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
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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)
Paul Ronney
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. Fe2O3(s) + 2Al(s) 
Al2O3(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?
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
Premixed flame (SHS, solid propellant similar)
Reaction zone
2000K
Product
concentration
Direction of propagation
Speed relative to unburned gas = SL
Temperature
Reactant
concentration
300K
Distance from reaction zone
Convection-diffusion zone
 - /SL = 0.3 - 6 mm
Reaction-diffusion systems - characteristics
 After initial transient, fronts typically propagate at a steady
rate
 Propagation speed (SL) ~ (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
 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!
 T
T


E Tad  T
ad
Ze  

(T ) T
T  RT
Tad
T Tad  ad
 ad
ad
 Flammability or extinction limits when loss rate of
autocatalyst ≈ production rate of autocatalyst

Instability mechanisms
 Instability mechanisms may preclude steady flat front
 Turing instability - when ratio of reactant to autocatalyst
diffusivity differs significantly from 1
Thermal fronts: Dautocatalyst/Dreactant = 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
Direction of
propagation
Fuel
diffusion
Unburned gas
Heat
diffusion
Heat
diffusion
Fuel
diffusion
Flame
front
Burned gas
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 (Ri*):
I  R1* + R2* - highest activation energy step
e.g. (NH4)2S2O8  2NH4SO4*
 Followed by addition of a radical to a monomer (M):
M + Ri*  RiM* - initiates polymer chain, grows by
addition:
RiMn* + M  RiMn+1*
 Most of heat release occurs through addition step
 Note not chain-branching like flames
 Chain growth eventually terminated by radical-radical
reactions:
RiMn* + RjMm*  RiMn+mRj
 Chain length can be controlled by chain transfer agents affects properties of final product
Polymerization front
Reaction zone
500K
Polymer
concentration
10 cm2/s
1.2
Polymerization front
Monomer concentration
Temperature
0.001 cm2/s
Viscosity (log scale) 0.01 cm2/s
300K
Distance from reaction zone
Density
relative
to
reactants
0.96
5 mm
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 Tad <
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!
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
Polymerization front
 Typical speeds 0.01 cm/s, SL ≈ ()1/2  -1 ≈ 14 s
 From plot of ln(SL) vs. 1/Tad can infer E ≈ 13.5 kcal/mole, Ze ≈ 20
 Extinction at Pe ≈ (0.004 cm/s)(1.6 cm)/(0.0014 cm2/s) ≈ 4.6 - close
to classical flame theory predictions
 Plot of SL vs. “fuel” concentration approaches vertical at
extinction limit as theory predicts
 With insulation, limiting SL and %AA much lower
0.016
16 mm tube
Uninsulated
16 mm tube
10% AP
0.014
0.01
0.008
Front speed (cm/s)
Front speed (cm/s)
0.03
Mass % AP
0.006
5%
8%
10%
12%
15%
0.004
0.012
0.01
0.008
0.006
0.004
Insulated
Uninsulated
0.002
0.002
0
15
20
25
30
35
Mass percent AA
40
45
10
15
20
25
Mass percent AA
30
35
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
80
Temperature (ыC)
Temperature (ыC)
100
80
Slope = 0.056ыC/s
60
27.5% AA / 10% AP
16 mm tube
40
Insulated
Uninsulated
Adiabatic
20
14.7% AA, insulated
22.2% AA, uninsulated
70
60
50
40
30
10% AP
16 mm tube
20
0
100
200
300
400
Time (seconds)
500
600
700
0
500
1000
1500
2000
Time (seconds)
2500
3000
Polymerization front
 High Lewis number - spiral & travelling-wave instabilities
like flames (middle and right videos, viscosity-enhancing
agent added to suppress buoyant instabilities)
Quick Time™a nd a YUV4 20 cod ec dec ompr esso r ar e need ed to see this pictur e.
Quick Time™a nd a YUV4 20 cod ec dec ompr esso r ar e need ed to see this pictur e.
Quick Time™a nd a YUV4 20 cod ec dec ompr esso r ar e need ed to see this pictur e.
Movies courtesy Prof. J. Pojman, University of Southern Mississippi
Lean C4H10-O2-He mixtures; Pearlman and Ronney, 1994
Autocatalytic aqueous reactions - motivation
 Models of premixed turbulent combustion don’t agree with
experiments nor each other!
Pope & Anand 1987 (zero heat release)
(large heat release)
30
Turbulent Burning Velocity (S
T
/S L )
Bray 1990 (zero heat release)
(large heat release,
 = 7)
Sivashinsky 1990
25
Yakhot 1988
Bychov 2000
=7
20
Experiment
(Bradley, 1992)
x (Re L=1,000)
15
10
Gouldin 1987 (Re
L
5
=1,000)
(Where Re is not reported, predictions are independent of Re
L
0
0
10
20
30
Turbulence Intensity (u'/S
40
L
)
L
)
50
Modeling of premixed turbulent flames
Most model employ assumptions not satisfied by
real flames, e.g.
 Adiabatic (sometimes ok)
 Homogeneous, isotropic turbulence over many LI
(never ok)
 Low Ka or high Da (thin fronts) (sometimes ok)
 Lewis number = 1 (sometimes ok, e.g. CH4-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!)
Autocatalytic front (bacterial fronts similar)
Reaction zone
Aqueous chemical front
Reactant concentration
Product
concentration
Viscosity (log scale) 0.01 cm2/s
0.01 cm2/s
303K
Temperature 300K
0.9994
Density relative
to reactants
Distance from reaction zone
0.01 mm
“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
2


