2. Dynamics of fronts in chemical and bacterial media: If you’ve seen one front, you’ve seen them all Paul Ronney Department of Aerospace & Mechanical Engineering Univ. of Southern California, Los Angeles, CA, 90089

3. University of Southern California  Established 125 years ago this week!  …jointly by a Catholic, a Protestant and a Jew - USC has always been a multi-ethnic, multi-cultural, coeducational university  Today: 32,000 students, 3000 faculty  2 main campuses: University Park and Health Sciences  USC Trojans football team ranked #1 in USA last 2 years

4. USC Viterbi School of Engineering  Naming gift by Andrew & Erma Viterbi  Andrew Viterbi: co-founder of Qualcomm, co-inventor of CDMA  1900 undergraduates, 3300 graduate students, 165 faculty, 30 degree options  $135 million external research funding  Distance Education Network (DEN): 900 students in 28 M.S. degree programs; 171 MS degrees awarded in 2005  More info: http://viterbi.usc.edu http://viterbi.usc.edu

5. Paul Ronney  B.S. Mechanical Engineering, UC Berkeley  M.S. Aeronautics, Caltech  Ph.D. in Aeronautics & Astronautics, MIT  Postdocs: NASA Glenn, Cleveland; US Naval Research Lab, Washington DC  Assistant Professor, Princeton University  Associate/Full Professor, USC  Research interests  Microscale combustion and power generation (10/4, INER; 10/5 NCKU)  Microgravity combustion and fluid mechanics (10/4, NCU)  Turbulent combustion (10/7, NTHU)  Internal combustion engines  Ignition, flammability, extinction limits of flames (10/3, NCU)  Flame spread over solid fuel beds  Biophysics and biofilms (10/6, NCKU)

6. Paul Ronney

7. Motivation  Propagating fronts are ubiquitous in nature  Flames »(Fuel & Oxidant) + Heat  More heat  Solid rocket propellant fuels »(Fuel & Oxidant) + Heat  More heat  Self-propagating high-temperature synthesis (SHS) - reaction of metal with metal oxide or nitride, e.g. Fe 2 O 3 (s) + 2Al(s)  Al 2 O 3 (s) + 2Fe(l) »(Fuel & Oxidant) + Heat  More heat  Frontal polymerization »Monomer + initiator + heat  polymer + more heat  Autocatalytic chemical reactions (non-thermal front) »Reactants + H +  Products + more H +  Bacterial front (non-thermal front) »Nutrient + bugs  more bugs  All of these might be construed as “reaction-diffusion systems”  Today’s topic: what is similar and what is different about these different types of fronts?

8. Reaction-diffusion systems  Two essential ingredients  Reactive medium (e.g. fuel-air mixture)  Autocatalyst - product of reaction that also accelerates the reaction (e.g. thermal energy)  Self-propagation occurs when the autocatalyst diffuses into the reactive medium, initiating reaction and creating more autocatalyst, e.g. A + nB  (n+1)B  Enables reaction-diffusion fronts to propagate at steady rates far from any initiation site

9. Premixed flame (SHS, solid propellant similar)

10. Reaction-diffusion systems - characteristics  After initial transient, fronts typically propagate at a steady rate  Propagation speed (S L ) ~ (D  ) 1/2 »D = diffusivity of autocatalyst or reactant »  = characteristic reaction rate = (reaction time) -1  D depends on “sound speed” (c) & “mean free path” ( ) »D ~ c »D ~ c  Propagation rate generally faster in turbulent media due to wrinkling (increased surface area) of front  Thermal fronts require high Zeldovich number (Ze) so that  products >>  reactants, otherwise reaction starts spontaneously!  Flammability or extinction limits when loss rate of autocatalyst ≈ production rate of autocatalyst

11. Instability mechanisms  Instability mechanisms may preclude steady flat front  Turing instability - when ratio of reactant to autocatalyst diffusivity differs significantly from 1 Thermal fronts: D autocatalyst /D reactant = Lewis number  Low Le: additional thermal enthalpy loss in curved region is less than additional chemical enthalpy gain, thus local flame temperature in curved region is higher, thus reaction rate increases drastically, thus “blip” grows  High Le: pulsating or travelling wave instabilities  Hydrodynamics - thermal expansion, buoyancy, Saffman-Taylor

