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Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls.The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems, heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap. Systems of granular particles (e.g. sand) exhibit many interesting phenomena, such as segregation under vibration or shear, density waves in the outflow through hoppers, and probably most strikingly, the formation of heap and convection cell under vibration.

We study deep bed filtration, where particles suspended in a fluid are trapped while passing through a porous medium, using numerical simulations in various network models for flow in the bed. We first consider cellular automata models, where filtrate particles move in a fixed background flow field, with either no-mixing or complete-mixing rules for motion at a flow junction. The steady-state and time-dependent properties of the trapped particle density and filter efficiency are studied. The complete mixing version displays a phase transition from open to clogged states as a function of the mean particle size, while such a transition is absent in the (more relevant) no-mixing version. The concept of a trapping zone is found to be useful in understanding the time-dependent properties. We next consider a more realistic hydrodynamic network model, where the motion of the fluid and suspended particles is determined from approximate solutions of the time-dependent Stokes equation, so that the pressure field constantly changes with particle movement. We find that the steady-state and time-dependent behavior of the network model is similar to that of the corresponding cellular automata model, but the long computation times necessary for the simulations make a quantitative comparison difficult. Furthermore, the detailed behavior is extremely sensitive to the shape of the pore size distribution, making experimental comparisons subtle.