Granular Continuum-Transition Regime

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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.