12. Polymerization fronts  First demonstrated by Chechilo and Enikolopyan (1972); reviewed by Pojman et al. (1996), Epstein & Pojman (1998)  Decomposition of the initiator (I) to form free radicals (R i * ): I  R 1 * + R 2 * - highest activation energy step e.g. (NH 4 ) 2 S 2 O 8  2NH 4 SO 4 *  Followed by addition of a radical to a monomer (M): M + R i *  R i M * - initiates polymer chain, grows by addition: R i M n * + M  R i M n+1 *  Most of heat release occurs through addition step  Note not chain-branching like flames  Chain growth eventually terminated by radical-radical reactions: R i M n * + R j M m *  R i M n+m R j  Chain length can be controlled by chain transfer agents - affects properties of final product

13. Polymerization front

14. Polymerization fronts  Potential applications  Rapid curing of polymers without external heating  Uniform curing of thick samples  Solventless preparation of some polymers  Filling/sealing of structures having cavities of arbitrary shape without having to heat the structure externally  Limitations / unknowns  Thermally driven system - need significant  T between reactants and products to have  products >>  reactants  Previous studies: use very high pressures or high boiling point solvent (e.g. DMSO) to avoid boiling since mixtures with T ad < 100˚C won’t propagate  …but water at ambient pressure is the solvent required for many practical applications  Idea: use a very reactive monomer (acrylic acid) highly diluted with water to minimize peak temperature, and control heat losses to avoid extinction  …but nothing is known about the extinction mechanisms!

15. Polymerization fronts - approach  Simple apparatus – round tubes  Need bubble-free model polymerization systems  2-hydroxyethyl methacrylate (HEMA) monomer in DMSO solvent  Acrylic acid (AA) monomer in water solvent  Both systems: ammonium persulfate (AP) initiator, Cab-o-sil (fumed silica powder) viscosity enhancer  Control thermal boundary conditions & assess heat loss  Varying tube diameter  Water bath, ambient air or insulated tube to control external temperature

16. Polymerization front  Typical speeds 0.01 cm/s, S L ≈ (  ) 1/2   -1 ≈ 14 s  From plot of ln(S L ) vs. 1/T ad can infer E ≈ 13.5 kcal/mole, Ze ≈ 20  Extinction at Pe ≈ (0.004 cm/s)(1.6 cm)/(0.0014 cm 2 /s) ≈ 4.6 - close to classical flame theory predictions  Plot of S L vs. “fuel” concentration approaches vertical at extinction limit as theory predicts  With insulation, limiting S L and %AA much lower

17. Polymerization fronts - thermal properties  Far from limit  Peak T same with or without insulation, speed and slope of T profile same, uninsulated case shows thermal decay in products  Close to limit  Uninsulated case shows substantial thermal decay in products; ratio (peak + slope)/(peak - slope) ≈ 12  Insulated case much slower, thicker flame, little or no thermal decay, limit not well defined

18. Movies courtesy Prof. J. Pojman, University of Southern Mississippi Polymerization front  High Lewis number - spiral & travelling-wave instabilities like flames (middle and right videos, viscosity-enhancing agent added to suppress buoyant instabilities) Lean C 4 H 10 -O 2 -He mixtures; Pearlman and Ronney, 1994

19. Autocatalytic aqueous reactions - motivation  Models of premixed turbulent combustion don’t agree with experiments nor each other!

20. Modeling of premixed turbulent flames  Most model employ assumptions not satisfied by real flames, e.g.  Adiabatic (sometimes ok)  Homogeneous, isotropic turbulence over many L I (never ok)  Low Ka or high Da (thin fronts) (sometimes ok)  Lewis number = 1 (sometimes ok, e.g. CH 4 -air)  Constant transport properties (never ok, ≈ 25x increase in and  across front!)  u’ doesn’t change across front (never ok, thermal expansion across flame generates turbulence) (but viscosity increases across front, decreases turbulence, sometimes almost cancels out)  Constant density (never ok!)

