Continuum description of granular flows: Simulation and experiment

Granular flows with strong hydrodynamic effects are studied numerically and experimentally. We introduce a model for grain flow in the presence of an interstitial gas in the approximation that inertia may be neglected. The model thus describes the grains as moving at their local terminal velocity relative to the interstitial gas, which is described by a local Darcy law. In addition to these two fields there is also a fluidization field that turns the granular motion on or off. This allows for the description of stagnant zones inside a granular flow as well as a free surface and heap formation. Experiments are carried out to study both a simple bubble rising through a tube and the more complex flow of grains out through a hopper. There is a reasonable quantitative agreement between experiment and simulation for the bubble flow. Ln the hopper flow the stagnation zones forming on the sides of the hopper during outflow are compared. Simulations and experiments agree quantitatively to the level of exponents characterizing the stagnation zones. In contrast to earlier experiments the present experiments use smooth grains and geometrically rough walls. This causes the present exponent to differ from that obtained in the earlier experiments. We finally apply the model to study the dynamics of a two-dimensional bubble.