Convective dispersion without molecular diffusion

Kevin D. Dorfman, Howard Brenner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish (US)
Pages (from-to)180-194
Number of pages15
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - May 1 2003

Bibliographical note

Funding 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
  • Homogenization
  • Macrotransport theory


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