21. Autocatalytic front (bacterial fronts similar)

22. “Liquid flame” idea  Use propagating acidity fronts in aqueous solution  Studied by chemists for 100 years  Recent book: Epstein and Pojman, 1998  Generic form A + nB  (n+1)B - autocatalytic   /  << 1 - no self-generated turbulence   T ≈ 3 K - no change in transport properties  Zeldovich number  ≈ 0.05 vs. 10 in gas flames Aqueous fronts not affected by heat loss!!!  Large Schmidt number [= /D ≈ 500 (liquid flames) vs. ≈ 1 (gases)] - front stays "thin” even at high Re

23. Approach - chemistry  Iodate-hydrosulfite system IO 3 - + 6 H + + 6e -  I - + 3 H 2 O S 2 O 4 -2 + 4 H 2 O  6 e - + 8 H + + 2 SO 4 -2 _________________________________________________ IO 3 - + S 2 O 4 -2 + H 2 O  I - + 2 SO 4 -2 + 2 H +  Comparison with turbulent combustion model assumptions  Adiabatic  Homogeneous, isotropic turbulence over many L I  Low Ka or high Da (thin fronts) due to high Schmidt #  Constant transport properties  u’ doesn’t change across front  Constant density  Conclusion: liquid flames better for testing models!

24. Gaseous vs. liquid flames  Most model employ assumptions not satisfied by real flames  Adiabatic (sometimes ok) (Liquid flames TRUE!)  Homogeneous, isotropic turbulence over many L I (never ok) (Liquid flames: can use different apparatuses where this is more nearly true)  Low Ka or high Da (thin fronts) (sometimes ok) (Liquid flames: more often true due to higher Sc)  Lewis number = 1 (sometimes ok, e.g. CH 4 -air) (Liquid flames: irrelevant since heat transport not a factor in propagation)  Constant transport properties (never ok, ≈ 25x increase in and  across front!) (Liquid flames: TRUE)  u’ doesn’t change across front (never ok, thermal expansion across flame generates turbulence) (but viscosity increases across front, decreases turbulence, sometimes almost cancels out) (Liquid flames: TRUE)  Constant density (never ok!) (Liquid flames: true, although buoyancy effects still exist due to small density change)  Conclusion: liquid flames better for testing models!

25. Taylor-Couette apparatus

26. Capillary-wave apparatus

27. Results - liquid flames

28. Results  Thin "sharp" fronts at low Ka (< 5)  Thick "fuzzy" fronts at high Ka (> 10)  No global quenching observed, even at Ka > 2500 !!!  High Da - S T /S L in 4 different flows consistent with Yakhot model  Low Da - S T /S L lower than at high Da - consistent with Damköhler model over 1000x range of Ka!  Rising, buoyantly-unstable fronts in Hele-Shaw flow show unexpected wrinkling - subject of separate investigation

29. Liquid flames - comparison to Yahkot (1988)

30.  Data on S T /S L in flamelet regime (low Ka) consistent with Yakhot model - no adjustable parameters  Transition flamelet to distributed at Ka ≈ 5 Results - liquid flames - propagation rates

31.  Data on S T /S L in distributed combustion regime (high Ka) consistent with Damköhler’s model - no adjustable parameters

32. Front propagation in one-scale flow  Turbulent combustion models not valid when energy concentrated at one spatial/temporal scale  Experiment - Taylor-Couette flow in “Taylor vortex” regime (one-scale)  Result - S T /S L lower in TV flow than in turbulent flow but consistent with model for one-scale flow probably due to "island" formation & reduction in flame surface (Joulin & Sivashinsky, 1991)

33. Fractal analysis in CW flow  Fractal-like behavior exhibited  D ≈ 1.35 (  2.35 in 3-d) independent of u'/SL  Same as gaseous flame front, passive scalar in CW flow  Theory (Kerstein & others):  D = 7/3 for 3-d Kolmogorov spectrum (not CW flow)  Same as passive scalar (Sreenivasan et al, 1986)  Problem - why is d seemingly independent of  Propagating front vs. passively diffusing scalar  Velocity spectrum  Constant or varying density  Constant or varying transport properties  2-d object or planar slice of 3-d object

