CNCS Graduate Certificate Recipient

Meenakshi Dutt

Thesis Title: Numerical Studies of Substrate Friction in Granular Materials

Ph.D. Final Defense Date:  August 30, 2002

Ph.D. Dissertation Committee:

Robert P. Behringer (Chair)
David G. Schaeffer
Joshua E. S. Socolar
Stephen Teitsworth
John E. Thomas

Abstract:

Experimental, theoretical and numerical studies on particle-substrate systems (Domenech, et al. 1987, Kondic 1999 and others) have emphasized the critical role substrate friction plays as a coupling between the particle and the underlying substrate and the consequences of this coupling on the dynamics of individual particles and the over all system. However, most numerical experiments neglect the frictional coupling between particles and the underlying substrate and focus solely on the collisional interaction between the constitutive particles of the system under scrutiny. Our work has followed a very different approach: we have developed particle-substrate models where we account for the substrate frictional coupling between the particles and the underlying substrate and have adapted the model so as to make it conducive to integrate processes such as interparticle collisional dynamics. We have followed this approach for both our 1-D and 2-D models. Our research of the impact of substrate friction on a multiparticle system commenced by studying 1-D cooling granular systems, due to their simplicity. We introduced the various types of interactions, mentioned above, by two methods: first, by assuming loss of a fraction of the center of mass momentum of the colliding particles to the substrate, after impact, and second, by considering the effect of substrate frictional forces on the particles. One of the most significant effects of doing so was that the problem of inelastic collapse was largely suppressed. To obtain a better insight into the nature of the interactions mentioned above and their manifestations in realistic laboratory situations, we used our 2-D model to study a hypothetical quasi 2-D bound granular system with substrate friction which allowed particle-particle and particle-wall interactions. Our results indicate that the walls act like momentum and energy sinks, resulting in the accumulation of the particles in their vicinity. To benchmark our 2-D numerical model, we carried out a simulation of the granular collider experiment of Painter et al. The reasonable correlation between our numerical results for final state configurations, autocorrelation calculations for inter-particle distances and velocity distributions and results analogous to the experiments supports the physical accuracy of the model. We further explored parameter space to determine how the properties of the system evolved with changes in the input energy, number of particles, coefficients of friction and collisional parameters

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