Propriedades de transporte em meios granulares unidimensionais

Abstract

We study two problems involving granular media, the heat transport in viscous granular gases and the mechanical pulse propagation in a granular chains of toroidal ring. To study the heat transport in granular gases, we consider two mechanisms of viscous dissipation during collisions between grains. In the first mechanism, the dissipative force is proportional to the speed of the grain and dissipates not only energy but also momentum. On the other hand, the dissipative force is proportional to the relative velocity of grains and therefore conserves momentum when it dissipates energy. This allows us to explore the role of the conservation of momentum in the heat transport properties of one-dimensional nonlinear systems. We found a thermal conductivity not divergent with or without conservation of momentum. For the system where there is conservation of momentum we obtain the heat flux decreases faster than the energy loss by inelastic dissipation due to shocks, unlike what happens with the momentum conserving system, indicating that the conservation of momentum has a role relevant. We also implemented an approximation of binary collisions to study the propagation of pulses in a onedimensional chain of O-rings. In particular, we get the analytical results from which the pulse velocity is obtained by simple quadrature. The pulse velocity thus calculated is compared with the velocity obtained by numerical integration of the equations of motion. We study chains with and without precompression, chains precompressed by a constant force at both ends (constant precompression), chains precompressed by gravity (variable precompression). The application of binary collisions approximation for precompressed chains gives us an important generalization of a theory, which until then had been developed for chains without precompression, in other words sonic vacuum state. The velocities calculated using the approximation of binary collisions showed a good agreement with the results obtained from numerical simulations, with relative errors lesser than 8%.