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A two-stage reaction with initially separated reactants

Author

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  • Cox, Stephen M.
  • Clifford, Michael J.
  • Roberts, E.P.L.

Abstract

A two-stage reaction (A+B→R,B+R→S) is studied, where the reactants A and B lie initially in an array of alternating striations. The product R is desired, and S is an unwanted by-product. A corresponding reaction–diffusion system in one spatial dimension is analysed in two special cases, and comparison is made with numerical simulations of the reaction and diffusion in a periodic array of lamellae for realistic parameter values. For lamellar widths of the order of 1μm or less, diffusion rapidly smears out the lamellar structure, and the yields of R and S are nearly equal to those in a spatially homogeneous, well-mixed system. For thicker lamellae, of around one millimetre in width, the yields are significantly different in the lamellar case from the well-mixed case. The differences are quantified and discussed.

Suggested Citation

  • Cox, Stephen M. & Clifford, Michael J. & Roberts, E.P.L., 1998. "A two-stage reaction with initially separated reactants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 65-86.
    • Handle: RePEc:eee:phsmap:v:256:y:1998:i:1:p:65-86
    DOI: 10.1016/S0378-4371(98)00091-0
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    References listed on IDEAS

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    1. Taitelbaum, Haim, 1993. "Segregation in reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 155-164.
    2. Havlin, S. & Araujo, M. & Larralde, H. & Stanley, H.E. & Trunfio, P., 1992. "Diffusion-controlled reaction, A+B→C, with initially separated reactants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 143-152.
    3. Sokolov, I.M. & Blumen, A., 1992. "Diffusion-controlled reactions in nonstoichiometrical layered systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 177-181.
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    1. Clifford, MichaelJ. & Cox, StephenM. & Roberts, E.P.L., 1999. "Reaction and diffusion in a lamellar structure: the effect of the lamellar arrangement upon yield," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(3), pages 294-306.

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