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Development of FDO Patterns in the BZ Reaction

Development of FDO Patterns in the BZ Reaction. Steve Scott University of Leeds. Acknowledgements. Jonnie Bamforth (Leeds) Rita T ó th (Debrecen) Vilmos G áspár (Debrecen) British Council/Hungarian Academy of Science ESF REACTOR programme.

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Development of FDO Patterns in the BZ Reaction

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  1. Development of FDO Patterns in the BZ Reaction Steve Scott University of Leeds

  2. Acknowledgements • Jonnie Bamforth (Leeds) • Rita Tóth (Debrecen) • Vilmos Gáspár (Debrecen) • British Council/Hungarian Academy of Science • ESF REACTOR programme

  3. Kuznetsov, Andresen, Mosekilde, Dewel, Borckmans Flow Distributed Oscillations • patterns without differential diffusion or flow • Very simple reactor configuration: plug-flow tubular reactor fed from CSTR • reaction run under conditions so it is oscillatory in batch, but steady-state in CSTR

  4. Simple explanation • CSTR ensures each “droplet” leaves with same “phase” • Oscillations occur in each droplet at same time after leaving CSTR and, hence, at same place in PFR

  5. Explains: existence of stationary patterns need for “oscillatory batch” reaction BZ system with f = 0.17 cm s-1 [BrO3-] = 0.24 M, H+ = 0.15M[MA] = 0.4 M, [Ferroin] = 7 ´ 10-4 M Images taken at 2 min intervals

  6. wavelength = velocity ´ period

  7. Using simple analysis of Oregonator model, predict:

  8. Doesn’t explain critical flow velocity nonlinear dependence of wavelength on flow velocity other responses observed, especially the dynamics of pattern development

  9. Analysis • Oregonator model: Has a uniform steady state uss, vss

  10. Perturbation: u = U + uss, v = V + vss linearised equations Seek solutions of the form

  11. Dispersion relation Tr = j11 + j22 D = j11j22 – j12j21

  12. Absolute to Convective Instability Look for zero group velocity, i.e. find k = k0such that gives so Setting Im(w(k0)) = 0 gives fAC

  13. Bifurcation to Stationary Patterns Required condition is w = 0 with Im(k) = 0 Setting w = 0 yields So Im(k) = 0 gives critical flow velocity

  14. Bifurcation Diagram

  15. Initial Development of Stationary Pattern • Oregonator modele = 0.25f = 1.0q = 8  10-4f = 2 0.4 time units per frame

  16. Space-time plot

  17. Experimental verification BZ system with f = 0.17 cm s-1[BrO3-] = 0.2 M, H+ = 0.15M[MA] = 0.4 M, [Ferroin] = 7 ´ 10-4 M

  18. Oregonator model as before, Pattern already established now change f from 2.0 to 4.0 Adjustment of wavelength to change in flow velocity

  19. space-time plot

  20. Nonlinear l-f response e = 0.8 e = 0.5 e = 0.25

  21. Complex Pattern Development e = 0.25f = 1.0q = 8  10-4f = 1.5 0.4 time units per frame

  22. space-time plot f = 1.5

  23. more complexity f = 1.4

  24. CDIMA reaction Patterns but unsteady

  25. Lengyel-Epstein model • a= 0.5f = 5 0.12 time units per frame

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