u' /LT
 LI u' D
1/ 2 u'
1
Ka  2
~
~
Re
Sc

L 
SL /D u' LI LT SL2 
S
 L 
2
Approach - chemistry
 Iodate-hydrosulfite system
IO3- + 6 H+ + 6e-  I- + 3 H2O
-2 + 4 H O  6 e- + 8 H+ + 2 SO -2
S
O
2
4
2
4
_________________________________________________
IO3- + S2O4-2 + H2O  I- + 2 SO4-2+ 2 H+
 Comparison
assumptions







with
turbulent
combustion
Adiabatic
Homogeneous, isotropic turbulence over many LI
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!
model
Taylor-Couette apparatus
Motor
Rotation
Ar +-ion Laser
Sheet
Product
(Not fluorescing)
Inner
cylinder
s
ST
Mirror
Reactant
(Fluorescing)
LDV Probe
Cylindrical
Lens
Outer
Cylinder
Beam
Splitter
Rotation
3-D Traversing
System
Fiber-Optic
Transmitte r
+
Ar
Laser
Fiber
Motor
Photomultiplier
FFT
Signal
Analyzer
Computer
Capillary-wave apparatus
Ar +-ion
Laser
Sheet
Mirror
Vibration
Product
(Not fluorescing)
Reactant
(Fluorescing)
s
LDV Probe
Cylindrical
Lens
Vibrating
Platform
Beam
Splitter
Optical
Fiber
Loudspeaker
Fiber-Optic
Transmitter
+
Ar
Laser
Photomultiplier
FFT
Signal
Analyzer
3-D Traversing
System
Computer
Results - liquid flames
QuickTi me™ a nd a MPEG-4 Vid eo d eco mpres sor a re ne eded to see this picture.
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 - ST/SL in 4 different flows consistent with Yakhot
model
 u' S 2 
ST  exp
L

2


SL
S
S


 T L 
 Low Da - ST/SL 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
Propagation rate (S T /S L )
Liquid flames - comparison to Yahkot (1988)
Hele-Shaw
Capillary wave
T aylor-Couette
Vibrating grid (Shy et al. )
T heory (Yakhot)
Power law fit to expts.
100
10
Power law fit (u'/S L > 2):
S T /S L = 1.61 (u'/S L ).7 42
1
0.1
1
10
100
"Turbulence" intensity (u'/S L )
1000
Results - liquid flames - propagation rates
Capillary wave experiments
Taylor-Couette experiments
1
0.1
Flamelet
Distributed
T
L
S /S (experiment) / S
T
L
/S (theory, Yakhot)
 Data on ST/SL in flamelet regime (low Ka) consistent with Yakhot
model - no adjustable parameters
 Transition flamelet to distributed at Ka ≈ 5
0.01
0.1
1
10
100
Karlovitz number (Ka)
1000
10
4
Results - liquid flames - propagation rates
3
1
0.8
Flamelet
0.6
Distributed
Experiments (Taylor-Couette)
Experiments (capillary wave)
0.4
T
L
S /S (experiment) / S
T
L
/S (theory, Damköhler)
 Data on ST/SL in distributed combustion regime (high Ka)
consistent with Damköhler’s model - no adjustable parameters
0.1
1
10
100
Karlovitz number (Ka)
1000
10
4
Front propagation in one-scale flow


