Exact Calculation of Mobility and Diffusion Coefficient in a Drift Motion of Reactive Particles

This paper presents analytical expressions for the mobility ( [[EQUATION]] ) and diffusion coefficient ( [[EQUATION]] ) of a chemical compound [[EQUATION]] that react with a carrier [[EQUATION]] giving a product [[EQUATION]] in the presence of drift. A one-dimensional lattice gas of [[EQUATION]] sites, with free boundary conditions and nearest neighbor transitions, is used to analyze the problem. The presence of drift is directly associated to the asymmetry in the rate transitions, and the dynamics of the process is governed by a set of [[EQUATION]] coupled differential equations. Two different approaches are used to obtain the expressions of [[EQUATION]] and [[EQUATION]] as function of the rate transitions, reaction rate and [[EQUATION]] concentration. In addition, two Monte Carlo simulations schemes are developed to reproduce the results obtained by those analytical approaches. The numerical integration is also included to determine the validity range of the two solutions. These problem mimics the movement of enantiomers in capillary electrophoresis (CE) techniques, where the expression for the mobility is obtained based on phenomenological arguments