Paul Ronney

Dynamics of fronts in chemical Dynamics of fronts in chemical and bacterial media:and bacterial media:

If you’ve seen one front, you’ve seen them allIf you’ve seen one front, you’ve seen them all Paul RonneyPaul Ronney

Department of Aerospace & Mechanical EngineeringDepartment of Aerospace & Mechanical Engineering Univ. of Southern California, Los Angeles, CA, 90089 Univ. of Southern California, Los Angeles, CA, 90089

University of Southern CaliforniaUniversity of Southern California

Established 125 years ago Established 125 years ago this week!this week! ……jointly by a Catholic, a Protestant and a Jew - USC has jointly by a Catholic, a Protestant and a Jew - USC has

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Today: 32,000 students, 3000 facultyToday: 32,000 students, 3000 faculty 2 main campuses: University Park and Health Sciences2 main campuses: University Park and Health Sciences USC Trojans football team ranked #1 in USA last 2 yearsUSC Trojans football team ranked #1 in USA last 2 years

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degree optionsdegree options $135 million external research funding$135 million external research funding Distance Education Network (DEN): 900 students in 28 M.S. Distance Education Network (DEN): 900 students in 28 M.S.

degree programs; degree programs; 1171 MS degrees awarded in 200571 MS degrees awarded in 2005 More info: More info: http://viterbi.usc.eduhttp://viterbi.usc.edu

http://viterbi.usc.edu/

Paul RonneyPaul Ronney B.S. Mechanical Engineering, UC BerkeleyB.S. Mechanical Engineering, UC Berkeley M.S. Aeronautics, CaltechM.S. Aeronautics, Caltech Ph.D. in Aeronautics & Astronautics, MITPh.D. in Aeronautics & Astronautics, MIT Postdocs: NASA Glenn, Cleveland; US Naval Research Lab, Postdocs: NASA Glenn, Cleveland; US Naval Research Lab,

Washington DCWashington DC Assistant Professor, Princeton UniversityAssistant Professor, Princeton University Associate/Full Professor, USCAssociate/Full Professor, USC Research interestsResearch interests

Microscale combustion and power generation Microscale combustion and power generation (10/4, INER; 10/5 NCKU)(10/4, INER; 10/5 NCKU)

Microgravity combustion and fluid mechanics Microgravity combustion and fluid mechanics (10/4, NCU)(10/4, NCU) Turbulent combustion Turbulent combustion (10/7, NTHU)(10/7, NTHU) Internal combustion enginesInternal combustion engines Ignition, flammability, extinction limits of flames Ignition, flammability, extinction limits of flames (10/3, NCU)(10/3, NCU) Flame spread over solid fuel bedsFlame spread over solid fuel beds Biophysics and biofilms Biophysics and biofilms (10/6, NCKU)(10/6, NCKU)

Paul RonneyPaul Ronney

MotivationMotivation Propagating fronts are ubiquitous in naturePropagating fronts are ubiquitous in nature

FlamesFlames»(Fuel & Oxidant) + Heat (Fuel & Oxidant) + Heat More More heatheat

Solid rocket propellant fuelsSolid rocket propellant fuels»(Fuel & Oxidant) + Heat (Fuel & Oxidant) + Heat More More heatheat

Self-propagating high-temperature synthesis (SHS) - reaction Self-propagating high-temperature synthesis (SHS) - reaction of metal with metal oxide or nitride, e.g. Feof metal with metal oxide or nitride, e.g. Fe22OO33(s) + 2Al(s) (s) + 2Al(s) AlAl22OO33(s) + 2Fe(l) (s) + 2Fe(l)

»(Fuel & Oxidant) + Heat (Fuel & Oxidant) + Heat More More heatheat Frontal polymerizationFrontal polymerization

»Monomer + initiator + heat Monomer + initiator + heat polymer + more polymer + more heatheat Autocatalytic chemical reactions Autocatalytic chemical reactions (non-thermal front)(non-thermal front)

»Reactants + HReactants + H++ Products + more H Products + more H++ Bacterial front Bacterial front (non-thermal front)(non-thermal front)

»Nutrient + bugs Nutrient + bugs more bugs more bugs All of these might be construed as “reaction-diffusion All of these might be construed as “reaction-diffusion

systems”systems” Today’s topic: what is similar and what is different about Today’s topic: what is similar and what is different about

these different types of fronts?these different types of fronts?

