Granular Continuum-Transition Regime

颗粒材料无处不在，在工农业生产中居于核心地位。拟议的项目将把重点放在它们的流态化阶段，也就是我们所说的“颗粒气”。动力学理论的强大方法已经被用来非常成功地产生颗粒气体的流体动力学描述。流体动力学仅限于较低的克努森数(平均自由程与相关宏观尺度之比)，因此不适用；例如，不适用于激波或稀薄(颗粒)气体内部。当克努森数远大于单位时，玻耳兹曼方程的无碰撞极限适用，然而，当它是单位数量级时，需要对动力学进行详细的研究。这定义了“连续体转变机制”，它在分子冲击和涉及稀薄气体的系统方面有相似之处，例如在高空飞行和芯片生产反应堆中遇到的情况。拟议项目的目标是产生颗粒连续统转变机制的连续统描述，并将这些描述应用于特定系统，该范例是垂直振动的颗粒气体。这计划通过利用最近开发的强大的计算机辅助分析工具来研究相关的Boltzmann方程(使用Grad矩展开作为方法之一)，并结合有效的数值模拟来实现。

Granular materials are ubiquitous and Nature and central in industry and agriculture. The proposed project will focus on their fluidized phase, known as the "granular gas". Powerful methods of kinetic theory have been employed to produce highly successful hydrodynamic descriptions of granular gases. Hydrodynamics is restricted to low Knudsen numbers (ratio of the mean free path to the pertinent macroscopic scales), and it therefore does; not apply to e.g., the interior of shocks or rarefied (granular) gases. When the Knudsen number is much larger than unity the collisionless limit of the Boltzmann equation applies, however, when is it of the order of unity a detailed study of the kinetics is called for. This defines the "continuum transition regime", which has parallels in e.g., molecular shocks and systems that involve rarefied gases as encountered e.g., in high altitude flights and chip-producing reactors. The goal of the proposed project is to produce continuum descriptions of the granular continuum transition regime and apply these to specific systems, the paradigm being vertically vibrated granular gases. This is planned to be achieved by harnessing recently developed powerful computer-aided analytic tools for the study of the pertinent Boltzmann equation (using the Grad moment expansion as one of the methods) in conjunction with efficient numerical simulations.