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Semi-analytical solutions for a Gray-Scott reaction-diffusion cell with an applied electric field

Journal Article


Abstract


  • An ionic version of the GrayScott chemical reaction scheme is considered in a reactiondiffusion cell, with an applied electric field, which causes migration of the reactant and autocatalyst in a preferred direction. The Galerkin method is used to reduce the governing partial differential equations to an approximate model consisting of ordinary differential equations. This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations. Bifurcation analysis of the semi-analytical model is performed by using singularity theory to analyse the static multiplicity and a stability analysis to determine the dynamic multiplicity. The application of the electric field causes variation in the parameter regions, in which multiple steady-state and oscillatory solutions occur. Moreover, as the reactor is not symmetric, reversal of the direction of the electric field can cause bifurcation in the reactor between high and low conversion states. Comparisons with numerical solutions of governing partial differential equations confirms the accuracy and usefulness of the semi-analytical model.

Publication Date


  • 2008

Citation


  • Thornton, A. & Marchant, T. R. (2008). Semi-analytical solutions for a Gray-Scott reaction-diffusion cell with an applied electric field. Chemical Engineering Science, 63 (2), 495-502.

Scopus Eid


  • 2-s2.0-36148965145

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2673

Number Of Pages


  • 7

Start Page


  • 495

End Page


  • 502

Volume


  • 63

Issue


  • 2

Place Of Publication


  • http://www.elsevier.com/locate/ces

Abstract


  • An ionic version of the GrayScott chemical reaction scheme is considered in a reactiondiffusion cell, with an applied electric field, which causes migration of the reactant and autocatalyst in a preferred direction. The Galerkin method is used to reduce the governing partial differential equations to an approximate model consisting of ordinary differential equations. This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations. Bifurcation analysis of the semi-analytical model is performed by using singularity theory to analyse the static multiplicity and a stability analysis to determine the dynamic multiplicity. The application of the electric field causes variation in the parameter regions, in which multiple steady-state and oscillatory solutions occur. Moreover, as the reactor is not symmetric, reversal of the direction of the electric field can cause bifurcation in the reactor between high and low conversion states. Comparisons with numerical solutions of governing partial differential equations confirms the accuracy and usefulness of the semi-analytical model.

Publication Date


  • 2008

Citation


  • Thornton, A. & Marchant, T. R. (2008). Semi-analytical solutions for a Gray-Scott reaction-diffusion cell with an applied electric field. Chemical Engineering Science, 63 (2), 495-502.

Scopus Eid


  • 2-s2.0-36148965145

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2673

Number Of Pages


  • 7

Start Page


  • 495

End Page


  • 502

Volume


  • 63

Issue


  • 2

Place Of Publication


  • http://www.elsevier.com/locate/ces