A stochastic technique for solving the Lorentz-Boltzmann equation for hard spheres: Application to the kinetics of gas absorption

摘要

The Lorentz-Boltzmann equation for tagged particle motion in a hard sphere fluid may be interpreted as describing the motion of a particle propagating via a series of binary uncorrelated collisions in a structureless bath of fluid particles with a Maxwellian distribution of velocities. 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. Having reproduced several known results for the Lorentz-Boltzmann equation we extend the method to a simple reaction process where there is no analytic result-the kinetics of gas absorption for a gas confined between two plates. For this process there are two simple analytic limits-the Knudsen limit (in which there are no collisions between absorbing particles) and the diffusive limit (where there are a large number of collisions between absorbing particles). We show that regardless of the Knudsen number, Kn, the Knudsen limit describes the very short time kinetics and the diffusive limit describes the long time kinetics. However, at moderate values of the Knudsen number the rate constant characterizing the long time kinetics differs from the diffusive value. This discrepancy scales away slowly (as 1/Kn) with increasing Knudsen number. (C) 1998 American Institute of Physics. [References: 17]