Microscopic Particle Image Velocimetry technique Part -...

Copyright Copyright ©© by Dr. by Dr. HuiHui HuHu @ Iowa State University. All Rights Reserved!@ Iowa State University. All Rights Reserved!

HHui Huui HuDepartment of Aerospace Engineering, Iowa State University Department of Aerospace Engineering, Iowa State University

Ames, Iowa 50011, U.S.AAmes, Iowa 50011, U.S.A

Microscopic Particle Image Microscopic Particle Image VelocimetryVelocimetry techniquetechniquePart Part -- 22

AerEAerE 545545 class notes class notes #34#34


System Setup of a conventional PIV systemSystem Setup of a conventional PIV system

Illumination system(Laser and optics)

cameraSynchronizer

seed flow withtracer particles

Host computer

Particle tracers: Particle tracers: to track the fluid movement. to track the fluid movement. Illumination system: Illumination system: to illuminate the flow field in the interest region.to illuminate the flow field in the interest region.Camera: Camera: to capture the images of the particle tracers.to capture the images of the particle tracers.Synchronizer: Synchronizer: the control the timing of the laser illumination and the control the timing of the laser illumination and

camera acquisition.camera acquisition.Host computer: Host computer: to store the particle images and conduct image processing. to store the particle images and conduct image processing.


System Setup of a Typical MicroSystem Setup of a Typical Micro-- PIV systemPIV system

Microscope LensMicroscope Lens(NA=1.4, 60x)(NA=1.4, 60x)

LensLens

1030 x 1300 x 12 bit1030 x 1300 x 12 bitInterline TransferInterline TransferCooled CCD CameraCooled CCD Camera

Nd:YAGNd:YAG LaserLaser

Beam Beam ExpanderExpander

EpiEpi--fluorescentfluorescentPrism / Filter CubePrism / Filter Cube

l = 532 nml = 532 nm

l = 560 nml = 560 nm

Microfluidic deviceMicrofluidic device


Differences between conventional PIV and Differences between conventional PIV and μμ--PIV PIV

•• Particle tracers:Particle tracers:–– Conventional PIV:Conventional PIV:

•• Tracer particle size is about ~1 Tracer particle size is about ~1 μμm m for gaseous flows and ~ 10 for gaseous flows and ~ 10 μμm m for liquid flowsfor liquid flows•• To detect scattering light signalTo detect scattering light signal

–– MicroMicro--PIV:PIV:•• Coated fluorescent particles.Coated fluorescent particles.•• Particle size is much smaller 200 nm ~1000 nm for liquid flowsParticle size is much smaller 200 nm ~1000 nm for liquid flows•• To detect fluorescent light signalTo detect fluorescent light signal

58586161

446 (blue)446 (blue)473 (blue)473 (blue)

388 (UV388 (UV--violet)violet)412 (violet) 412 (violet)

BlueBlue

70708181

611 (red)611 (red)446 (blue)446 (blue)

541 (green)541 (green)365 (UV) 365 (UV)

RedRed

4040509 (green)509 (green)469 (blue)469 (blue)GreenGreen

Stokes Stokes Shift Shift (nm)(nm)

Emission Maxima Emission Maxima (nm)(nm)Excitation Maxima (nm)Excitation Maxima (nm)ColorColor

Spectral Properties of Standard Fluorescent Spectral Properties of Standard Fluorescent MicrospheresMicrospheres ::


Diameter of Particle Images for MicroDiameter of Particle Images for Micro--PIVPIV

DiffractionDiffraction--limited limited spot size:spot size:

Effective size of the Effective size of the tracer particles: tracer particles:


OutOut--ofof--Plane Spatial Resolution for MicroPlane Spatial Resolution for Micro--PIVPIV

•• Conventional Conventional ““MacroMacro””--PIV measurements:PIV measurements:–– The light sheet illuminates only particles contained within the The light sheet illuminates only particles contained within the depth of focus of the depth of focus of the

recording lens, providing high quality inrecording lens, providing high quality in--focus particle images to be recorded with low focus particle images to be recorded with low levels of background noise being emitted from the outlevels of background noise being emitted from the out--ofof--focus particles. focus particles.

–– The outThe out--ofof--plane spatial resolution of the velocity measurements is definedplane spatial resolution of the velocity measurements is defined clearly by the clearly by the thickness of the illuminating light sheet.thickness of the illuminating light sheet.

•• MicroMicro--PIV measurements:PIV measurements:–– Due to the small length scales associated with Due to the small length scales associated with μμ--PIV, it is difficult if not impossible to PIV, it is difficult if not impossible to

form a light sheet that is only a few microns thick, and even moform a light sheet that is only a few microns thick, and even more difficult to align a light re difficult to align a light sheet with the object plane of an objective lens. sheet with the object plane of an objective lens.

