Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model

Alexandre M. Tartakovsky, David Barajas-Solano

Research output: Contribution to journalArticlepeer-review


We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection–dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. ** to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell-shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.

Original languageEnglish (US)
Article number103729
JournalAdvances in Water Resources
StatePublished - Nov 2020


  • Bimolecular reactions
  • Incomplete mixing
  • Mechanical mixing
  • Stochastic transport model
  • Tracer test

ASJC Scopus subject areas

  • Water Science and Technology


Dive into the research topics of 'Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model'. Together they form a unique fingerprint.

Cite this