2018/03/18 by Alexandre M. Tartakovsky, Tartakovsky, Alexandre M., David A. Barajas‐Solano +1
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1803.06693
openalex publication_date 2018/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction 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 with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficients, but only the effective diffusion coefficient contributes to the mixing-controlled reactions, indicating that such systems do not get fully mixed at the Representative Elementary Volume scale where the deterministic equations and dispersion coefficient are defined. We use the experimental results of Gramling et al. \citeGramling to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the concentration of the reaction product by as much as 60%.