Garzó V, Dufty J W
Department of Physics, University of Florida, Gainesville, Florida 32611, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt B):5895-911. doi: 10.1103/physreve.59.5895.
The revised Enskog theory for inelastic hard spheres is considered as a model for rapid flow granular media at finite densities. A normal solution is obtained via the Chapman-Enskog method for states near the local homogeneous cooling state. The analysis is performed to first order in the spatial gradients, allowing identification of the Navier-Stokes order transport coefficients associated with the heat and momentum fluxes. In addition, the cooling rate is calculated to first order in the gradients and expressed in terms of the transport coefficients. The transport coefficients are determined from linear integral equations analogous to those for elastic collisions. The solubility conditions for these equations are confirmed and the transport coefficients are calculated as explicit functions of the density and restitution coefficient using a Sonine polynomial expansion. The results are not limited to small dissipation. Finally, the analysis is repeated using a simpler kinetic model. Excellent agreement is obtained with the results from the revised Enskog equation.
修正后的非弹性硬球恩斯科格理论被视为有限密度下快速流动颗粒介质的模型。通过查普曼 - 恩斯科格方法，针对接近局部均匀冷却状态的状态获得了一个正规解。分析在空间梯度的一阶进行，从而确定与热通量和动量通量相关的纳维 - 斯托克斯阶输运系数。此外，冷却速率在梯度的一阶进行计算，并根据输运系数表示。输运系数由类似于弹性碰撞的线性积分方程确定。这些方程的可解性条件得到确认，并且使用索宁多项式展开将输运系数计算为密度和恢复系数的显式函数。结果不限于小耗散情况。最后，使用一个更简单的动力学模型重复分析。与修正后的恩斯科格方程的结果取得了极好的一致性。
