时，热坍缩才能被阻止。这为各种初始稀薄颗粒流中形成密集堆积的颗粒团簇提供了自然的解释。