Reaction-diffusion systemsReaction-diffusion systems

Two essential ingredientsTwo essential ingredients Reactive mediumReactive medium (e.g. fuel-air mixture) (e.g. fuel-air mixture) AutocatalystAutocatalyst - product of reaction that also accelerates the - product of reaction that also accelerates the

reaction (e.g. thermal energy)reaction (e.g. thermal energy) Self-propagation occurs when the autocatalyst diffuses into Self-propagation occurs when the autocatalyst diffuses into

the reactive medium, initiating reaction and creating more the reactive medium, initiating reaction and creating more autocatalyst, e.g. A + nB autocatalyst, e.g. A + nB (n+1)B (n+1)B

Enables reaction-diffusion fronts to propagate at steady Enables reaction-diffusion fronts to propagate at steady rates far from any initiation siterates far from any initiation site

Premixed flame (SHS, solid propellant similar)Premixed flame (SHS, solid propellant similar)

Reaction zone

Temperature

Reactantconcentration

Productconcentration

2000K

300K

δ ≈ α/SL = 0.3 - 6 mm

Distance from reaction zone

- Convection diffusion zone

Direction of propagation Speed relative to unburned gas = SL

Reaction-diffusion systems - characteristicsReaction-diffusion systems - characteristics After initial transient, fronts typically propagate at a steady After initial transient, fronts typically propagate at a steady

raterate Propagation speed (SPropagation speed (SLL) ~ (D) ~ (D))1/21/2

»D = diffusivity of autocatalyst or reactantD = diffusivity of autocatalyst or reactant = characteristic reaction rate = (reaction time)= characteristic reaction rate = (reaction time)-1-1

D depends on “sound speed” (c) & “mean free path” (D depends on “sound speed” (c) & “mean free path” () ) »D ~ cD ~ c

Propagation rate generally faster in turbulent media due to Propagation rate generally faster in turbulent media due to wrinkling (increased surface area) of frontwrinkling (increased surface area) of front

Thermal fronts require high Zeldovich number (Ze) so that Thermal fronts require high Zeldovich number (Ze) so that productsproducts >> >> reactantsreactants, otherwise reaction starts spontaneously!, otherwise reaction starts spontaneously!

Flammability or extinction limits when loss rate of Flammability or extinction limits when loss rate of autocatalyst ≈ production rate of autocatalystautocatalyst ≈ production rate of autocatalyst

€

Ze ≡Tad

Ω(Tad )

∂Ω

∂T T=Tad

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ΔT

Tad=E

RTad

Tad −T∞

Tad

Instability mechanismsInstability mechanisms Instability mechanisms may preclude steady flat frontInstability mechanisms may preclude steady flat front Turing instability - when ratio of reactant to autocatalyst Turing instability - when ratio of reactant to autocatalyst

diffusivity differs significantly from 1 diffusivity differs significantly from 1 Thermal fronts: DThermal fronts: Dautocatalystautocatalyst/D/Dreactantreactant = Lewis number = Lewis number Low Le: additional thermal enthalpy loss in curved region is less Low Le: additional thermal enthalpy loss in curved region is less

than additional chemical enthalpy gain, thus local flame temperature than additional chemical enthalpy gain, thus local flame temperature in curved region is higher, thus reaction rate increases drastically, in curved region is higher, thus reaction rate increases drastically, thus “blip” growsthus “blip” grows

High Le: pulsating or travelling wave instabilitiesHigh Le: pulsating or travelling wave instabilities Hydrodynamics - thermal expansion, buoyancy, Saffman-TaylorHydrodynamics - thermal expansion, buoyancy, Saffman-Taylor

Flamefront

Burned gas

Unburned gasDirection of propagation

Heatdiffusion

Heatdiffusion

Fueldiffusion

Fueldiffusion

Polymerization frontsPolymerization fronts First demonstrated by Chechilo and Enikolopyan (1972); First demonstrated by Chechilo and Enikolopyan (1972);

reviewed by Pojman reviewed by Pojman et al.et al. (1996), Epstein & Pojman (1998) (1996), Epstein & Pojman (1998) Decomposition of the initiator (I) to form free radicals (RDecomposition of the initiator (I) to form free radicals (R ii

**):):

I I R R11** + R + R22

** - highest activation energy step - highest activation energy step

e.g. (NHe.g. (NH44))22SS22OO88 2NH 2NH44SOSO44**

Followed by addition of a radical to a monomer (M):Followed by addition of a radical to a monomer (M):M + RM + Rii

** R RiiMM** - initiates polymer chain, grows by - initiates polymer chain, grows by

addition:addition:RRiiMMnn

** + M + M R RiiMMn+1n+1**

Most of heat release occurs through addition stepMost of heat release occurs through addition step Note not chain-branching like flamesNote not chain-branching like flames Chain growth eventually terminated by radical-radical Chain growth eventually terminated by radical-radical

reactions:reactions:RRiiMMnn

** + R + RjjMMmm** R RiiMMn+mn+mRRjj

Chain length can be controlled by chain transfer agents - Chain length can be controlled by chain transfer agents - affects properties of final productaffects properties of final product

Polymerization frontPolymerization front

Reaction zone

Distance from reaction zone

Temperature

Monomer concentration

Density relative to reactants

Polymerconcentration

Viscosity (log scale)

0.96

1.2

500K

300K

0.01 cm2/s

0.001 cm2/s

10 cm2/s

5 mm

Polymerization front

Polymerization frontsPolymerization fronts Potential applicationsPotential applications

Rapid curing of polymers without external heatingRapid curing of polymers without external heating Uniform curing of thick samplesUniform curing of thick samples Solventless preparation of some polymersSolventless preparation of some polymers Filling/sealing of structures having cavities of arbitrary shape Filling/sealing of structures having cavities of arbitrary shape

without having to heat the structure externallywithout having to heat the structure externally Limitations / unknownsLimitations / unknowns

