Dilution of Reactive Plumes: Evolution of Concentration Statistics Under Diffusion and Nonlinear Reaction

Concentration fields of solutes in porous media often exhibit large fluctuations, driven by physical and chemical heterogeneity from the pore to Darcy scale. For many applications, ranging reactive transport modeling toxicology, knowledge mean concentrations is not sufficient, quantifying concentration variability necessary. The probability density function (PDF) quantifies frequency occurrence values throughout a spatial domain. While evolution equations analytical solutions for PDF exist conservative solutes, less known about its under joint action reaction. In this work, we investigate how dilution plume diffusion affects statistics concentrations. mixing has no effect on first-order reactions, coupling with nonlinear reactions leads non-trivial effective kinetics relevant broad range problems. We study reaction one dimension, which represents critical step toward further heterogeneous advection. show that dependence scalar dissipation rate encodes impact diffusive derive dynamical equation time evolution. Using weak-coupling approximation dynamics, predictions moments. Our results provide new insights into control open opportunities models reactions.