Examination of Fickian and Non-Fickian Multi-Species Reactive Plume Development and Steady-State

Abstract:

Non-Fickian transport, in which the mean square displacement is not proportional to time, is ubiquitous in disordered environments including dispersion of contaminant plumes in aquifers, nutrients in surface water and sediments, proteins and morphogens in crowded cells, and electric signals in spiny dendrites of the cerebellar cortex. In highly heterogeneous sediments, reactive plume particles in groundwater experience a broad velocity distribution as the particles are transported preferentially through interconnected low and high permeability zones. The effect of this non-Fickian transport is exhibited by the power law tails in concentration versus time breakthrough curves. Recently, new continuous time random walk (CTRW) governing equations have been developed for non-Fickian multi-species plume transport that also include first-order sequential reactions. These new equations indicate that first-order reactions are coupled to plume transport, which requires additional investigation. Both 1-D analytical solutions and numerical particle tracking simulations indicate that the steady-state, non-Fickian plume flux-averaged concentration distribution in highly heterogeneous media resembles the Fickian plume distribution in moderately heterogeneous media because first-order reactions truncate the waiting times between particle displacements and thus remove the lower velocity spectrum of particles during transport. Although both models can approach the same steady-state distribution, results of 1-D semi-analytical transient calculations show differences between non-Fickian and Fickian reactive plume models during plume development.