34. Fractal analysis in CW flow

35.  Many bacteria (e.g. E. coli) are motile - swim to find favorable environments - diffusion-like process - and multiply (react with nutrients)  Two modes: run (swim in straight line) & tumble (change direction) - like random walk  Longer run times if favorable nutrient gradient  Suggests possiblity of “flames” Bacterial fronts

36. http://www.rowland.org/bacteria/movies.html Motile bacteria  Bacteria swim by spinning flagella - drag on rod is about twice as large in crossflow compared to axial flow (G. I. Taylor showed this enables propulsion even though Re ≈ 10 -4 ) (If you had flagella, you could swim in quicksand or molasses)  Flagella rotate as a group to propel, spread out and rotate individually to tumble

37. Analogy with flames

38. Fronts show a steady propagation rate after an initial transient Reaction-diffusion behavior of bacteria  Bacterial strains: E.coli K-12 strain W3110 derivatives, either motile or non-motile  Standard condition: LB agar plates (agar concentration of 0.1 - 0.4%)  Variable nutrient condition: Tryptone/NaCl plates (agar concentration of 0.1, 0.3%)  All experiments incubated at 37˚C

39. Propagation rates of motile bacteria fronts  As agar concentration increases, motility of bacteria (in particular “sound speed” (c)) decreases, decreases effective diffusivity (D) and thus propagation speed (s) decreases substantially  No effect of depth of medium  Above 0.4% agar, bacteria grow along the surface only  Recently: very similar results for Bacillius subtilis - very different organism - E. coli & B. subtilis evolutionary paths separated 2 billion years ago

40. Effect of nutrient concentration  Increasing tryptone nutrient concentration increases propagation speed (either due to increased swimming speed or increased division rate) but slightly decreases propagation rate beyond a certain concentration - typically motility decreases for high nutrient concentrations (detectors saturated?)

41. 6 mm wide channel 35 mm wide channel E. coli, 0.1% agar, 100 µl of kanamycin per side, 6.5 hours after inoculation Quenching limit of bacteria fronts  Quenching limit: min. or max. value of some parameter (e.g. reactant concentration or channel width) for which steady front can exist  Quenching “channels” made using filter paper infused with antibiotic - bacteria killed near the wall, mimics heat loss to a cold wall in flames  Bacteria can propagate through a wide channel but not the narrow channel, indicating a quenching limit  Quenching described in terms of a minimum Peclet Number:  Pe = sw/D (w = channel width)  For the test case shown s ≈ 1.75 x 10 -4 cm/s, D = 3.7 x 10 -5 cm 2 /s, w at quenching limit ≈ 2.1 cm  Pe ≈ 9.8 - similar to flames and polymer fronts

42. Comparison of fronts in Mot+ and Mot- bacteria  Some mutated strains are non-motile but D due to Brownian motion ≈ 10 4 smaller  Fronts of Mot- bacteria also propagate, but more slowly than Mot+ bacteria

43. Quantitative analysis  Bacteria D as estimated from measured front speeds  S L for Mot+ ≈ 5.3 x 10 -5 cm/s for 0.3% agar  Reproduction time scale (  ) of E.coli ≈ 20 min  D ≈ s 2  ≈ (5.3 x 10 -5 cm/s) 2 (1200s) ≈ 3.3 x 10 -6 cm 2 /s  Similarly, D ≈ 3.7 x 10 -5 cm 2 /s in 0.1% agar  Bacteria diffusivity estimated from molecular theory  “Mean free path” ( ) estimated as the “sound speed” (c) multiplied by the time (t) bacteria swim without changing direction  c ≈ 21 µm/s, t ≈ 1.4 s  ≈ 3.0 x 10 -3 cm, D ≈ 6.3 x 10 -6 cm 2 /s, similar to value inferred from propagation speed  Diffusivity of Mot- E. coli due to Brownian motion (0.75 µm radius particles in water at 37˚C) ≈ 2.9 x 10 -9 cm 2 /s, ≈ 1700x smaller than Mot+ bacteria  Fronts should be (1700) 1/2 ≈ 40x slower in Mot- bacteria  Consistent with experiments (e.g. 8 mm/hr vs. 0.2 mm/hr at 0.1% agar)

