Grains and gas flow: molecular dynamics with hydrodynamic interactions

We introduce a simple model for granular flows with hydrodynamic interactions. The hydrodynamic part of the model relies on a coarse grained picture of the granular medium, and is described in terms of the pressure by a local Darcy law. The model thus avoids the large computational cost of solving for detailed hydrodynamic flow fields between grains. The solid phase is described explicitly in terms of grains by event driven molecular dynamics. In the first two test cases, the model is employed to simulate a sedimenting and a fluidized particle bed. It is shown that the qualitative aspects of both phenomena are correctly captured: The sedimenting particles form a sharp upper front and move according to the theoretical prediction, which is also given. When external pressure gradients are applied the bed fluidizes, and spontaneously produces bubbles of the shape observed experimentally. Moreover, these bubbles are seen to merge, as is experimentally observed.