Mitrano Peter P, Garzó Vicente, Hrenya Christine M
Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA.
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):020201. doi: 10.1103/PhysRevE.89.020201. Epub 2014 Feb 10.
A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to previous attempts, our results (which are based on the solution to the inelastic Enskog equation to NS order) are not restricted to nearly elastic systems since they take into account the complete nonlinear dependence of the NS transport coefficients on the coefficients of restitution α(ij). The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations in flows of strong dissipation (α(ij) ≥ 0.7) and moderate solid volume fractions (ϕ ≤ 0.2). We find excellent agreement between MD and kinetic theory for the onset of velocity vortices, indicating the applicability of NS hydrodynamics to polydisperse flows even for strong inelasticity, finite density, and particle dissimilarity.
对纳维-斯托克斯（NS）颗粒流体动力学方程进行线性稳定性分析，以确定颗粒致密二元混合物中涡旋和团簇不稳定性开始出现时的临界长度尺度。与之前的尝试不同，我们的结果（基于非弹性恩斯科格方程到NS阶的解）并不局限于近弹性系统，因为它们考虑了NS输运系数对恢复系数α(ij)的完全非线性依赖。将临界长度尺度的理论预测与强耗散流（α(ij)≥0.7）和中等固体体积分数（ϕ≤0.2）下的分子动力学（MD）模拟进行了比较。我们发现MD与动力学理论在速度涡旋开始出现时具有极好的一致性，这表明NS流体动力学即使对于强非弹性、有限密度和颗粒差异的多分散流也适用。