–– It is common practice in It is common practice in μμ--PIV to illuminate the test section with a volume of light, and PIV to illuminate the test section with a volume of light, and rely on the depth of field of the lens to define the outrely on the depth of field of the lens to define the out--ofof--plane thickness of the plane thickness of the measurement plane.measurement plane.


OutOut--ofof--Plane Spatial Resolution for MicroPlane Spatial Resolution for Micro--PIVPIV

A typical MicroA typical Micro--PIV imagePIV image


Visibility of Particles tracersVisibility of Particles tracers

••For a given set of recording optics, particle For a given set of recording optics, particle visibility can be increased : visibility can be increased :

••By decreasing particle concentration, C, By decreasing particle concentration, C, ••By decreasing test section thickness, L.By decreasing test section thickness, L.

••For a fixed particle concentration, the visibility For a fixed particle concentration, the visibility can be increased by can be increased by

••By decreasing the particle diameter, By decreasing the particle diameter, •• By increasing the numerical aperture of By increasing the numerical aperture of the recording lens.the recording lens.

••Visibility depends only weakly on Visibility depends only weakly on magnification, and object distance, so.magnification, and object distance, so.


Effect of Brownian Motion on microEffect of Brownian Motion on micro--PIV measurementsPIV measurements

•• Brownian motion is the random thermal motion of a particle Brownian motion is the random thermal motion of a particle suspended in a fluid. The motion results from collisions betweensuspended in a fluid. The motion results from collisions betweenfluid molecules and suspended particles.fluid molecules and suspended particles.

•• The velocity spectrum of a particle due to Brownian motion The velocity spectrum of a particle due to Brownian motion consists of frequencies too high to be resolved fully and is consists of frequencies too high to be resolved fully and is commonly modeled as Gaussian white noise.commonly modeled as Gaussian white noise.

•• A quantity more readily characterized is the particleA quantity more readily characterized is the particle’’s average s average displacement after many velocity fluctuations. displacement after many velocity fluctuations.

•• For time intervals For time intervals ΔΔtt much larger than the particle inertial much larger than the particle inertial response time, the dynamics of Brownian motion are response time, the dynamics of Brownian motion are independent of inertial parameters such as particle and fluid independent of inertial parameters such as particle and fluid density.density.

•• The mean square distance of diffusion is proportional to The mean square distance of diffusion is proportional to DDΔΔtt, , where D is the diffusion coefficient of the particle.where D is the diffusion coefficient of the particle.

•• For a spherical particle subject to Stokes drag law, the diffusiFor a spherical particle subject to Stokes drag law, the diffusion on coefficient D was first given by Einstein (1905) as:coefficient D was first given by Einstein (1905) as:

Particle response time:Particle response time:

For 300 nm diameter polystyrene latex spheres immersed in water,For 300 nm diameter polystyrene latex spheres immersed in water, the particle response time is ~10the particle response time is ~10--99 s. s.

where where ddpp is the particle diameter, is the particle diameter, κκ is Boltzmann's constant, T is the absolute temperature of the is Boltzmann's constant, T is the absolute temperature of the fluid, and fluid, and μμ is the dynamic viscosity of the fluid.is the dynamic viscosity of the fluid.


Effect of Brownian Motion on microEffect of Brownian Motion on micro--PIV measurementsPIV measurements

•• The errors estimated by above Equations show that the relative The errors estimated by above Equations show that the relative Brownian intensity error decreases as the time of measurement Brownian intensity error decreases as the time of measurement increases. Larger time intervals produce flow displacements increases. Larger time intervals produce flow displacements proportional to proportional to ΔΔtt while the root mean square of the Brownian particle while the root mean square of the Brownian particle displacements grow as displacements grow as ΔΔtt1/21/2..

•• In practice, Brownian motion is an important consideration when In practice, Brownian motion is an important consideration when tracing 50 to 500 nm particles in flow field experiments with fltracing 50 to 500 nm particles in flow field experiments with flow ow velocities of less than about 1 mm/s. velocities of less than about 1 mm/s.

•• For a velocity on the order of 0.5 mm/s and a 500 nm seed particFor a velocity on the order of 0.5 mm/s and a 500 nm seed particle, the le, the lower limit for the time spacing is approximately 100 lower limit for the time spacing is approximately 100 μμss for a 20% error for a 20% error due to Brownian motion.due to Brownian motion.

•• This error can be reduced by both averaging over several partiThis error can be reduced by both averaging over several particles in a cles in a single interrogation spot and by ensemble averaging over severalsingle interrogation spot and by ensemble averaging over severalrealizations. realizations.