Thermally driven system - need significant Thermally driven system - need significant T between T between reactants and products to havereactants and products to have productsproducts >> >> reactantsreactants

Previous studies: use very high pressures or high boiling Previous studies: use very high pressures or high boiling point solvent (e.g. DMSO) to avoid boiling since mixtures with point solvent (e.g. DMSO) to avoid boiling since mixtures with TTadad < 100˚C won’t propagate < 100˚C won’t propagate

……but water at ambient pressure is the solvent required for but water at ambient pressure is the solvent required for many practical applicationsmany practical applications

Idea: use a very reactive monomer (acrylic acid) highly diluted Idea: use a very reactive monomer (acrylic acid) highly diluted with water to minimize peak temperature, and control heat with water to minimize peak temperature, and control heat losses to avoid extinctionlosses to avoid extinction

……but nothing is known about the extinction mechanisms!but nothing is known about the extinction mechanisms!

Polymerization fronts - approachPolymerization fronts - approach

Simple apparatus – round tubesSimple apparatus – round tubes Need bubble-free model polymerization systemsNeed bubble-free model polymerization systems

2-hydroxyethyl methacrylate (HEMA) monomer in DMSO 2-hydroxyethyl methacrylate (HEMA) monomer in DMSO solventsolvent

Acrylic acid (AA) monomer in water solventAcrylic acid (AA) monomer in water solvent Both systems: ammonium persulfate (AP) initiator, Cab-o-sil Both systems: ammonium persulfate (AP) initiator, Cab-o-sil

(fumed silica powder) viscosity enhancer(fumed silica powder) viscosity enhancer Control thermal boundary conditions & assess heat lossControl thermal boundary conditions & assess heat loss

Varying tube diameter Varying tube diameter Water bath, ambient air or insulated tube to control external Water bath, ambient air or insulated tube to control external

temperaturetemperature


Typical speeds 0.01 cm/s, STypical speeds 0.01 cm/s, SLL ≈ ( ≈ (αα))1/21/2 -1-1 ≈ 14 s ≈ 14 s From plot of ln(SFrom plot of ln(SLL) vs. 1/T) vs. 1/Tadad can infer E ≈ 13.5 kcal/mole, Ze ≈ 20 can infer E ≈ 13.5 kcal/mole, Ze ≈ 20 Extinction at Pe ≈ (0.004 cm/s)(1.6 cm)/(0.0014 cmExtinction at Pe ≈ (0.004 cm/s)(1.6 cm)/(0.0014 cm22/s) ≈ 4.6 - close /s) ≈ 4.6 - close

to classical flame theory predictionsto classical flame theory predictions Plot of SPlot of SLL vs. “fuel” concentration approaches vertical at vs. “fuel” concentration approaches vertical at

extinction limit as theory predictsextinction limit as theory predicts With insulation, limiting SWith insulation, limiting SLL and %AA much lower and %AA much lower

0.002

0.004

0.006

0.0080.01

0.03

15 20 25 30 35 40 45

5%8%10%12%15%

Mass percent AA

Mass % AP

16 mm tubeUninsulated

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

10 15 20 25 30 35

InsulatedUninsulated

Mass percent AA

16 mm tube10% AP

Polymerization fronts - thermal propertiesPolymerization fronts - thermal properties

Far from limitFar from limit Peak T same with or without insulation, speed and slope of T profile Peak T same with or without insulation, speed and slope of T profile

same, uninsulated case shows thermal decay in productssame, uninsulated case shows thermal decay in products Close to limitClose to limit

Uninsulated case shows substantial thermal decay in products; ratio Uninsulated case shows substantial thermal decay in products; ratio (peak + slope)/(peak - slope) ≈ 12 (peak + slope)/(peak - slope) ≈ 12

Insulated case much slower, thicker flame, little or no thermal decay, Insulated case much slower, thicker flame, little or no thermal decay, limit not well definedlimit not well defined

20

40

60

80

100

0 100 200 300 400 500 600 700

InsulatedUninsulatedAdiabatic

Time (seconds)

Slope = 0.056˚C/s

27.5% AA / 10% AP16 mm tube

20

30

40

50

60

70

80

0 500 1000 1500 2000 2500 3000

14.7% AA, insulated22.2% AA, uninsulated

Time (seconds)

10% AP16 mm tube

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.QuickTime™ and aYUV420 codec decompressorare needed to see this picture.QuickTime™ and aYUV420 codec decompressorare needed to see this picture.

Movies courtesy Prof. J. Pojman, University of Southern MississippiMovies courtesy Prof. J. Pojman, University of Southern Mississippi


High Lewis number - spiral & travelling-wave instabilities High Lewis number - spiral & travelling-wave instabilities like flames (middle and right videos, viscosity-enhancing like flames (middle and right videos, viscosity-enhancing agent added to suppress buoyant instabilities)agent added to suppress buoyant instabilities)

Lean CLean C44HH1010-O-O22-He mixtures; Pearlman and Ronney, 1994-He mixtures; Pearlman and Ronney, 1994

Autocatalytic aqueous reactions - motivationAutocatalytic aqueous reactions - motivation Models of premixed turbulent combustion don’t agree with Models of premixed turbulent combustion don’t agree with

experiments nor each other! experiments nor each other!

