nonuniform interfacial tracer distributions and … · 2011-10-21 · 22 steady fully-developed...
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NONUNIFORM INTERFACIAL TRACER DISTRIBUTIONS AND IMPLICATIONS FOR
MICROSCALE PIVMinami Yoda
G. W. Woodruff School of Mechanical [email protected]
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OUTLINE Introduction / Motivation
• Nano-PIV for interfacial velocimetry
• Multilayer nano-particle image velocimetry (MnPIV)
Poiseuille flows• Particle distributions
• Shear rate and slip length
Electrokinetically driven flows• Particle distributions
• Diffusion coefficients
Conclusions
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Applications• “Lab on a Chip” (LOC):
separation, identification of small (pL – nL) biochemical samples
• Microscale chemical reactors• Single-use medical diagnostics• Thermal management: heat pipes,
heat spreaders At these spatial scales, surface
forces become significant• Is there new flow physics at the
microscale?
MICROFLUIDICSMicroflows with overall dimension h ≈ 1–500 µm
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Track motion of tracer assuming tracer follows flow Particle tracer-based techniques
• Micro-particle image velocimetry (µPIV): spatial resolution >2 µm; near-wall capability 0.5–1 µm Santiago et al. 98
• Laser-Doppler velocimetry (LDV): resolution ~2.5 µm; near-wall capability 40 µm: point data Czarske et al. 02
• Confocal scanning µPIV: resolution >1.3 µm; near-wall capability ~1.3 µm Park et al. 04, Kinoshita et al. 07
Molecular tracer-based techniques• Molecular tagging velocimetry (MTV): (in-plane) resolution
~160 µm Roetmann et al. 08
• Fluorescence correlation spectroscopy (FCS): (wall-normal) resolution ~1.6 µm: point data Lumma et al. 03
MICROSCALE VELOCIMETRY
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INTERFACIAL TRANSPORT Are there new interfacial phenomena at the microscale?
• Recent studies report there may be “slip” within O(0.1 µm) of the wall, especially for hydrophobic surfaces
• “Local” methods (e.g. µPIV, FCS) for studying interfacial transport based on velocities of colloidal tracers
• Standard (µ)PIV assumes tracers follow flow and uniformly sample fluid velocity u(z)
• DLVO theory ⇒ nonuniform near-wall distribution due to electric double layer (EDL) interactions, van der Waals effects
• External electric field (electrokinetically driven flows) ⇒ tracer electrophoresis, charge polarization
z u(z)
b
uw
0
1
z
uz
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INTERFACIAL PIV Evanescent wave-based particle-image velocimetry
• Evanescent waves created by TIR of light at glass-water interface: illumination created at and bounded by interface
• at glass-water interface• Typically image over z ≤ 4zp based on camera noise floor
• Exploit nonuniform illumination intensity to estimate tracer z-positions from their image intensity Ip(z) assuming exponential decay with length scale zp
• Given variations in tracer properties (variations in Ip of 9% for tracers at same z), collect ensemble of z-positions for O(105) tracers ⇒ near-wall tracer distribution
Near-wall velocimetry and Brownian diffusion studiesZettner & Yoda 03, Kihm et al. 04, Pouya et al. 05, Huang et al. 07, Lasne et al. 08
o p p( ) exp{ / }; 100 nmI z I z z z
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MULTILAYER NPIV
1 / &
z
Ip
z
ub
Obtain velocities at different z-positions within 400 nm of wall• Separate tracers based on Ip(z) into
3–4 layers: brighter particles closer to wall
• Separately process layers ⇒ velocities u(z)
• Linear regression gives slope ( = shear rate), |intercept| b
Validated for 2D Poiseuille flows in hydrophilic microchannels• within 5% of analytical
predictions for b = 0 Li & Yoda 08
1/ &&
&
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∆t0
BIASES IN MNPIVSimulations using synthetic images show: Far away from wall, velocities underestimated due to
