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. 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 Kuznetsov, Andresen, Mosekilde, Dewel, Borckmans

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 [BrO 3  ] = 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 u ss, v ss

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

11. Dispersion relation Tr = j 11 + j 22  = j 11 j 22 – j 12 j 21

12. Absolute to Convective Instability Look for zero group velocity, i.e. find  =  0 such that gives so Setting Im(  0 )) = 0 gives  AC

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

14. Bifurcation Diagram

15. Initial Development of Stationary Pattern Oregonator model  = 0.25 f = 1.0 q = 8  10  4  = 2 0.4 time units per frame

17. Space-time plot

18. Experimental verification BZ system with f = 0.17 cm s  1 [BrO 3  ] = 0.2 M, H + = 0.15M [MA] = 0.4 M, [Ferroin] = 7  10  4 M

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

21. space-time plot

22. Nonlinear -  response  = 0.25  = 0.5  = 0.8

23.  = 0.25 f = 1.0 q = 8  10  4  = 1.5 0.4 time units per frame Complex Pattern Development

25. space-time plot  = 1.5

26. more complexity  = 1.4

27. CDIMA reaction Patterns but unsteady

28. Lengyel-Epstein model  = 0.5  = 5 0.12 time units per frame