Particle-tracking simulation of fractional diffusion-reaction processes

Abstract

Abstract. Computer simulation of reactive transport in heterogeneous systems remains a challenge, due to the multi-scale nature of reactive dynamics and the non-Fickian behavior of transport. This study develops a fully Lagrangian approach via particle tracking to describe the reactive transport controlled by the tempered super-or sub-diffusion. In the particle-tracking algorithm, the local-scale reaction is affected by the interaction radius between adjacent reactants, whose motion can be simulated by the Langevin equations corresponding to the tempered stable models. Lagrangian simulation results show that the transient superdiffusion enhances reaction by enhancing the degree of mixing of reactants. The proposed particle-tracking scheme can also be extended conveniently to multi-scaling super-diffusion. For the case of transient sub-diffusion, the trapping of solutes in the immobile phase can either decrease or accelerate the reaction rate, depending on the initial condition of reactant particles. Further practical applications show that the new solver efficiently captures bimolecular reactions observed in laboratories.

Improved understanding of bimolecular reactions in deceptively simple homogeneous media: From laboratory experiments to Lagrangian quantification

“…Second, how will anomalous diffusion affect bimolecular reactions in a sand column? To address this question, we develop particle‐based models by combining previously developed Lagrangian approaches [ Zhang and Papelis , ; Zhang et al ., ] to quantify reactions coupled with anomalous diffusion. Finally, can a predictive physical model be built for reactive transport in a deceptively simple “homogeneous” medium?…”

On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow

“…Without loss of generality we assume unit activity coefficients. This type of reaction has been studied experimentally and theoretically because of its simplicity and dependence on local mixing (e.g., [32,33,34,35,36,37,38]). The plates are separated by aperture b = 1 mm, and the molecular diffusion coefficient is 10 −3 mm 2 /s.…”

Fractional dynamics of tracer transport in fractured media from local to regional scales

“…First, the vector Langevin approach developed by Zhang et al [51] can be used to approximate the vector transport model (2), where the combination of the mixing measure M and the eigenvectors of H defines the multi-dimensional jumps of tracer particles. Numerical examples of this step can be found in Zhang and Papelis [54]. The second step is to solve the immobile process (5), by calculating and assigning the random waiting time for each particle using a wellvalidated time Langevin approach [52].…”