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

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

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

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

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

wavelength = velocity  period

Using simple analysis of Oregonator model, predict:

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

Analysis Oregonator model: Has a uniform steady state u ss, v ss

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

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

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

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

Bifurcation Diagram

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

Space-time plot

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

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

space-time plot

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

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

space-time plot  = 1.5

more complexity  = 1.4

CDIMA reaction Patterns but unsteady

Lengyel-Epstein model  = 0.5  = time units per frame