nonuniform illumination• Brighter particles contribute more to cross-correlation• Use particle-tracking approaches instead
Close to wall, velocities overestimated • Asymmetric hindered diffusion particles likelier to
move away from the wall, sampling larger velocitiesSadr et al. 07
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OUTLINE Introduction / Motivation
• Nano-PIV for interfacial velocimetry
• Multilayer nano-particle image velocimetry (MnPIV)
Poiseuille flows• Particle distributions
• Shear rate and slip length
Electrokinetically driven flows• Particle distributions
• Diffusion coefficients
Conclusions
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Use MnPIV to study slip in steady fully-developed flow• Compare near-wall shear rate with exact solution for flow
between parallel plates (H = 33 µm)
• Re = 0.05–0.22 • Linear velocity profile for z < 400 nm:
≈ 500–2300 s–1
• Hydrostatically driven: ∆p / L = 0.25–1.2 Bar/m
∀µ ⇒ T at exit
POISEUILLE FLOW
2
( ) 12
H p z zu z
L H H
&
&
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IMAGING AND ILLUMINATION
Laser beam
Inverted epi-fluorescent microscope • 31.5× magnification (63× objective + 0.5× camera adaptor) • Longpass beamsplitter cube transmits wavelengths > 515 nm
Prism-coupled evanescent-wave illumination• Up to 0.15 W at 488 nm from Ar+ laser shuttered by AOM• zp = 96 ± 5 nm
Image pairs acquired by EMCCD by “frame straddling”• Time interval within pair ∆t = 1.5 ms; exposure 0.8 ms• 2 sets of 300 653 × 100 pixels
(154 µm × 24 µm) image pairs each acquired over ~33 s
• Time between image pairs 20–220 ms
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EXPERIMENTAL DETAILS Working fluids
• Ammonium bicarbonate (NH4HCO3) and ammonium acetate (CH3COONH4) solutions at molar salt concentrations C = 2 and 10 mM at pH7.6–7.8 and 6.2–6.6, respectively
• Tracers: radius a ≈ 50 nm fluorescent PS spheres (Invitrogen FluoSpheres) labeled with Bodipy FL; φ ≈ 20 ppm
• Working fluid degassed shortly before each experiment Microchannels
• 33 µm × 530 µm fused-silica channels wet-etched on same wafer under identical conditions
• “Bare” walls naturally hydrophilic• Coated with ~2 nm thick OTS monolayer (chloroform
solution) ⇒ hydrophobic surface with contact angle 100 ± 4°
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ATTACHED PARTICLES
Inverted images averaged over all 600 image pairs: more particles stick to hydrophobic surface• Electrostatic effects: OTS coating changes surface charge from
–3.5 mV to ~0 mV (streaming-potentials w/ pH 6.8 phosphate buffer)
• Chemical affinity• Projected area O(10–4) of total image area
Hydrophilic
Hydrophobic 24
154 µm
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Identify and locate particles• Rescale images to correct for camera nonlinearities • Determine maximum grayscale value at particle center ≡ Ip• Minimize flocculated/overlapped particle images
by removing all images with eccentricities > 0.1 Estimate near-wall particle distribution
• Edge distance • max. grayscale value of particles attached to
wall (determined in separate calibration): std. dev. ~9%, vs. particle polydispersity 6%
• Uncertainty (95% conf. int.) in particle z-position 17–23 nm Displacements from particle tracking Baek & Lee 96
• Subtract average “background” image for hydrophobic cases• Minimize underestimation due to nonuniform illumination
IMAGE PROCESSING
0p p pln{ / }h z I I z a
0pI
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Nonuniform distribution: particle depletion at h/a < 1 • Distribution shifts slightly ← for hydrophobic channel • Distribution shifts slightly ← salt molar concentration ↑
Divide O(105) particle images into 3 sublayers, each containing ~1/3 of particles• 0 ≤ hI / a ≤ 2; 2 ≤ hII / a ≤ 4; 4 ≤ hIII / a ≤ 6
Hydrophobic
2 mM Acetate 10 mM Acetate 2 mM Bicarb. 10 mM Bicarb.
