TY - JOUR

T1 - Approximating the large time asymptotic reaction zone solution for fractional order kinetics AnBm

AU - Trevelyan, Philip

PY - 2012/2/1

Y1 - 2012/2/1

N2 - Consider the reaction front formed when two initially separated reactants A and B are brought into contact and react at a rate proportional to A^n B^m when the concentrations A and B are positive. Further, suppose that both n and m are less than unity. Then the leading order large time asymptotic reaction rate has compact support, i.e. the reaction zone where the reaction takes place has a finite width and the reaction rate is identically zero outside of this region. In the large time asymptotic limit an analytical approximate solution to the reactant concentrations is constructed in the vicinity of the reaction zone. The approximate solution is found to be in good agreement with numerically obtained solutions. For n > m the location of the maximum reaction rate does not coincide with the centre of mass of the reaction, and further for n not equal to m this local maximum is shifted slightly closer to the zone that initially contained species A, with the reverse holding when m > n. The three limits m -> 0, n -> 1 and m, n -> 1 are given special attention.

AB - Consider the reaction front formed when two initially separated reactants A and B are brought into contact and react at a rate proportional to A^n B^m when the concentrations A and B are positive. Further, suppose that both n and m are less than unity. Then the leading order large time asymptotic reaction rate has compact support, i.e. the reaction zone where the reaction takes place has a finite width and the reaction rate is identically zero outside of this region. In the large time asymptotic limit an analytical approximate solution to the reactant concentrations is constructed in the vicinity of the reaction zone. The approximate solution is found to be in good agreement with numerically obtained solutions. For n > m the location of the maximum reaction rate does not coincide with the centre of mass of the reaction, and further for n not equal to m this local maximum is shifted slightly closer to the zone that initially contained species A, with the reverse holding when m > n. The three limits m -> 0, n -> 1 and m, n -> 1 are given special attention.

KW - Reaction-diffusion

KW - fractional order kinetics

KW - large time asymptotic

KW - approximate solutions

UR - https://www.aimsciences.org/article/doi/10.3934/dcdss.2012.5.219

UR - https://pure.southwales.ac.uk/en/publications/approximating-the-large-time-asymptotic-reaction-zone-solution-for-fractional-order-kinetics-anbm(6b7f8107-9baf-4737-83d4-59f203ee3fa6).html

U2 - 10.3934/dcdss.2012.5.219

DO - 10.3934/dcdss.2012.5.219

M3 - Article

VL - 5

SP - 219

EP - 234

JO - Discrete and Continuous Dynamics Systems Series S

JF - Discrete and Continuous Dynamics Systems Series S

IS - 1

ER -