Granular Temperature

Abstract

Granular materials consist of a large number of small particles arranged in a random way. However, while the geometrical organization of an individual particle assembly is complex, these materials can nevertheless be well characterized by a small number of parameters. Systems of this type are the subject matter of thermodynamics, and so it seems reasonable to suppose that the methods employed in thermodynamics may be able to be applied to characterizing the behavior of particle assemblies. This paper describes an extension of classic thermodynamics to granular assemblies subjected to an energy flux through the granular assembly. By means of a Carnot engine, the granular temperature and entropy of a particle assembly is defined. The principal value of introducing the notion of granular temperature is that it defines a physically realistic internal variable for the granular assembly, which controls the evolution of the system after it is has been perturbed from its equilibrium state. The concept of granular thermodynamic equilibrium is then extended to non‐equilibrium granular thermodynamics. Chemical kinetic theory is employed to describe the relaxation of a granular assembly after it is perturbed by a sudden change in granular temperature. A particle vibration theory has been introduced to explain the behavior of soil subject to a white noise energy flux. While the theory described provides quantitative information about soil behavior, just as importantly, the theory provides a new qualitative insight into soil behavior.