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Waves and Patterns in Chemical Reactions

Waves and Patterns in Chemical Reactions. Steve Scott Nonlinear Kinetics Group School of Chemistry University of Leeds steves@chem.leeds.ac.uk. Outline. Background Patterns DIFICI FDO Waves excitable media wave block. Feedback. non-elementary processes

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Waves and Patterns in Chemical Reactions

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  1. Waves and Patterns in Chemical Reactions Steve Scott Nonlinear Kinetics Group School of Chemistry University of Leeds steves@chem.leeds.ac.uk

  2. Outline • Background • Patterns DIFICI FDO • Waves excitable media wave block

  3. Feedback non-elementary processes intermediate species influence rate of own production and, hence, overall reaction rate.

  4. Waves & Patterns

  5. Turing Patterns • Turing proposal for “morphogenesis” (1952) • “selective diffusion” in reactions with feedback • requires diffusivity of feedback species to be reduced compared to other reactants • recently observed in experiments • not clear that this underlies embryo development A. Hunding, 2000 Castets et al. Phys Rev. Lett 1990

  6. Ouyang and Swinney Chaos 1991 CDIMA reaction Turing Patterns spots and stripes: depending on Experimental Conditions

  7. “Turing Patterns” in flames “thermodiffusive instability” • first observed in Leeds (Smithells & Ingle 1892) requires thermal diffusivity < mass diffusivity

  8. DIFICI • differential-flow induced chemical instability • still requires selective diffusivity but can be any species Menzinger and Rovinsky Phys. Rev. Lett., 1992,1993

  9. BZ reaction: DIFICI • immobilise ferroin on ion-exchange resin • flow remaining reactants down tube • above a “critical” flow velocity, distinct “stripes” of oxidation (blue) appear and travel through tube

  10. Experiment • = 2.1cm cf = 0.138 cm s-1 f = 2.8 s frame-1 [BrO3-] = 0.8 M [BrMA] = 0.4 M [H2SO4] = 0.6 M Rita Toth, Attila Papp (Debrecen), Annette Taylor (Leeds)

  11. Experimental results imaging system: vary “driving pressure” slope ~ 1 Not possible to determine “critical flow velocity”

  12. BZ reaction • Involves competition between: HBrO2 + Br- 2BrMA and HBrO2 + BrO3- + 2Mred 2HBrO2 + 2Mox • Also BrMA + 2MoxfBr- + 2Mred

  13. Theoretical analysis: • Dimensionless equations u = [HBrO2], v = [Mox] : take d = 0 e and f depend on initial reactant concentrations

  14. main results • DIFICI patterns in range of operating conditions separate from oscillations fcr® ¥ convective instab. no instab. fcr increasing fcr = 0 no instability absolute instability f

  15. Space-time plot showing position of waves back to dimensional terms : predict cf,cr = 1.3 ´ 10-2 cm s-1 Forcf,cr = 2.4 ´ 10-2 cm s-1 l = 0.42 cm note: initiation site moves down tube

  16. 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 CSTR

  17. 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

  18. Explains: need for “oscillatory batch” reaction stationary pattern wavelength = velocity ´ oscill period • Doesn’t explain critical flow velocity other responses observed

  19. CDIMA reaction chlorine dioxide – iodine - malonic acid reaction: Lengyel-Epstein model (1) MA + I2 IMA + I + H+ (2) ClO2 + IClO2 + ½ I2 (3) ClO2 + 4 I + 4 H+ Cl + 2 I2

  20. Dimensionless equations u = [I-], v = [ClO2-]: uniform steady-state is a solution of these equations, but is it stable?

  21. J. Bamforth et al., PCCP, 2000, 2, 4013

  22. absolute and convective instability

  23. stationary FDO pattern Relevance to somatogenesis?

  24. Waves in Excitable Media • What is an “excitable medium? • Where do they occur?

  25. Excitability system sits at a steady state steady state is stable to small perturbations Large (suprathreshold) perturbations initiate an excitation event. System eventually recovers but is refractory for some period

  26. Excitability in Chemical Systems • BZ reaction: oscillations targets

  27. Spirals broken waves ends evolve into spirals

  28. O2-effects on BZ waves propagate BZ waves in thin films of solution under different atmospheres: main point is that O2 decreases wave speed and makes propagation harder: this effect is more important in thin layers of solution

  29. O2 inhibition Inhibited layer due to presence of O2 (O2 favours reduced state!)

  30. Mechanistic interpretation Modify “Process C” – clock resetting process: Mox + Org  Mred + MA. + H+ MA.g Br MA. + O2 ( + 1) MA. rate = k10(O2)V (cf. branched chain reaction) Presence of O2 leads to enhanced production of Br- which is inhibitor of BZ autocatalysis

  31. Analysis • Can define a “modified stoichiometric factor”, feff: where a is a ratio of the rate coefficients for MA. branching and production of Br- and increases with O2. • Increasing O2 increases f and makes system less excitable

  32. computations Can compute wavespeed for different O2 concentrations: see quenching of wave at high O2

  33. computed wave profiles allows computation of wavespeed with depth O2 profile computed by Zhabotinsky: J. Phys. Chem., 1993

  34. targets and spirals in flames target and spiral structures observed on a propagating flame sheet: Pearlman, Faraday Trans 1997; Scott et al. Faraday Trans. 1997

  35. Biological systems • wave propagation widespread: signalling sequencing of events co-ordination of multiple cellular responses

  36. nerve signal propagation • 1D pulse propagation

  37. Electrical Activity in Heart

  38. Cardiac activity and arrhythmia Electrical signal and contraction propagate across atria and then into ventricles 3D effects

  39. spirals and fibrillation L. Glass, Physics Today, August 1996 Simple waves may break due to local reduced excitability: ischemia infarction scarring actually 3D structures - scrolls canine heart

  40. scrolls in the BZ system Can exploit inhibitory effect of O2 on BZ system to generate scroll waves wave under air then N2 wave under O2 then under N2 A.F. Taylor et al. PCCP, 1999

  41. 2D waves on neuronal tissue Spreading depression wave in chicken retina (Brand et al., Int. J. Bifurc. Chaos, 1997)

  42. Universal relationship dispersion relation: relates speed of wave to period or wavelength

  43. Wave Failure and Wave Block Industrial problem: “reaction event” propagating in a non-continuous medium: sometimes fails

  44. Wave Propagation in Heterogeneous Media Jianbo Wang

  45. Pyrotechnics - SHS Arvind Varma: Sci. Am. Aug, 2000 “thermal diffusion” between reactant particles – heat loss in void spaces

  46. Myelinated nerve tissue propagation by “hopping” from one Node to next Propgn failure occurs in MS

  47. Ca2+ waves intra- and inter- cellular waves airway epithelial cells (Sneyd et al. FASEB J. 1995)

  48. intra- and intercellular waves

  49. Analysis • Some previous work – mainly directed at determining “critical” (single) gap width

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