A method-of-moments scheme is invoked to compute the asymptotic, long-time mean (or composite) velocity and dispersivity (effective diffusivity) of a two-state particle undergoing one-dimensional convective-diffusive motion accompanied by a reversible linear transition ("chemical reaction" or "change in phase") between these states. The instantaneous state-specific particle velocity is assumed to depend only upon the instantaneous state of the particle, and the transition between states is assumed to be governed by spatially independent, first-order kinetics. Remarkably, even in the absence of molecular diffusion, the average transport of the "composite" particle exhibits gaussian diffusive behavior in the long-time limit, owing to the effectively stochastic nature of the overall transport phenomena induced by the interstate transition. The asymptotic results obtained are compared with numerical computations.
|Original language||English (US)|
|Number of pages||15|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - May 1 2003|
Bibliographical noteFunding Information:
This work was supported in part by a Graduate Research Fellowship awarded to KDD by the National Science Foundation. We acknowledge useful discussions regarding the numerical solutions with Scott D. Phillips of MIT.
- Brownian motion
- Generalized Taylor dispersion
- Macrotransport theory