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arXiv 1002.0618cond-mat.stat-mechcond-mat.soft
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高密度下二维硬、软颗粒材料的压力和粘度行为

Behavior of pressure and viscosity at high densities for two-dimensional hard and soft granular materials

Michio Otsuki, Hisao Hayakawa, Stefan Luding

摘要:

数值研究了二维剪切颗粒集合体中的压力和粘性。当从没有耗散的单分散硬盘系统开始并向(i)多分散,(ii)具有(iii)相当大的耗散的软颗粒系统移动时,压力和粘度的行为都是平稳地定性变化的。在单分散体系的刚性、弹性限度中,粘度与与$ϕ_η \simeq 0.7$的面积分数差近似成反比,但在$ϕ_η$处压力仍然有限。另一方面,在适度软的、耗散的和多分散的系统中,我们证实了最近的理论预测,即标度压力(除以动力学温度$T$)和标度粘度(除以$\sqrt{T}$)在相同的密度下发散,即,干扰转变点$ϕ_J > ϕ_η$,其指数分别为-2和-3。此外,我们观察到,干扰过渡的临界区域变得不可见的恢复系数接近统一,即消失耗散。为了理解这两种不同的预测之间的冲突的压力和粘度的发散,从软到硬的颗粒的过渡进行了详细的研究,并定义为各种时间尺度的比值的无量纲控制参数。我们引入了一个无量纲数,即耗散率和剪切速率的比率,它可以识别从非常硬的,即刚性磁盘的缩放到软的,干扰制度的缩放的交叉。

英文摘要:

The pressure and the viscosity in two-dimensional sheared granular assemblies are investigated numerically. The behavior of both pressure and viscosity is smoothly changing qualitatively when starting from a mono-disperse hard-disk system without dissipation and moving towards a system of (i) poly-disperse, (ii) soft particles with (iii) considerable dissipation. In the rigid, elastic limit of mono-disperse systems, the viscosity is approximately inverse proportional to the area fraction difference from $ϕ_η \simeq 0.7$, but the pressure is still finite at $ϕ_η$. In moderately soft, dissipative and poly-disperse systems, on the other hand, we confirm the recent theoretical prediction that both scaled pressure (divided by the kinetic temperature $T$) and scaled viscosity (divided by $\sqrt{T}$) diverge at the same density, i.e., the jamming transition point $ϕ_J > ϕ_η$, with the exponents -2 and -3, respectively. Furthermore, we observe that the critical region of the jamming transition becomes invisible as the restitution coefficient approaches unity, i.e. for vanishing dissipation. In order to understand the conflict between these two different predictions on the divergence of the pressure and the viscosity, the transition from soft to hard particles is studied in detail and the dimensionless control parameters are defined as ratios of various time-scales. We introduce a dimensionless number, i.e. the ratio of dissipation rate and shear rate, that can identify the crossover from the scaling of very hard, i.e. rigid disks to the scaling in the soft, jamming regime.

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