NONUNIFORM INTERFACIAL TRACER DISTRIBUTIONS AND IMPLICATIONS FOR

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					NONUNIFORM INTERFACIAL
 TRACER DISTRIBUTIONS
 AND IMPLICATIONS FOR
    MICROSCALE PIV
                                   Minami Yoda
  G. W. Woodruff School of Mechanical Engineering
                                minami@gatech.edu
                       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
IMA Workshop (11/09)                                        2
                  MICROFLUIDICS
  Microflows with overall dimension h  1–500 m
   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?
IMA Workshop (11/09)                               3
   MICROSCALE VELOCIMETRY
    Track motion of tracer assuming tracer follows flow
    Particle tracer-based techniques
       • Micro-particle image velocimetry (PIV): spatial resolution
           >2 m; near-wall capability 0.5–1 m             Santiago et al. 98
       •   Laser-Doppler velocimetry (LDV): resolution ~2.5 m;
           near-wall capability 40 m: point data            Czarske et al. 02
       •   Confocal scanning PIV: resolution >1.3 m; near-wall
           capability ~1.3 m               Park et al. 04, Kinoshita et al. 07

    Molecular tracer-based techniques
       • Molecular tagging velocimetry (MTV): (in-plane) resolution
         ~160 m                                    Roetmann et al. 08
       • Fluorescence correlation spectroscopy (FCS): (wall-normal)
         resolution ~1.6 m: point data                Lumma et al. 03

IMA Workshop (11/09)                                                              4
     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. PIV, FCS) for studying interfacial
         transport based on velocities of colloidal tracers
     •   Standard ()PIV assumes tracers follow flow and uniformly
         sample fluid velocity u(z)
                                                        z    u(z)
     •   DLVO theory  nonuniform near-wall
         distribution due to electric double layer
         (EDL) interactions, van der Waals effects          uw      1
     •   External electric field (electrokinetically              u
         driven flows)  tracer electrophoresis,        b         z z  0
         charge polarization
IMA Workshop (11/09)                                                         5
                   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
     •   I ( z )  I o exp{ z / zp }; zp  100 nm 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 studies
         Zettner & Yoda 03, Kihm et al. 04, Pouya et al. 05, Huang et al. 07, Lasne et al. 08

IMA Workshop (11/09)                                                                            6
                MULTILAYER NPIV
   Obtain velocities at different z-
     positions within 400 nm of wall             z
      •   Separate tracers based on Ip(z) into
          3–4 layers: brighter particles
          closer to wall
                                                         Ip
      •   Separately process layers 
          velocities u(z)
      •   Linear regression gives slope 1 /         z
          (  = shear rate), |intercept| b
   Validated for 2D Poiseuille flows
                                                              1/ 
     in hydrophilic microchannels
      •    within 5% of analytical                                  u
          predictions for b = 0 Li & Yoda 08     b
IMA Workshop (11/09)                                                     7
                 BIASES IN MNPIV
   Simulations 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 velocities
                                                             Sadr et al. 07




           0                                           t

IMA Workshop (11/09)                                                          8
                       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
IMA Workshop (11/09)                                        9
                POISEUILLE FLOW
  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 m)
                     H 2 p  z      z 
            u( z )          H  1  H 
                     2 L             
     •   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
     •     T at exit

IMA Workshop (11/09)                                                 10
  IMAGING AND ILLUMINATION
   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      Laser
          (154 m  24 m) image pairs    beam
          each acquired over ~33 s
      •   Time between image pairs 20–220 ms

IMA Workshop (11/09)                                                  11
          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;   20 ppm
      •   Working fluid degassed shortly before each experiment
   Microchannels
      • 33 m  530 m 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°
IMA Workshop (11/09)                                                    12
            ATTACHED PARTICLES
  Hydrophilic



  Hydrophobic




                                                                         24
                                 154 µm
  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
IMA Workshop (11/09)                                                      13
              IMAGE PROCESSING
    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 h  zp ln{I p0 / I p }  z  a
       • I p0 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
IMA Workshop (11/09)                                                          14
                           PARTICLE DISTRIBUTIONS
                                              10 mM Acetate                      2 mM Acetate
                                                                              
  # Density [/(1016 m3)]


                                                                                  10 mM Acetate
                                                                                 2 mM Bicarb.
                                                                                 10 mM Bicarb.

                                                                                      a = 50 nm




                                               Hydrophilic                        Hydrophobic

                                            h/a                                 h/a
   Divide O(105)distribution: particle3depletion ateach< 1
    Nonuniform particle images into sublayers, h/a
                            • Distribution shifts slightly 
                           containing ~1/3 of particles for hydrophobic channel [inset]
                           •   Distribution 2  slightly   hIII / a  6
                               0  hI / a  2;shiftshII / a  4; 4salt molar concentration 
IMA Workshop (11/09)                                                                              15
           HYDROPHILIC RESULTS
    10 mM NH4HCO3; bare
       fused-silica channel
      Velocity u placed at z-
       location based on
       particle distribution


