Santos Andrés
Departamento de Física, Universidad de Extremadura, Badajoz E-06071, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 1):051101. doi: 10.1103/PhysRevE.67.051101. Epub 2003 May 1.
The homogeneous steady state of a fluid of inelastic hard spheres immersed in a bath of elastic hard spheres kept at equilibrium is analyzed by means of the first Sonine approximation to the (spatially homogeneous) Enskog-Boltzmann equation. The temperature of the granular fluid relative to the bath temperature and the kurtosis of the granular distribution function are obtained as functions of the coefficient of restitution, the mass ratio, and a dimensionless parameter beta measuring the cooling rate relative to the friction constant. Comparison with recent results obtained from an iterative numerical solution of the Enskog-Boltzmann equation [Biben et al., Physica A 310, 308 (2002)] shows an excellent agreement. Several limiting cases are also considered. In particular, when the granular particles are much heavier than the bath particles (but have a comparable size and number density), it is shown that the bath acts as a white noise external driving. In the general case, the Sonine approximation predicts the lack of a steady state if the control parameter beta is larger than a certain critical value beta(c) that depends on the coefficient of restitution and the mass ratio. However, this phenomenon appears outside the expected domain of applicability of the approximation.
通过对（空间均匀的）恩斯科格 - 玻尔兹曼方程的一阶索宁近似，分析了沉浸在处于平衡态的弹性硬球浴中的非弹性硬球流体的均匀稳态。得到了颗粒流体相对于浴温的温度以及颗粒分布函数的峰度，它们是恢复系数、质量比以及一个无量纲参数β的函数，β衡量了相对于摩擦常数的冷却速率。与最近从恩斯科格 - 玻尔兹曼方程的迭代数值解得到的结果[Biben等人，《物理A》310, 308 (2002)]进行比较，显示出极好的一致性。还考虑了几种极限情况。特别地，当颗粒比浴颗粒重得多（但具有可比的尺寸和数密度）时，表明浴起到了白噪声外部驱动的作用。在一般情况下，如果控制参数β大于某个取决于恢复系数和质量比的临界值β(c)，索宁近似预测不存在稳态。然而，这种现象出现在该近似预期的适用范围之外。