ST  exp u' SL 1 exp u' SL 


S S 
SL
S
S
 T L 
 T L 
Front propagation rate (s/c)
 Turbulent combustion models not valid when energy
concentrated at one spatial/temporal scale
 Experiment - Taylor-Couette flow in “Taylor vortex” regime
(one-scale)
 Result - ST/SL 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)
250
Th eory (Eq. 1)
Th eory (1-s cal e)
CW e xp erime nt
TC e xp erime nt
1-s cal e expe rimen t
200
150
100
50
0
0
100
200
300
400
Turbulence intensity (q/c)
500
600
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
Fractal analysis in CW flow
10 5
1.5
1.4
u'/S L = 220
Slope = 0.732
d = 1.268
Fractal dimension
Area (number of pixels)
u'/S L = 77
Slope = 0.776
d = 1.224
1.3
1.2
Al l da ta a t u'/S
1.1
L
> 60:
Mean = 1 .31, RMS deviation 0.06
10 4
1
1
10
Measurement scale (number of pixels)
0
50
100
150
Disturbance intensity (u'/S
200
L
250
)
Bacterial fronts
 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”
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
QuickTi me™ and a Sor enson Video decompr essor ar e needed to see this picture.
http://www.rowland.org/bacteria/movies.html
Analogy with flames
Flame or molecular
property
Temperature
Fuel
Heat diffusivity Е c
Fuel diffusivity
Sound speed (c)
Mean fr ee path ()
Reaction timescale
Heat loss
Extinguishment
Microbiological equivalent
Concentration of b acteria
Nutrients
Diffusivity of bacteria
Diffusivity of nutr ient
Swimming speed of bacterium in "run" mode
c multipled by av erage time to switch f rom run
mode to tumble mode and back
Reproduction time
Death (of individual bacterium)
Death (of all bacteria)
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
60
0.2% agar
0.3% agar
Front diameter (mm)
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
Time (hours)
Fronts show a steady propagation rate after an initial transient
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
Front speed (mm/hr)
10
8
6
4
2
0
0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
Agar concentration, %
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?)
Front Speed (mm/h)
4.5
4
3.5
3
2.5
2
1.5
1
0
0.2
0.4
0.6
0.8
Tryptone Concentration (%)
1
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 cm2/s, w at
quenching limit ≈ 2.1 cm  Pe ≈ 9.8 - similar to flames and polymer fronts
6 mm wide channel
35 mm wide channel
E. coli, 0.1% agar, 100 µl of kanamycin per side, 6.5 hours after inoculation
Comparison of fronts in Mot+ and Mot- bacteria
 Some mutated strains are non-motile but D due to Brownian
motion ≈ 104 smaller
 Fronts of Mot- bacteria also propagate, but more slowly
than Mot+ bacteria
1.2
Front speed (mm/hr)
1
0.8
0.6
0.4
0.2
0
0
0.05
0.1
0.15
Agar %
0.2
0.25
Quantitative analysis
 Bacteria D as estimated from measured front speeds




SL for Mot+ ≈ 5.3 x 10-5 cm/s for 0.3% agar
Reproduction time scale () of E.coli ≈ 20 min
D ≈ s2 ≈ (5.3 x 10-5 cm/s)2(1200s) ≈ 3.3 x 10-6 cm2/s
Similarly, D ≈ 3.7 x 10-5 cm2/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 cm2/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 cm2/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)
Comparison of fronts in Mot+ and Mot- bacteria
 Dnutrient (≈ 10-5 cm2/s) close to Dbacteria, 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
(Dautocatalyst) by ≈ 1700x but nutrient diffusivity (Dreactant) is unchanged decreases the effective “Lewis number”
 Mot- fronts “cellular” but Mot+ fronts smooth - consistent with “Lewis
number” analogy
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)
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)
Biofilm experiments - laminar flow in tubes
No biofilm above
interface
Dense biofilm at
air-medium interface
Low-density biofilm
below interface
LB + E. coli
(1) 12 hr incubation
(2) Biofilm initiated
Peristaltic
pump
LB only
Waste
(3) Flow testing
(4) Sectioning & analysis
Biofilms - images
Control (incubated but not placed in flow
apparatus)
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 hr
2 ml/min, 3.5 hr
0.6 ml/min, 24 hr
16 ml/min, 3.5 hr
Experiments show an effect of flow velocity or shear rate on growth
rate and upstream spread
Biofilms
Abs or banc e ( ar b. uni t s)
2.5
Flow = 0.6 ml/min
1/8" diameter tube
u = 0.13 cm/s
2
m
um/d = 3.2/s
Control
10 min
28 min
76 min
210 min
12 hr
24 hr
1.5
1
0.5
0
-6
-4
-2
0
2
4
6
Distance from inoculation point (cm)
Fixed flow / varying elapsed time: more time, more growth, but maybe
some sloughing at long times
Biofilms
Abs or banc e ( ar b. uni t s)
3
2.5
Elapsed time 3.5 hr
1/8" diameter tube
u = 0.21 cm/s for 1 ml/min
m
2
0 ml/min
0.3 ml/min
0.6 ml/min
2.0 ml/min
7.8 ml/min
16 ml/min
1.5
1
0.5
0
-4
-2
0
2
4
Distance from inoculation point (cm)
Fixed elapsed time / varying flow: optimal flow/shear rate that
maximizes growth
Biofilms - Taylor Couette cell concept
Motor
Waste
outlet
Rotation
Fluid
region
Inner
cylinder
Fluid
region
LDV Probe
Optical
fiber
bundle
Outer
Cylinder
+
Ar
Laser
3-D Trav ersing
System
Rotation
Motor
Fiber-Optic
Transmitter
Photomultiplier
Media
inlet
FFT
Signal
Analyzer
Computer
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
Thanks to…
 National Cheng-Kung University
 Prof. Y. C. Chao, Prof. Shenqyang Shy
 Combustion Institute (Bernard Lewis Lectureship)