Reliability of the usual differential collision operator in describing the relaxation of a heavy-particle flow in a light gas

Abstract

The reliability of the usual (approximate) differential collision operator for heavy particles in a light gas (Rayleigh gas, brownian particles) is examined when the heavy particles, having initially temperature T 0 and flow (or drift) velocity <−<ν− > 0, relax in a background gas in equilibrium at temperature T. It is found that severe limitations must be imposed on T 0/ T and |〈ν〉 0|, in order that the usual approximate collision operator can have a fair reliability at the initial time.