Reaction on a solid surface supplied by an anomalous mass transfer source

2021

Fractal Fract

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

Section: Introductionmentioning

confidence: 99%

Diffusion in Heterogenous Media and Sorption—Desorption Processes

Koltun

2021

Fractal Fract

“…In many cases, the diffusing elements may suffer chemical reactions that change the concentration of particles, so the diffusion process is altered as the process takes place [5]. There are plenty of examples of processes involving simultaneous diffusion and chemical reactions, such as in engineering [6], biological systems [7], chemistry [8], and physics [9][10][11], among many others. Reaction-diffusion systems have attracted great attention in recent years and have been studied in a wide variety of biological and chemical systems, such as in the theory of combustion [12] and nerve impulse propagation [13].…”

Section: Introductionmentioning

confidence: 99%

“…They often present complex behaviour and display challenging phenomena as, for instance, pattern formation, moving fronts, and oscillations [14][15][16]. Solutions for diffusion-reaction systems have been explored analytically [9], numerically [17], and, more recently, by means of convolutional neural networks [18]. In general, the above-mentioned phenomena are described in terms of differential equations, more specifically, by using the so-called diffusion equation [5], based on Fick's law, which connects the time-dependent movement of particles to the concentration gradients occurring in the sample.…”

Section: Introductionmentioning

confidence: 99%

“…Our results may be used as an alternative to describe reaction-diffusion systems from the propagation velocity perspective, thus providing a connection with experimental results where the velocity of propagation plays an important role. Indeed, since finite propagation velocity is intrinsic to the problem dealt here, systems involving reaction-diffusion [6][7][8][9][10][11] might now be revisited and propagation speed explored on the grounds of the model presented here.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solutions for a hyperbolic diffusion equation with linear reaction terms

Lenzi¹,

Lenzi²,

Evangelista³

2020

J. Stat. Mech.

General diffusion processes involve one or more diffusing species and are usually modelled by Fick’s law, which assumes infinite propagation velocity. In this article, searching for the effect of finite propagation speeds in a system with two reacting species, we investigate diffusing and reacting particles governed by a hyperbolic diffusion equation, that is, the Cattaneo equation, which describes a diffusion process with finite propagation velocity, in the presence of a constant external field and reaction terms. These reaction terms are linear and may be related to irreversible and reversible processes, including memory effects, depending on the choices of the reaction rates. We obtain exact solutions for the equilibrium concentrations and explore the rich variety of behaviours exhibited by the species involved in reaction processes. Our results may shine new light into systems with more than one kind of diffusing and reacting particles, as is the case in several industrial and biological process, when finite speeds and memory effects are involved.

“…These situations related to anomalous diffusion have been investigated by taking into account, for example, fractional diffusion equations [18][19][20][21], generalized Langevin equations [22,23], master equations [24,25], random walks [26], and nonlinear diffusion equations [27][28][29][30][31][32][33][34][35][36][37]. It is worth emphasizing that the nonlinear diffusion equations may be related to a thermodynamic [38] characterized by power-law distributions with a compact or a long-tailed behavior, which, in a suitable limit, can be connected with the Lévy distributions.…”

Section: Introductionmentioning

confidence: 99%

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Silva

et al. 2017

Entropy

Abstract:We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.