0

5

10

15

20

25

30

0 10 20 30 40 50

x

Turbulence Intensity (u'/SL)

Yakhot 1988

Gouldin 1987 (ReL=1,000)

Experiment(Bradley, 1992)

(ReL=1,000)

Bray 1990 (zero heat release)

(large heat release, θ = 7) & 1987 ( )Pope Anand zero heat release ( )large heat release

1990Sivashinsky

2000Bychovθ = 7

(Where ReL is not reported, predictions are independent of Re

L)

Modeling of premixed turbulent flamesModeling of premixed turbulent flames

Most model employ assumptions not satisfied by Most model employ assumptions not satisfied by real flames, e.g.real flames, e.g.Adiabatic Adiabatic (sometimes ok)(sometimes ok)Homogeneous, isotropic turbulence over many LHomogeneous, isotropic turbulence over many LII

(never ok)(never ok)Low Ka or high Da (thin fronts) Low Ka or high Da (thin fronts) (sometimes ok)(sometimes ok)Lewis number = 1 Lewis number = 1 (sometimes ok, e.g. CH(sometimes ok, e.g. CH44-air)-air)Constant transport properties Constant transport properties (never ok, ≈ 25x (never ok, ≈ 25x

increase in increase in and and αα across front!) across front!)u’ doesn’t change across front u’ doesn’t change across front (never ok, thermal (never ok, thermal

expansion across flame generates turbulence) (but expansion across flame generates turbulence) (but viscosity increases across front, decreases viscosity increases across front, decreases turbulence, sometimes almost cancels out)turbulence, sometimes almost cancels out)

Constant density Constant density (never ok!)(never ok!)

Autocatalytic front (bacterial fronts similar)Autocatalytic front (bacterial fronts similar)

Reaction zone

Temperature

Reactant concentration

Density relativeto reactants

Productconcentration

Viscosity (log scale)

0.9994

300K

0.01 cm2/s

0.01 mm Distance from reaction zone

Aqueous chemical front

0.01 cm2/s

303K

““Liquid flame” ideaLiquid flame” idea

Use propagating acidity fronts in aqueous solutionUse propagating acidity fronts in aqueous solution Studied by chemists for 100 yearsStudied by chemists for 100 years Recent book: Epstein and Pojman, 1998Recent book: Epstein and Pojman, 1998 Generic form Generic form

A + nB A + nB (n+1)B - (n+1)B - autocatalyticautocatalytic // << 1 - no self-generated turbulence << 1 - no self-generated turbulence T ≈ 3 K - no change in transport propertiesT ≈ 3 K - no change in transport properties Zeldovich number Zeldovich number ≈ 0.05 vs. 10 in gas flames ≈ 0.05 vs. 10 in gas flames

Aqueous fronts not affected by heat loss!!!Aqueous fronts not affected by heat loss!!! Large Schmidt number [= Large Schmidt number [= /D ≈ 500 (liquid flames) vs. ≈ 1 /D ≈ 500 (liquid flames) vs. ≈ 1

(gases)] - front stays "thin” even at high Re(gases)] - front stays "thin” even at high Re

€

Ka ≈u' /LTSL

2 /D~ν

u'LI

LILT

u'2

SL2

D

ν~ ReL

−1/ 2 u'

SL

⎛

⎝ ⎜

⎞

⎠ ⎟

2

Sc−1

Approach - chemistryApproach - chemistry

Iodate-hydrosulfite systemIodate-hydrosulfite system

IOIO33-- + 6 H + 6 H++ + 6e + 6e- - I I-- + 3 H + 3 H22OO

SS22OO44-2 -2 + 4 H+ 4 H22O O 6 e 6 e-- + 8 H + 8 H++ + 2 SO + 2 SO44

-2-2

__________________________________________________________________________________________________

IOIO33-- + S + S22OO44

-2 -2 + H+ H22O O I I-- + 2 SO + 2 SO44-2-2+ 2 H+ 2 H++

Comparison with turbulent combustion model Comparison with turbulent combustion model assumptionsassumptions Adiabatic Adiabatic Homogeneous, isotropic turbulence over many LHomogeneous, isotropic turbulence over many L II Low Ka or high Da (thin fronts) due to high Schmidt #Low Ka or high Da (thin fronts) due to high Schmidt # Constant transport properties Constant transport properties u’ doesn’t change across front u’ doesn’t change across front Constant densityConstant density Conclusion: liquid flames better for testing models!Conclusion: liquid flames better for testing models!

Taylor-Couette apparatusTaylor-Couette apparatus

Capillary-wave apparatusCapillary-wave apparatus

Results - liquid flamesResults - liquid flames

QuickTime™ and aMPEG-4 Video decompressorare needed to see this picture.

