Development of FDO Patterns in the BZ Reaction

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Development of FDO Patterns in the BZ Reaction

• Steve Scott
• University of Leeds

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Acknowledgements

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

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Flow Distributed Oscillations
Kuznetsov, Andresen, Mosekilde, Dewel, Borckmans

• 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

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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

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• Explains
• existence of stationary patterns
• need for oscillatory batch reaction

BZ system with f 0.17 cm s-1 BrO3- 0.24 M,
H 0.15MMA 0.4 M, Ferroin 7 10-4 M
Images taken at 2 min intervals
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wavelength velocity period
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• Using simple analysis of Oregonator model,
  predict

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• Doesnt explain
• critical flow velocity
• nonlinear dependence of wavelength on flow
  velocity
• other responses observed, especially the
  dynamics of pattern development

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Analysis

• Oregonator model
• Has a uniform steady state uss, vss

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• Perturbation u U uss, v V vss
• linearised equations
• Seek solutions of the form

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Dispersion relation
Tr j11 j22 D j11j22 j12j21
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Absolute to Convective Instability

• Look for zero group velocity, i.e. find k k0
  such that
• gives
• so
• Setting Im(w(k0)) 0 gives fAC

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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

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Bifurcation Diagram
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Initial Development of Stationary Pattern

• Oregonator model e 0.25 f 1.0 q 8 ?
  10-4 f 2 0.4 time units per frame

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Space-time plot
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Experimental verification
BZ system with f 0.17 cm s-1BrO3- 0.2 M,
H 0.15MMA 0.4 M, Ferroin 7 10-4 M
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Adjustment of wavelength to change in flow
velocity

• Oregonator model as before,
• Pattern already established
• now change f from 2.0 to 4.0

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space-time plot
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Nonlinear l-f response
e 0.8
e 0.5
e 0.25
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Complex Pattern Development
e 0.25 f 1.0 q 8 ? 10-4 f 1.5 0.4
time units per frame
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space-time plot
f 1.5
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more complexity
f 1.4
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CDIMA reaction
Patterns but unsteady
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Lengyel-Epstein model

• a 0.5 f 5 0.12 time units per frame

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