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