Transport theory of granular swarms.

The transport of trace granular gas (swarm) in a carrier granular fluid is studied by means of the Boltzmann-Lorentz kinetic equation. Time-dependent perturbation theory is used to follow the evolution of the granular swarm from an arbitrary initial distribution. A nonhydrodynamic extension of the diffusion equation is derived, with transport coefficients that are time dependent and implicitly depend on the wave vector. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann-Lorentz equation. For the special case of the initial distribution of swarm particles, transport coefficients are identified as time derivatives of the moments of the number density. Finally the granular particle transport theory is extended by the introduction of the concept of non-particle-conserving collisions.