ResultsResults

Thin "sharp" fronts at low Ka (< 5)Thin "sharp" fronts at low Ka (< 5) Thick "fuzzy" fronts at high Ka (> 10)Thick "fuzzy" fronts at high Ka (> 10) No global quenching observed, No global quenching observed, even at Ka > 2500 !!!even at Ka > 2500 !!! High Da - SHigh Da - STT/S/SLL in in 4 different flows4 different flows consistent with Yakhot consistent with Yakhot

modelmodel

Low Da - SLow Da - STT/S/SLL lower than at high Da - consistent with lower than at high Da - consistent with

Damköhler model over 1000x range of Ka!Damköhler model over 1000x range of Ka! Rising, buoyantly-unstable fronts in Hele-Shaw flow show Rising, buoyantly-unstable fronts in Hele-Shaw flow show

unexpected wrinkling - subject of separate investigationunexpected wrinkling - subject of separate investigation€

STSL

= expu ' SL( )

2

ST SL( )2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Liquid flames - comparison to Yahkot (1988)Liquid flames - comparison to Yahkot (1988)

1

10

100

0.1 1 10 100 1000

Hele-ShawCapillary waveTaylor-CouetteVibrating grid (Shy et al. )Theory (Yakhot)Power law fit to expts.

"Turbulence" intensity (u'/SL)

Power law fit (u'/SL > 2):

ST/S

L = 1.61 (u'/S

L).742

Data on SData on STT/S/SL L in flamelet regime (low Ka) consistent with Yakhot in flamelet regime (low Ka) consistent with Yakhot

model - model - no adjustable parametersno adjustable parameters Transition flamelet to distributed at Ka ≈ 5Transition flamelet to distributed at Ka ≈ 5

0.01

0.1

1

0.1 1 10 100 1000 104

Capillary wave experimentsTaylor-Couette experiments

Karlovitz number (Ka)

Flamelet Distributed

Results - liquid flames - propagation ratesResults - liquid flames - propagation rates

0 .0 10 .110 .111 01 0 01 0 0 01 04C a p illa ry w a v e e x p e rim e n tsTa y lo r-C o u e tte e x p e rim e n tsK a rlo v itz n u m b e r (K a )F la m e le tD is trib u te d

Results - liquid flames - propagation ratesResults - liquid flames - propagation rates Data on SData on STT/S/SL L in distributed combustion regime (high Ka) in distributed combustion regime (high Ka)

consistent with Damköhler’s model - consistent with Damköhler’s model - no adjustable parametersno adjustable parameters

0.4

0.6

0.8

1

3

0.1 1 10 100 1000 104

Experiments (Taylor-Couette)Experiments (capillary wave)

Karlovitz number (Ka)

Flamelet Distributed

Front propagation in one-scale flowFront propagation in one-scale flow

Turbulent combustion models not valid when energy Turbulent combustion models not valid when energy concentrated at one spatial/temporal scaleconcentrated at one spatial/temporal scale

Experiment - Taylor-Couette flow in “Taylor vortex” regime Experiment - Taylor-Couette flow in “Taylor vortex” regime (one-scale)(one-scale)

Result - SResult - STT/S/SLL lower in TV flow than in turbulent flow but lower in TV flow than in turbulent flow but

consistent with model for one-scale flow probably due to consistent with model for one-scale flow probably due to "island" formation & reduction in flame surface (Joulin & "island" formation & reduction in flame surface (Joulin & Sivashinsky, 1991)Sivashinsky, 1991)

€

STSL

= expu ' SLST SL

1− exp −u ' SLST SL

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

0

50

100

150

200

250

0 100 200 300 400 500 600

Theory (Eq. 1)Theory (1-scale)CW experimentTC experiment1-scale experiment

Turbulence intensity (q/c)

Fractal analysis in CW flowFractal analysis in CW flow

Fractal-like behavior exhibitedFractal-like behavior exhibited D ≈ 1.35 (D ≈ 1.35 ( 2.35 in 3-d) independent of u'/SL 2.35 in 3-d) independent of u'/SL Same as gaseous flame front, passive scalar in CW flowSame as gaseous flame front, passive scalar in CW flow Theory (Kerstein & others):Theory (Kerstein & others):

D = 7/3 for 3-d Kolmogorov spectrum (not CW flow)D = 7/3 for 3-d Kolmogorov spectrum (not CW flow) Same as passive scalar (Sreenivasan et al, 1986)Same as passive scalar (Sreenivasan et al, 1986)

Problem - why is d seemingly independent ofProblem - why is d seemingly independent of Propagating front vs. passively diffusing scalarPropagating front vs. passively diffusing scalar Velocity spectrumVelocity spectrum Constant or varying densityConstant or varying density Constant or varying transport propertiesConstant or varying transport properties 2-d object or planar slice of 3-d object2-d object or planar slice of 3-d object

Fractal analysis in CW flowFractal analysis in CW flow

104

105

1 10

Slope = 0.732d = 1.268

u'/S L = 220

Measurement scale (number of pixels)

