A STOCHASTIC TECHNIQUE FOR SOLVING THE LORENTZ-BOLTZMANN EQUATION FORHARD-SPHERES - APPLICATION TO THE KINETICS OF GAS-ABSORPTION

The Lorentz-Boltzmann equation for tagged particle motion in a hard sp here fluid may be interpreted as describing the motion of a particle p ropagating via a series of binary uncorrelated collisions in a structu reless bath of fluid particles with a Maxwellian distribution of veloc ities. We describe a very general stochastic technique for solving the equation. The method can also be extended to the Enskog level, valid up to somewhat higher densities, by a simple scaling of the time. Havi ng reproduced several known results for the Lorentz-Boltzmann equation we extend the method to a simple reaction process where there is no a nalytic result-the kinetics of gas absorption for a gas confined betwe en two plates. For this process there are two simple analytic limits-t he Knudsen limit (in which there are no collisions between absorbing p articles) and the diffusive limit (where there are a large number of c ollisions between absorbing particles). We show that regardless of the Knudsen number, Kn, the Knudsen limit describes the very short time k inetics and the diffusive limit describes the long time kinetics. Howe ver, at moderate values of the Knudsen number the rate constant charac terizing the long time kinetics differs from the diffusive value. This discrepancy scales away slowly (as 1/Kn) with increasing Knudsen numb er. (C) 1998 American Institute of Physics.