Theory of Dilute Binary Granular Gas Mixtures
Theory of Dilute Binary Granular Gas Mixtures
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稀二元颗粒气体混合物理论
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
I. Goldhirsch
中科院分区：
文献类型：
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作者：
D. Serero;S. H. Noskowicz;I. Goldhirsch
本文提出了一种计算机辅助的方法，用于精确地进行Boltzmann方程的Chapman-Enskog展开，包括它的非弹性变形，并用于推导光滑非弹性球的稀二元混合物的流体动力学描述。本构关系，正式有效的恢复系数的所有物理值，进行相关的Chapman-Enskog扩展到足够高的阶数的Sonine多项式，以确保数值收敛计算。由此产生的流体动力学描述被施加到一个垂直振动的二进制混合物的颗粒（重力下）的分析不同的只是在各自的恢复系数。它示出，即使有这个“小”的差异的混合物部分隔离，其稳定状态表现出一个类似的配置。
A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this “minor”difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.