Kinetics of Ballistically-Controlled Reactions

Abstract

We investigate the kinetics of generic single-species reaction processes when the reactants move ballistically, namely ballistic annihilation, A + A - 0, and a ballistic aggregation process which mimics traffic flow on a single-lane roadway. For ballistic annihilation, dimensional analysis shows that the concentration and root means square velocity decay as c - P and u N r-6, respectively, with a + fl = 1 in any spatial dimension. Analysis of the Boltzmann equation for the evolution of the velocity distribution predicts CY = (2 + 2p)/(3 + 2p) and fl = 1/(3 + 2p) for an initial velocity distribution P(v,r=O) - u@ as u - 0. New phenomena associated with discrete initial velocity distributions and with mixed ballistic and diffusive reactant motion are also discussed. In the aggregation process, each “car” moves at its initial velocity until the preceding car or cluster is overtaken after which the incident car assumes the velocity of the cluster which it has just joined. For PO@) - ufi as v - 0, the average cluster size grows as n N t(@+1)/(F+2) and the average velocity decays as u - t1/b+2). We also derive an asymptotic expression for the joint distribution function for the cluster mass and velocity.