PARTICLE DISTRIBUTIONS
h/a
a = 50 nm
# D
ens
ity
[/(
1016
m3)]
h/a
Hydrophilic
[inset]
10 mM Acetate
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10 mM NH4HCO3; bare fused-silica channel
Velocity u placed at z-location based on particle distribution• Avg. over 5 expts.• Slopes from curve-fits
(lines) accounting for uncertainties in u and z w/in 5% (on avg.) of analytical predictions for all hydrophilic cases
• Error bars 95% conf. int.
HYDROPHILIC RESULTS
z [
nm
]
u [mm/s]
= 491, 983, 1410, 1720, 2030, 2260 s–1
&
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2 mM CH3COONH4; OTS-coated channel
Mean velocity u placed at z-location based on particle distribution• Avg. over 5 expts.• Slopes from curve-fits
(lines) accounting for uncertainties in u, z w/in 5% (on avg.) of analytical predictions over all hydrophobic cases
HYDROPHOBIC RESULTS
z [
nm
]
u [mm/s]
= 493, 972, 1410, 1710, 2030, 2260 s–1
&
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SLIP LENGTHSb
[nm
]
Hydrophilic Hydrophobic
[s–1]&
2 mM Bicarb. 10 mM Bicarb.
2 mM Acetate 10 mM Acetate
[s–1]& In all but one case, b = 0 w/in experimental uncertainty
• Based on uncertainties in u, z• b = 23 22 nm for 2 mM NH4HCO3 at highest
• Hydrophobic case: b “more organized”; increases with
&&
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PARTICLE DIST. EFFECTS
z [
nm
]
u [mm/s]
10 mM CH3COONH4; OTS-coated channel• Compare results for u
corrected for nonuniform tracer distribution (filled) with results for u at center of each layer (open symbols)
• Shifting z-position of uI by ~20 nm increases b by 30–50 nm and gives within 15% of analytical predictions
& = 961, 1710, 2260 s–1&
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OUTLINE Introduction / Motivation
• Nano-PIV for interfacial velocimetry
• Multilayer nano-particle image velocimetry (MnPIV)
Poiseuille flows• Particle distributions
• Shear rate and slip length
Electrokinetically driven flows• Particle distributions
• Diffusion coefficients
Conclusions
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+ +
Electroosmotic flow (EOF): counterions in electric double layer driven by E• Particle displacements due to
EOF + electrophoresis (EP)
How does external electric field affect near-wall particle dynamics and distributions?• Consider two different sizes of Invitrogen fluorescent
polystyrene tracers of nominal radii 50 and 250 nm • Characterize particles by light scattering • a = 54 ± 7.3 nm; ζp = –53 ± 5.6 mV
• a = 240 ± 22 nm; ζp = –73 ± 2.7 mV
+
++
++ ++
+ +
−
−−
−
−
+
−+
+
−ζp
ELECTROKINETIC FLOWS
EP pP EO w( )uu uE
Wall
+ −
+
E
uEP
+ + + + +++− − − − − − ζw
uEO
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Steady fully-developed flow: E = 11–67 V/cm• Fused-silica wet-etched channels (306 µm × 38 µm)• Working fluid monovalent electrolyte solution: 1 mM
Na2B4O7 in Nanopure water (pH9.0, conductivity 165 mS/cm) ⇒ thin EDL (Debye length λD < 7 nm)
• Tracers at same nominal number density of 1.3 × 1016 m–3
⇒ φ = 7 ppm (a = 54 nm) and 925 ppm (a = 240 nm) Optics and imaging
• Prism-coupled evanescent-wave illumination: zp ≈ 193±4 nm
• Magnification 63× ; output power ~0.15 W from Ar+ laser shuttered by AOM
• Acquire 1500 image pairs over 60 s (∆t = 1.3−2.2 ms;exposure 0.5 ms) using new EMCCD camera
• 130 µm × 36.6 µm (512 × 144 pixels) images
EXPERIMENTAL DETAILS
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IMAGE PROCESSING Identify and locate particles
• After correcting for camera nonlinearities, locate particle centers by cross correlation (assuming Gaussian images)
