Bi-flux theory applied to the dispersion of particles in anisotropic substratum

Abstract

• A new bi-flux diffusion model is presented with two new coefficients reactivity and particle distribution between fluxes. • Particles can move from a main flow to a secondary flow, both present simultaneously in the process. • Particles’ movement can be controlled by some external agent or themselves. • The bi-flux model may lead to dispersion or concentration covering a wide class of phenomena. • The secondary flux may be excited by different potential laws. The flux dynamics of sensitive particles cannot be satisfactorily modeled using the classical diffusion theory . The presence of disturbing exogenous agents (DEAs) in the substratum can introduce critical modifications in the process that induce a bi-flux behavior. This paper presents an alternative approach to anomalous diffusion processes that comprise two simultaneous fluxes. The primary flux responds to the classical Fick’s law, whereas the secondary flux is governed by a new law. Particles can move from the primary to the secondary flux, thereby triggering a new dynamical process. The bi-flux behavior presents strong deviations from classical solutions; particularly in anisotropic media. According to common knowledge, localized anisotropy in a substratum disturbing the physical parameters of the diffusion process can act like an attractor of the flow. Besides physicochemical reactions, the population dynamics can also benefit from the new theory. The Hermite finite-element method is employed to obtain the numerical solution for the spatial domain and the backward-difference approach for the time domain.