Slope = 0.776d = 1.224

u'/S L = 77

1

1.1

1.2

1.3

1.4

1.5

0 50 100 150 200 250Disturbance intensity (u'/S

L)

All data at u'/SL > 60:

Mean = 1.31, RMS deviation 0.06

Many bacteria (e.g. Many bacteria (e.g. E. coliE. coli) are ) are motilemotile - swim to find - swim to find favorable environments - favorable environments - diffusiondiffusion-like process - and -like process - and multiply (multiply (reactreact with nutrients) with nutrients)

Two modes: run (swim in straight line) & tumble Two modes: run (swim in straight line) & tumble (change direction) - like random walk(change direction) - like random walk

Longer run times if favorable nutrient gradient Longer run times if favorable nutrient gradient Suggests possiblity of “flames”Suggests possiblity of “flames”

Bacterial frontsBacterial fronts

http://www.rowland.org/bacteria/movies.html

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

Motile bacteriaMotile bacteria

Bacteria swim by spinning Bacteria swim by spinning flagella - flagella - drag on rod is about twice as drag on rod is about twice as large in crossflow compared to axial flow (G. I. Taylor showed this large in crossflow compared to axial flow (G. I. Taylor showed this enables propulsion even thoughenables propulsion even though Re ≈ 10Re ≈ 10-4-4) (If you had flagella, you ) (If you had flagella, you could swim in quicksand or molasses)could swim in quicksand or molasses)

Flagella rotate as a group to propel, spread out and rotate Flagella rotate as a group to propel, spread out and rotate individually to tumbleindividually to tumble




Flame or molecularproperty

Microbiological equivalent

Temperature Concentration of bacteriaFuel NutrientsHeat diffusivity ≈ c Diffusivit y of bacteriaFue l diffusivity Diffusivit y of nutrientSound s peed(c) Swimming s peedo f bacteri umin "run" modeMe an fre e pat h () c multipl ed b y averag e ti met o switc h fr omrun

mo de totumbl e mode and backReactio n timescale Reproductio n timeH eatloss Deat h ( of individua l bacterium)Extinguishment Deat h ( ofall bacteria)

Analogy with flamesAnalogy with flames

Fronts show a steady propagation rate after an initial transient

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8

0.2% agar0.3% agar

Time (hours)

Reaction-diffusion behavior of bacteriaReaction-diffusion behavior of bacteria Bacterial strains: E.coli K-12 strain W3110 derivatives, either motile or Bacterial strains: E.coli K-12 strain W3110 derivatives, either motile or

non-motilenon-motile Standard condition: LB agar plates (agar concentration of 0.1 - 0.4%)Standard condition: LB agar plates (agar concentration of 0.1 - 0.4%) Variable nutrient condition: Tryptone/NaCl plates (agar concentration of Variable nutrient condition: Tryptone/NaCl plates (agar concentration of

0.1, 0.3%)0.1, 0.3%) All experiments incubated at 37˚CAll experiments incubated at 37˚C

Propagation rates of motile bacteria frontsPropagation rates of motile bacteria fronts As agar concentration increases, motility of bacteria (in particular “sound As agar concentration increases, motility of bacteria (in particular “sound

speed” (c)) decreases, decreases effective diffusivity (D) and thus speed” (c)) decreases, decreases effective diffusivity (D) and thus propagation speed (s) decreases substantiallypropagation speed (s) decreases substantially

No effect of depth of mediumNo effect of depth of medium Above 0.4% agar, bacteria grow along the surface onlyAbove 0.4% agar, bacteria grow along the surface only Recently: Recently: veryvery similar results for similar results for Bacillius subtilis - Bacillius subtilis - very different very different

organism - E. coli & B. subtilis evolutionary paths separated 2 billion organism - E. coli & B. subtilis evolutionary paths separated 2 billion years agoyears ago

0

2

4

6

8

10

0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45Agar concentration, %

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1

Tryptone Concentration (%)

Effect of nutrient concentrationEffect of nutrient concentration

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

6 mm wide channel 35 mm wide channelE. coli, 0.1% agar, 100 µl of kanamycin per side, 6.5 hours after inoculation

Quenching limit of bacteria frontsQuenching limit of bacteria fronts Quenching limit: min. or max. value of some parameter (e.g. reactant Quenching limit: min. or max. value of some parameter (e.g. reactant

concentration or channel width) for which steady front can existconcentration or channel width) for which steady front can exist Quenching “channels” made using filter paper infused with antibiotic - Quenching “channels” made using filter paper infused with antibiotic -

bacteria killed near the wall, mimics heat loss to a cold wall in flamesbacteria killed near the wall, mimics heat loss to a cold wall in flames Bacteria can propagate through a wide channel but not the narrow Bacteria can propagate through a wide channel but not the narrow

channel, indicating a quenching limitchannel, indicating a quenching limit Quenching described in terms of a minimum Peclet Number: Quenching described in terms of a minimum Peclet Number:

