2007
DOI: 10.1063/1.2759750
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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 obtain… Show more

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Cited by 8 publications
(24 citation statements)
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“…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].…”
Section: Models For Subdiffusion-limited Reactionssupporting
confidence: 54%
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“…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].…”
Section: Models For Subdiffusion-limited Reactionssupporting
confidence: 54%
“…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].…”
Section: Models For Subdiffusion-limited Reactionsmentioning
confidence: 66%
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“…Numerical solutions to Eq. (43) for α ∈ (0 1) lead to ∈ (1/3 1) [23,24]. Thus, we have found three relations, namely, Eqs.…”
Section: The Agreement Conditionsmentioning
confidence: 81%
“…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)…”
Section: Final Remarksmentioning
confidence: 99%