NONUNIFORM INTERFACIAL TRACER DISTRIBUTIONS AND … · 2011-10-21 · 22 Steady fully-developed...

NONUNIFORM INTERFACIAL TRACER DISTRIBUTIONS AND IMPLICATIONS FOR

MICROSCALE PIVMinami Yoda

G. W. Woodruff School of Mechanical [email protected]

IMA Workshop (11/09)

2

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


3

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


4

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


5

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


6

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


7

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/ &&

&


8

∆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


9








Conclusions


10

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

&

&


11

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


12

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°


13

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


14

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


15

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


16

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

&


17

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

&


18

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

&&


19

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&


20








Conclusions


21

+ +

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


22

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


23

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


24

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


25

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


26

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


27

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


28

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


29

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


30

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


31

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

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NONUNIFORM INTERFACIAL TRACER DISTRIBUTIONS AND … · 2011-10-21 · 22 Steady fully-developed...

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