Pe = sw/D (w = channel width)Pe = sw/D (w = channel width) For the test case shown s ≈ 1.75 x 10For the test case shown s ≈ 1.75 x 10-4-4 cm/s, D = 3.7 x 10 cm/s, D = 3.7 x 10-5-5 cm cm22/s, w at /s, w at

quenching limit ≈ 2.1 cm quenching limit ≈ 2.1 cm Pe ≈ 9.8 - similar to flames and polymer fronts Pe ≈ 9.8 - similar to flames and polymer fronts

Comparison of fronts in Mot+ and Mot- bacteriaComparison of fronts in Mot+ and Mot- bacteria

Some mutated strains are non-motile but D due to Brownian Some mutated strains are non-motile but D due to Brownian motion ≈ 10motion ≈ 1044 smaller smaller

Fronts of Mot- bacteria also propagate, but more slowly Fronts of Mot- bacteria also propagate, but more slowly than Mot+ bacteriathan Mot+ bacteria

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2 0.25

Agar %

Quantitative analysisQuantitative analysis

Bacteria D as estimated from measured front speedsBacteria D as estimated from measured front speeds SSLL for Mot+ ≈ 5.3 x 10 for Mot+ ≈ 5.3 x 10-5-5 cm/s for 0.3% agar cm/s for 0.3% agar Reproduction time scale (Reproduction time scale () of ) of E.coliE.coli ≈ 20 min ≈ 20 min D ≈ sD ≈ s22 ≈ (5.3 x 10 ≈ (5.3 x 10-5-5 cm/s) cm/s)22(1200s) (1200s) ≈ 3.3 x 10≈ 3.3 x 10-6-6 cm cm22/s/s Similarly, D ≈ 3.7 x 10Similarly, D ≈ 3.7 x 10-5-5 cm cm22/s in 0.1% agar/s in 0.1% agar

Bacteria diffusivity estimated from molecular theory Bacteria diffusivity estimated from molecular theory ““Mean free path” (Mean free path” () estimated as the “sound speed” (c) multiplied by ) estimated as the “sound speed” (c) multiplied by

the time (t) bacteria swim without changing directionthe time (t) bacteria swim without changing direction c ≈ 21 µm/s, t ≈ 1.4 sc ≈ 21 µm/s, t ≈ 1.4 s ≈ ≈ 3.0 x 103.0 x 10-3-3 cm, cm, D ≈ 6.3 x 10D ≈ 6.3 x 10-6-6 cm cm22/s/s, similar to value inferred from , similar to value inferred from

propagation speedpropagation speed Diffusivity of Mot- Diffusivity of Mot- E. coliE. coli due to Brownian motion (0.75 µm radius due to Brownian motion (0.75 µm radius

particles in water at 37˚C) ≈ 2.9 x 10particles in water at 37˚C) ≈ 2.9 x 10-9-9 cm cm22/s, ≈ 1700x smaller than /s, ≈ 1700x smaller than Mot+ bacteriaMot+ bacteria

Fronts should be (1700)Fronts should be (1700)1/21/2 ≈ 40x slower in Mot- bacteria ≈ 40x slower in Mot- bacteria Consistent with experiments (e.g. 8 mm/hr vs. 0.2 mm/hr at 0.1% Consistent with experiments (e.g. 8 mm/hr vs. 0.2 mm/hr at 0.1%

agar)agar)

Mot+ 5 hr 30 min after inoculation Mot+ 5 hr 30 min after inoculation Mot- 50 hr after inoculation Mot- 50 hr after inoculation 0.1% Agar dyed with a 5% Xylene Cyanol solution (Petri dish 9 cm diameter)0.1% Agar dyed with a 5% Xylene Cyanol solution (Petri dish 9 cm diameter)

Comparison of fronts in Mot+ and Mot- bacteriaComparison of fronts in Mot+ and Mot- bacteria DDnutrientnutrient (≈ 10 (≈ 10-5-5 cm cm22/s) close to D/s) close to Dbacteriabacteria, so “Lewis number” ≈ 1, so “Lewis number” ≈ 1 Do bacteria choose their run-tumble cycle time to produce D required for Do bacteria choose their run-tumble cycle time to produce D required for

Le ≈ 1 and avoid instabilies???Le ≈ 1 and avoid instabilies??? Switching from Mot+ to Mot- bacteria decreases the bacteria diffusivity Switching from Mot+ to Mot- bacteria decreases the bacteria diffusivity

(D(Dautocatalystautocatalyst) by ≈ 1700x but nutrient diffusivity (D) by ≈ 1700x but nutrient diffusivity (Dreactantreactant) is unchanged - ) is unchanged -

decreases the effective “Lewis number” decreases the effective “Lewis number” Mot- fronts “cellular” but Mot+ fronts smooth - consistent with “Lewis Mot- fronts “cellular” but Mot+ fronts smooth - consistent with “Lewis

number” analogynumber” analogy

BiofilmsBiofilms Until recently, most studies of bacteria conducted in Until recently, most studies of bacteria conducted in planktonicplanktonic

(free swimming) state, but most bacteria in nature occur in (free swimming) state, but most bacteria in nature occur in biofilmsbiofilms attached to surfaces attached to surfaces

Recently many studies of biofilms have been conducted, but the Recently many studies of biofilms have been conducted, but the effects of flow of the nutrient media have not been systematically effects of flow of the nutrient media have not been systematically assessedassessed No flow: no replenishment of consumed nutrients - little or no No flow: no replenishment of consumed nutrients - little or no

growthgrowth Very fast flow: attachment and upstream spread difficultVery fast flow: attachment and upstream spread difficult Most flow studies have reported only volumetric flow rate or flow Most flow studies have reported only volumetric flow rate or flow

velocity - not a useful parameter - why should it matter what the 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?is far from the surface when the biofilm is attached to the surface?

