Time Evolution Of The Reaction Front In A Subdiffusive System

Abstract

Using the quasistatic approximation we show that in a subdiffusion-reaction system with arbitrary non-zero values of subdiffusion coefficients, the reaction front x f (t) evolves in time according to the formula x f (t) = Kt α/2 , with α being the subdiffusion parameter and K which is controlled by the subdiffusion coefficients. The parameter K is determined by the equation derived in this paper. To check correctness of our analysis, we compare analytical functions derived in this paper with the results obtained numerically for the subdiffusion-reaction equations.

Mathematical Modelling of Subdiffusion-reaction Systems

“…In the case of subdiffusion, it has been found that W r ∼ t γ/6 , W d ∼ t γ/2 . The center of the reaction zone moves according to the law x r (t) ∼ t γ/2 [32]. The same scaling law has been found in the case of one non-diffusive and one subdiffusive reactant [33].…”

“…The center of the reaction zone moves according to the law x r (t) ∼ t γ/2 [32]. The same scaling law has been found in the case of one non-diffusive and one subdiffusive reactant [33]. In the general case, analytical and numerical solutions of (2.3), (2.4) have been obtained in [31].…”

“…For instance, Koszto lowicz and Lewandowska [33] have applied that kind of equations for modelling the formation of a carious lesion of the tooth enamel. The theoretically predicted scaling law x r (t) ∼ t γ/2 for the location of the reaction zone center has been used for finding the parameter γ from the experimental data.…”

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

“…Numerical solutions to Eq. (43) for α ∈ (0 1) lead to ∈ (1/3 1) [23,24]. Thus, we have found three relations, namely, Eqs.…”

“…We have also determined the time evolution of the amount of substance released from a thick membrane. [23,24]. The boundaries of this interval move with a velocity decreasing over time [23,24] ( ) = W ( ) = αB 2 1−α/2 (44)…”