Granular media modeled as mixtures with continuous diversity
Abstract: The theory of mixtures has been employed since long time to model different aspects of the physics of polydisperse granular media. But using standard mixture theory has the shortcoming that just a few constituents can be considered, otherwise calculations become unfeasible. In other words, the mixture must have a low diversity. This might be a crucial problem if one wants to model segregation, fragmentation and abrasion in granular media consisting of a large number of different grain types (e.g. a continuous distribution of grain sizes or many different levels of roughness). It is the intention of this presentation to show that, by considering a polydisperse medium as a mixture with continuous diversity, one reduces the problem of a large number of constituents to a simpler problem of just one constituent described in a higher dimensional space. Furthermore, abrasion and fragmentation arise spontaneously in such a theory, with a clear and simple mathematical interpretation. Finally, preliminary results suggesting that segregation might be modeled by concepts similar to "chemical potential" and "affinity" in a mixture with continuous diversity will be discussed.