                                   z [nm]
       • 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         = 491, 983, 1410,
           all hydrophilic cases            1720, 2030, 2260 s–1
       •   Error bars 95% conf. int.
                                            u [mm/s]
IMA Workshop (11/09)                                           16
       HYDROPHOBIC RESULTS
   2 mM CH3COONH4;
      OTS-coated channel
     Mean velocity u placed
      at z-location based on
      particle distribution


                                  z [nm]
      • Avg. over 5 expts.
      • Slopes from curve-fits
         (lines) accounting for
         uncertainties in u, z
         w/in 5% (on avg.) of
         analytical predictions              = 493, 972, 1410,
         over all hydrophobic              1710, 2030, 2260 s–1
         cases
IMA Workshop (11/09)
                                            u [mm/s]              17
                        SLIP LENGTHS
               Hydrophilic                   Hydrophobic
  b [nm]




                         2 mM Acetate                 2 mM Bicarb.
                         10 mM Acetate                10 mM Bicarb.

                         [s–1]                        [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 
IMA Workshop (11/09)                                                    18
         PARTICLE DIST. EFFECTS
  10 mM CH3COONH4;
    OTS-coated channel
     •   Compare results for u
         corrected for nonuniform
         tracer distribution



                                z [nm]
         (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         = 961, 1710, 2260 s–1
         predictions

IMA Workshop (11/09)
                                            u [mm/s]               19
                       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
IMA Workshop (11/09)                                        20
      ELECTROKINETIC FLOWS
   Electroosmotic flow (EOF): counterions in electric
     double layer driven by E                      E           uEO
                                                     + + +
      •   Particle displacements due to           +        +
          EOF + electrophoresis (EP)         +          p  +     
                           E                     +
                                               uEP 
                                                    +  +
                                                             +
          uP  uEO  uEP     ( p   w )
                                                     + +
                                               + ++ + + + + + ++ 
                                                           w
   How does external electric field           Wall
     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; p = –53  5.6 mV
      •   a = 240  22 nm; p = –73  2.7 mV
IMA Workshop (11/09)                                               21
          EXPERIMENTAL DETAILS
   Steady fully-developed flow: E = 11–67 V/cm
      • Fused-silica wet-etched channels (306 m  38 m)
      • Working fluid monovalent electrolyte solution: 1 mM
          Na2B4O7 in Nanopure water (pH9.0, conductivity
          165 mS/cm)  thin EDL (Debye length D < 7 nm)
      •   Tracers at same nominal number density of 1.3  1016 m–3
            = 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 m  36.6 m (512  144 pixels) images
IMA Workshop (11/09)                                                 22
             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: h  zp ln{ Ap / Ap }  z  a
                                                   0

            0
          Ap = 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

IMA Workshop (11/09)                                                    23
          FLOW VISUALIZATIONS
                       37 m
    a = 54 nm
      11
   E= 67 V/cm
     = 7 ppm
                                                              130 m

                                                          t = 1.3 ms
   a = 240 nm
      11
   E= 67 V/cm
   = 925 ppm

   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
IMA Workshop (11/09)                                                    24
                    PARTICLE DISTRIBUTIONS
                                  a = 54 nm          a = 240 nm
   # Density [/(1016 m3)]




                                 Poiseuille
                                 22 V/cm
                                 44 V/cm
                                 67 V/cm

                            h/a                h/a
  Nonuniform distribution: particle depletion near wall
  For a = 240 nm particles, number of particles  as E 
IMA Workshop (11/09)                                              25
     DIFFUSION COEFFICIENTS
   Tangential diffusion
     coefficient D from
     particle displacements
      •   Variance of Gaussian




                                    D /D
          distribution
      •   z-position of D
          corrected for
                                                          a = 54 nm
          nonuniform distribution                         a = 240 nm
   D for both a within 4%                                   Faxén
     of Faxén relation
                                             1         h/a
      D   9     1 3 45 4 1 5 
        1                                       z h
     D  16     8    256    16                  where     1
                                                           a a
IMA Workshop (11/09)                                                    26
                    PARTICLE DISTRIBUTIONS
                                              a = 54 nm                       a = 240 nm
   # Density [/(1016 m3)]




                                             Poiseuille
                                             22 V/cm
                                             44 V/cm
                                             67 V/cm

                                        h/a                             h/a
  Divide O(105) particle images into 4 sublayers
                        •   hI = 0–100 nm; hII = 100–200 nm; hIII = 200–300 nm; hIV =
                            300–400 nm
IMA Workshop (11/09)                                                                       27
                 EOF VELOCITIES
   After subtracting                          uEO  uP  uEP
     electrophoretic velocities                     uP  E  p / 
     uEP, MnPIV gives “plug”
     flow for electroosmotic




                                  uEO [mm/s]
     flow velocities uEO
      •   Thin EDL:  < 7 nm
      •   Slope electroosmotic
          mobility
      •   w = 132  10 mV based
          on curve-fits to data from                         a = 54 nm
          a = 54 nm and 240 nm                               a = 240 nm
          tracers           E
                   uEO    w
                                                      E [V/cm]
IMA Workshop (11/09)                                                       28
                    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
IMA Workshop (11/09)                                                      29
          ACKNOWLEDGEMENTS
    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



IMA Workshop (11/09)                                                30

				
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