Density relaxation of granular matter through Monte Carlo and granular dynamics simulations

Granular materials are the principal ingredients of the industrial complex involved with the handling and processing of bulk solids including pharmaceuticals, chemicals, agricultural and mining materials. Despite the enormous importance of these materials in society, their behavior is not well-understood; in fact, there is no known model available that is capable of predicting the wide range of phenomenon that have been observed. One of the most important of these is known as density relaxation. Here, a granular material undergoes an increase in solids fraction as a result of the application of discrete taps or continuous vibrations. In this dissertation, the density relaxation phenomenon is promoted by the application of discrete taps to a periodic system of monodisperse spheres. Both stochastic ( Monte Carlo) and deterministic (granular dynamics) simulations are employed in this work. The granular microstructure of the system particles was analyzed via radial distribution function, coordination number, and the distribution of sphere centers in the vertical direction. In the MC simulations, the effect of a tap applied to the system is modeled using two different approaches: (1) vertical position-dependent expansion of the particles, and (2) uniformly lifting the entire ensemble on a small displacement above the supporting floor. Both methods resulted in an increase in the system density after numerous thousands of taps. However, method (1) exhibited a strong dependence of the final system density on the fill height, which has not been experimentally reported in the literature. On the other hand, this dependency was not seen when the expansion of type (2) was used. The MC evolution of the bulk solids fraction was found to be in qualitative agreement with an inverse log form that has been reported in the experimental literature. The simulated results illustrated that the bulk density is related to amount of the lift in method (2), with a critical value producing the most favorable results. Most striking is the finding that as the taps evolve, the particles self-organize into quasi-crystalline layers, initiated by the planar floor. The granular dynamics approach makes use of uniform, inelastic, and frictional spheres that interact via laws from well-founded collision-mechanics principles. The equations of motion are numerically integrated to obtain the positions and velocities of the particles. The tapping disturbance consisted of a harmonic intermittent oscillation of the floor. The same type of self-organization into quasi-crystalline layers first identified in the MC simulations was also found here, strongly supporting the conjecture that this is a universal mechanism of the density relaxation process