Biofilms can spread upstream - is spread rate ~ shear as with Biofilms can spread upstream - is spread rate ~ shear as with upstream flame spread on a solid fuel bed? upstream flame spread on a solid fuel bed?

Fluid mechanics tells us the shear rate at the surface is the keyFluid mechanics tells us the shear rate at the surface is the key Our approach: use flow in tubes (shear not separated from mean Our approach: use flow in tubes (shear not separated from mean

flow rate) and Taylor-Couette cells (shear and mean flow flow rate) and Taylor-Couette cells (shear and mean flow independently controlled)independently controlled)

Biofilm experiments - laminar flow in tubes Biofilm experiments - laminar flow in tubes

LB + E. coli

(1) 12 hr incubation (2) Biofilm initiated

No biofilm above

interface

Dense biofilm at

air-medium interface

Low-density biofilm

below interface

LB only

(3) Flow testing

Waste

Peristaltic

pump

(4) Sectioning & analysis

Experiments show an effect of flow velocity or shear rate on growth Experiments show an effect of flow velocity or shear rate on growth rate and upstream spreadrate and upstream spread

Biofilms - imagesBiofilms - images

Control (incubated but not placed in flowapparatus)

0.3 ml/min, 3.5 hr

0.6 ml/min, 3.5 hr 0.6 ml/min, 3.5 hr

0.6 ml/min, 12 hr2 ml/min, 3.5 hr

0.6 ml/min, 24 hr16 ml/min, 3.5 hr

BiofilmsBiofilms

0

0.5

1

1.5

2

2.5

-6 -4 -2 0 2 4 6

Control

10 min

28 min

76 min

210 min

12 hr

24 hr

A

b

s

o

r

b

a

n

c

e

(

a

r

b

.

u

nit

s

)

Distance from inoculation point (cm)

Flow = 0.6 ml/min

1/8" diameter tube

u

m

= 0.13 cm/s

u

m

/d = 3.2/s

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

BiofilmsBiofilms

0

0.5

1

1.5

2

2.5

3

-4 -2 0 2 4

0 ml/min

0.3 ml/min

0.6 ml/min

2.0 ml/min

7.8 ml/min

16 ml/min

A

b

s

o

r

b

a

n

c

e

(

a

r

b

.

u

nit

s

)

Distance from inoculation point (cm)

Elapsed time 3.5 hr

1/8" diameter tube

u

m

= 0.21 cm/s for 1 ml/min

Fixed elapsed time / varying flow: Fixed elapsed time / varying flow: optimal flow/shear rate that optimal flow/shear rate that maximizes growthmaximizes growth

Biofilms - Taylor Couette cell conceptBiofilms - Taylor Couette cell concept

Ar

+

Laser

3-D Traversing

System

LDV Probe

Optical

fiber

bundle

Inner

cylinder

Outer

Cylinder

Fiber-Optic

Transmitter

Photo-

multiplier

Computer

Rotation

Rotation

Motor

Motor

FFT

Signal

Analyzer

Media

inlet

Waste

outlet

Fluid

region

Fluid

region

ConclusionsConclusions

Broad analogies can be drawn between different types of Broad analogies can be drawn between different types of reaction-diffusion fronts in disparate types of physical / reaction-diffusion fronts in disparate types of physical / chemical / biological systemschemical / biological systems Steady propagation ratesSteady propagation rates Effects of reactant and product diffusivitiesEffects of reactant and product diffusivities Instabilities (i.e. pattern formation)Instabilities (i.e. pattern formation) Quenching behaviorQuenching behavior

Applications toApplications to Combustion enginesCombustion engines Solid propellant rocketsSolid propellant rockets Synthesis of ceramicsSynthesis of ceramics Polymer synthesisPolymer synthesis Assessment of turbulent combustion modelsAssessment of turbulent combustion models Colonization of new environments by swarms of bacteriaColonization of new environments by swarms of bacteria Biofilms - bacteria growing on surfaces - far more resistant to Biofilms - bacteria growing on surfaces - far more resistant to

antibiotics & other stresses than “planktonic” (free-swimming) antibiotics & other stresses than “planktonic” (free-swimming) bacteriabacteria

Thanks to…Thanks to…

National Cheng-Kung UniversityNational Cheng-Kung University Prof. Y. C. Chao, Prof. Shenqyang ShyProf. Y. C. Chao, Prof. Shenqyang Shy Combustion Institute (Bernard Lewis Lectureship)Combustion Institute (Bernard Lewis Lectureship)

Documents

Paul Ronney