44. Mot+ 5 hr 30 min after inoculation Mot- 50 hr after inoculation Mot+ 5 hr 30 min after inoculation Mot- 50 hr after inoculation 0.1% Agar dyed with a 5% Xylene Cyanol solution (Petri dish 9 cm diameter) Comparison of fronts in Mot+ and Mot- bacteria  D nutrient (≈ 10 -5 cm 2 /s) close to D bacteria, so “Lewis number” ≈ 1  Do bacteria choose their run-tumble cycle time to produce D required for Le ≈ 1 and avoid instabilies???  Switching from Mot+ to Mot- bacteria decreases the bacteria diffusivity (D autocatalyst ) by ≈ 1700x but nutrient diffusivity (D reactant ) is unchanged - decreases the effective “Lewis number”  Mot- fronts “cellular” but Mot+ fronts smooth - consistent with “Lewis number” analogy

45. Biofilms  Until recently, most studies of bacteria conducted in planktonic (free swimming) state, but most bacteria in nature occur in biofilms attached to surfaces  Recently many studies of biofilms have been conducted, but the effects of flow of the nutrient media have not been systematically assessed  No flow: no replenishment of consumed nutrients - little or no growth  Very fast flow: attachment and upstream spread difficult  Most flow studies have reported only volumetric flow rate or flow velocity - not a useful parameter - why should it matter what the flow is far from the surface when the biofilm is attached to the surface?  Biofilms can spread upstream - is spread rate ~ shear as with upstream flame spread on a solid fuel bed?  Fluid mechanics tells us the shear rate at the surface is the key  Our approach: use flow in tubes (shear not separated from mean flow rate) and Taylor-Couette cells (shear and mean flow independently controlled)

46. Biofilm experiments - laminar flow in tubes

47. Experiments show an effect of flow velocity or shear rate on growth rate and upstream spread Biofilms - images

48. Biofilms Fixed flow / varying elapsed time: more time, more growth, but maybe some sloughing at long times

49. Biofilms Fixed elapsed time / varying flow: optimal flow/shear rate that maximizes growth

50. Biofilms - Taylor Couette cell concept

51. Summary Property Gaseous flame (e.g. CH 4 -air) SHS Aqueous autocatalytic front Polymer front Bacterial front Reactant(s) Fuel, oxidant Reductant, oxidant Reactants (e.g. IO 3 - - S 2 O 4 2- ) Monomer & initiator (e.g. IO 3 - - S 2 O 4 2- ) nutrient Product(s) CO 2, H 2 O, thermal energy Metal, metal oxide or nitride productpolymerbacteria Autocatalyst Thermal energy, free radicals Thermal energy H+H+H+H+ bacteria Flame speed (S) 400 mm/s 10 mm/s 0.2 mm/s 0.1 mm/s 0.001 mm/s Zeldovich # (Ze) 10 - 20 0.05200 Heat loss ImportantImportant Unimportant (Ze<<1) ImportantNone Prandtl # (Pr) 1∞710001000 Lewis # (Le) 1∞ 70 (but irrelevant) nearly infinite 1 (Mot+); 10 -4 (Mot-) Density ratio    a  /   6 (monotonic) 0.1 0.0006 (monotonic) -0.2 (non- monotonic) ? Viscosity ratio  a  ∞  /  25∞/∞0.1 1 - ∞ 1

52. Conclusions  Broad analogies can be drawn between different types of reaction-diffusion fronts in disparate types of physical / chemical / biological systems  Steady propagation rates  Effects of reactant and product diffusivities  Instabilities (i.e. pattern formation)  Quenching behavior  Applications to  Combustion engines  Solid propellant rockets  Synthesis of ceramics  Polymer synthesis  Assessment of turbulent combustion models  Colonization of new environments by swarms of bacteria  Biofilms - bacteria growing on surfaces - far more resistant to antibiotics & other stresses than “planktonic” (free-swimming) bacteria

53. Thanks to…  National Cheng-Kung University  Prof. Y. C. Chao, Prof. Shenqyang Shy  Combustion Institute (Bernard Lewis Lectureship)