•• The diffusive uncertainty decreases as 1/The diffusive uncertainty decreases as 1/√√N, where N is the total number N, where N is the total number of particles in the averageof particles in the average


SaffmanSaffman effecteffect

•• Particles are found to intend to stay away from the Particles are found to intend to stay away from the regimes with high velocity gradient .regimes with high velocity gradient .

•• PoiseuillePoiseuille (1836) is generally acknowledged to be the first (1836) is generally acknowledged to be the first modern scientist who recorded evidence of particle modern scientist who recorded evidence of particle migration with his observations that blood cells flowing migration with his observations that blood cells flowing through capillaries tended to stay away from the walls of through capillaries tended to stay away from the walls of the capillaries. the capillaries.

•• Taylor (1955) scanned the crossTaylor (1955) scanned the cross--section of a tube section of a tube carrying a suspension and noticed areas of reduced cell carrying a suspension and noticed areas of reduced cell concentration not only near the walls, but also near the concentration not only near the walls, but also near the center of the channel. center of the channel.

•• SegrSegréé and Silberberg (1962) systematically performed and Silberberg (1962) systematically performed experiments that confirmed both observationsexperiments that confirmed both observations——migration migration away from the walls and migration away from the center away from the walls and migration away from the center of the channel and determined that migration rate was of the channel and determined that migration rate was proportional to the square of the mean velocity in the proportional to the square of the mean velocity in the channel as well as the fourth power of the particle radius. channel as well as the fourth power of the particle radius.

•• SaffmanSaffman (1965) analytically considered the case of a rigid (1965) analytically considered the case of a rigid sphere translating in a linear unbounded shear field. sphere translating in a linear unbounded shear field.

G :G : velocity gradientvelocity gradientVs :Vs : is slip velocityis slip velocityVmVm: migration velocity: migration velocity


Micro-PIV setup


Correlation averaging method:Correlation averaging method:

instantaneous PIV instantaneous PIV image pairimage pair

Averaged Velocity Averaged Velocity vectorsvectors

Instantaneous Instantaneous Correlation coefficient Correlation coefficient

distributiondistribution

averaging processingaveraging processingFind peak and subFind peak and sub--pixel pixel

interpolationinterpolationAveraged correlation Averaged correlation

coefficient distributioncoefficient distribution

Correlation averaging methodCorrelation averaging method

instantaneous PIV instantaneous PIV image pairimage pair

instantaneous instantaneous Velocity vectorsVelocity vectors

Averaged Velocity Averaged Velocity vectorsvectorsConventional method:Conventional method:

averaging processingaveraging processingFind peak and subFind peak and sub--pixel pixel interpolationinterpolation

Instantaneous Instantaneous Correlation coefficient Correlation coefficient

distributiondistribution

Correlation averaging methodCorrelation averaging method


Near Wall Flow Measurement Using MicroNear Wall Flow Measurement Using Micro--PIVPIV


Total Internal ReflectionTotal Internal Reflection

•• TIR occurs when nTIR occurs when n22 < n< n11 and and θθii > > θθcc

)/(sin2/

sinsin

121

1max2

1221

1

2

2

1

nnnn

nn

cri−=⇒=

>⇒>

=

ϕπϕϕϕ

ϕϕ


NanoNano--PIVPIV


NanoNano--PIVPIV

C. M. C. M. ZettnerZettner. and M. Yoda,. and M. Yoda,Experiments in Fluids (2002)Experiments in Fluids (2002)


A Study of Insulin Occlusion Using Insulin PumpA Study of Insulin Occlusion Using Insulin Pump

Objective lens

Dichroicmirror

Emitter filter

Mirror

Digital delay generator

CCD camera(SensiCam)

microchannel

Host computer

optics

Flexible tubing (I.D. 356μm)

Nd:Yag Laser

Beaker Insulin pump


MicroMicro--PIV Measurement ResultsPIV Measurement Results

-1

0

1

2

3

4

0 20 40 60 80 100 120 140 160 180 200

Time (s)

Mic

roch

anne

l cen

terli

ne v

elco

ity (m

m/s

)

300300μμmm

X (mm)

Y(m

m)

0 0.1 0.2 0.3 0.4 0.5

0

0.1

0.2

0.3

0.4

0.010 0.050 0.090 0.130 0.170 0.210 0.250

Velocity(mm/s)

Channel Wall

Channel Wall


MicroMicro--PIV Measurement ResultsPIV Measurement Results

X (mm)

Y(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

0.1

0.2

0.3

0.4

0.5

0.10 0.50 0.90 1.30 1.70 2.10 2.50 2.90 3.30Velocity(mm/s)

Channel Wall

Channel Wall

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