Moon Sung Joon, Swift J B, Swinney Harry L
Center for Nonlinear Dynamics and Department of Physics, University of Texas, Austin, Texas 78712, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 1):031301. doi: 10.1103/PhysRevE.69.031301. Epub 2004 Mar 4.
Particles in granular flows are often modeled as frictionless (smooth) inelastic spheres; however, there exist no frictionless grains, just as there are no elastic grains. Our molecular dynamics simulations reveal that friction is essential for realistic modeling of vertically oscillated granular layers: simulations of frictionless particles yield patterns with an onset at a container acceleration about 30% smaller than that observed in experiments and simulations with friction. More importantly, even though square and hexagonal patterns form for a wide range of the oscillation parameters in experiments and in our simulations of frictional inelastic particles, only stripe patterns form in the simulations without friction, even if the inelasticity is increased to obtain as much dissipation as in frictional particles. We also consider the effect of particle friction on the shock wave that forms each time the granular layer strikes the container. While a shock wave still forms for frictionless particles, the spatial and temporal dependence of the hydrodynamic fields differ for the cases with and without friction.
颗粒流中的粒子通常被建模为无摩擦（光滑）的非弹性球体；然而，并不存在无摩擦的颗粒，就如同不存在弹性颗粒一样。我们的分子动力学模拟表明，摩擦力对于垂直振荡颗粒层的真实建模至关重要：无摩擦粒子的模拟产生的模式起始于容器加速度，该加速度比有摩擦的实验和模拟中观察到的加速度小约30%。更重要的是，尽管在实验以及我们对有摩擦非弹性粒子的模拟中，方形和六边形模式在广泛的振荡参数范围内形成，但在无摩擦的模拟中，即使将非弹性增加以获得与有摩擦粒子相同的耗散量，也只会形成条纹模式。我们还考虑了粒子摩擦力对颗粒层每次撞击容器时形成的冲击波的影响。虽然无摩擦粒子仍会形成冲击波，但有摩擦和无摩擦情况下流体动力学场的空间和时间依赖性有所不同。