• Remove overlapping particle images• Calculate area intensity of particle image Ap
Determine near-wall particle distribution• Particle edge-wall distance:
= area intensity of particles at wall• Errors in h and z ≡ h+a are 4−17 nm and 19−22 nm (larger
because of polydispersity), respectively Determine tracer displacements using particle tracking
0p p pln{ / }h z A A z a
0pA
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a = 240 nmE= 11 V/cm
φ = 925 ppm
a = 54 nmE= 11 V/cm
φ = 7 ppm
a = 54 nmE= 67 V/cm
φ = 7 ppm
a = 240 nmE= 67 V/cm
φ = 925 ppm
FLOW VISUALIZATIONS
∆t = 1.3 ms
130 µm
37 µm
Tracers within 400 nm of wall at same number density• “Blinking” due to Brownian diffusion, esp. for a = 54 nm• Fewer a = 240 nm particles near wall at higher E
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Nonuniform distribution: particle depletion near wall For a = 240 nm particles, number of particles ↓ as E ↑
PARTICLE DISTRIBUTIONSa = 54 nm a = 240 nm
Poiseuille 22 V/cm
44 V/cm 67 V/cm
h/a
# D
ensi
ty [
/(10
16 m
3 )]
h/a
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DIFFUSION COEFFICIENTS
D /D
∞
a = 54 nm a = 240 nm
Faxén
13 4 59 1 45 1
116 8 256 16
PD
D
h/a
Tangential diffusion coefficient D from particle displacements• Variance of Gaussian
distribution• z-position of D
corrected for nonuniform distribution
D for both a within 4% of Faxén relation
1z ha a
where
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Divide O(105) particle images into 4 sublayers• hI = 0–100 nm; hII = 100–200 nm; hIII = 200–300 nm; hIV =
300–400 nm
PARTICLE DISTRIBUTIONSa = 54 nm a = 240 nm
Poiseuille 22 V/cm
44 V/cm 67 V/cm
h/a
# D
ensi
ty [
/(10
16 m
3 )]
h/a
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EOF VELOCITIES After subtracting
electrophoretic velocities uEP, MnPIV gives “plug” flow for electroosmotic flow velocities uEO
• Thin EDL: < 7 nm • Slope electroosmotic
mobility
∀w = 132 10 mV based on curve-fits to data from a = 54 nm and 240 nm tracers
E [V/cm]
uE
O [
mm
/s]
EO P EP
P p /u u u
u E
a = 54 nm a = 240 nm
EO w
Eu
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CONCLUSIONS Multilayer nPIV
• Interfacial velocimetry technique for obtaining velocities at different distances from, but within 400 nm of, the wall
• Gives direct estimate of near-wall tracer distributions Poiseuille flows
• Shear rates within 5% of analytical predictions for 2D flow• Slip lengths for wetting and nonwetting channels zero within
measurement uncertainties • Hydrophobic channels have more particles attached to wall
and more “organized” slip length behavior Electrokinetically driven flows
• Diffusion coefficients within 4% of Faxén relation• Electroosmotic velocities in agreement with theory• a = 240 nm particles repelled from wall at higher E
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Colleagues• Yutaka Kazoe, Haifeng Li, Reza Sadr, Claudia Zettner: GT• A.T. Conlisk, S. Dhatta, S. V. Olesik, G. Philibert: OSU • J.M. Ramsey, J.P. Alarie, P. Mucha: UNC• M. Bevan: JHU
$ponsors• NSF• ONR• AFOSR• DARPA
ACKNOWLEDGEMENTS
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Image fluorescent PS particle on micropipette tip• Move towards wall with
mechanical stage• Illuminate w/evanescent
waves (zp = 91 nm)
• Curve-fit max. grayscale value in particle image Ip to
exponential function: Ip / Ip
0 = exp{– h / zp}
• z′p = 99±14 nm over 10 runs Use maximum grayscale
value as particle intensity h [nm]
z′p1 = 93 nm
TRACER INT. CALIBRATIONS
a = 250 nm