MicroPIV技术介绍 英文版_18页.pdf

8Micro-PIV8.1 IntroductionThere are many areas in science and engineering where it is importantto determine the flow field at the micron scale.Industrial applications ofmicrofabricated fluidic devices are present in the aerospace,computer,automotive,and biomedical industries.In the aerospace industry,for instance,micron-scale supersonic nozzles measuring approximately 35m are beingdesigned for JPL/NASA to be used as microthrusters on micro-satellites andfor AFOSR/DARPA as flow control devices for palm-size micro-aircraft 277.In the computer industry,inkjet printers,which consist of an array of noz-zles with exit orifices on the order of tens of microns in diameter,accountfor 65%of the computer printer market 277.The biomedical industry iscurrently developing and using microfabricated fluidic devices for patient di-agnosis,patient monitoring,and drug delivery.The i-STAT device(i-STAT,Inc.)is the first microfabricated fluidic device that has seen routine use in themedical community for blood analysis.Other examples of microfluidic devicesfor biomedical research include microscale flow cytometers for cancer cell de-tection,micromachined electrophoretic channels for DNA fractionation,andpolymerase chain reaction(PCR)chambers for DNA amplification 293.Thedetails of the fluid motion through these small channels,coupled with non-linear interactions between macromolecules,cells,and the surface-dominatedphysics of the channels create very complicated phenomena,which can bedifficult to simulate numerically.A wide range of diagnostic techniques have been developed for experi-mental microfluidic research.Some of these techniques have been designed toobtain the highest spatial resolution and velocity resolution possible,whileother techniques have been designed for application in nonideal situationswhere optical access is limited 287,or in the presence of highly scatter-ing media 280.Several of the common macroscopic full-field measurementtechniques have been extended to microscopic length scales.These are Scalar2428 Micro-PIVImage Velocimetry 467,Molecular Tagging Velocimetry469,as well asPIV,which at small length scales has become known as micro-PIV or PIV.In 1998 Santiago et al.297 demonstrated the first PIV system aPIV system with a spatial resolution sufficiently small enough to be able tomake measurements in microscopic systems.Since then the technique hasgrown in importance at a tremendous rate.As of 2007 there are well over 350PIV journal articles.Because of this large amount of activity,well over anorder of magnitude more than the previously described techniques combined,the remainder of this chapter will concentrate on PIV,its applications andextensions.The first PIV system was demonstrated measuring slow flows velocitieson the order of hundreds of microns per second with a spatial resolution of6.96.91.5m3297.The system used an epi-fluorescent microscope and anintensified CCD camera to record 300nm-diameter polystyrene flow-tracingparticles.The particles are illuminated using a continuous Hg-arc lamp.Thecontinuous Hg-arc lamp is chosen for situations that require low levels ofillumination light(e.g.,flows containing living biological specimens)and wherethe velocity is sufficiently small enough so that the particle motion can befrozen by the CCD cameras electronic shutter(figure 8.1).Koutsiaris etal.286 demonstrated a system suitable for slow flows that used 10m glassspheres for tracer particles and a low spatial resolution,high-speed videosystem to record the particle images yielding a spatial resolution of 26.2m.They measured the flow of water inside 236m round glass capillaries andfound agreement between the measurements and the analytical solution withinthe measurement uncertainty.Microscope lensLens(Intensified)CCD CameraNd:YAG LaserBeamExpanderEpi-fluorescentPrism/Filter Cube=532 nm=560nmMicrofluidicdeviceImmersion fluidFig.8.1Schematic of a PIV system.A pulsed Nd:YAG laser is used to illuminatefluorescent 200nm flow-tracing particles,and a cooled CCD camera is used to recordthe particle images.8.1 Introduction243Later applications of the PIV technique moved steadily toward fasterflows more typical of aerospace applications.The Hg-arc lamp was replacedwith a NewWave two-headed Nd:YAG laser that allowed cross-correlationanalysis of singly exposed image pairs acquired with sub-microsecond timesteps between images.At macroscopic length scales this short time step wouldallow analysis of supersonic flows.However,because of the high magnification,the maximum velocity measurable with this time step is on the order of metersper second.Meinhart et al.406 applied PIV to measure the flow fieldTable 8.1.Comparison of High-Resolution Velocimetry Techniques 288.TechniqueAuthorFlow Tracer Spatial Resolution Observation(m)LDATieu et al.5 5 1048 fringes limits(1995)velocity resolutionOpticalChen et al.1.7m5 15Can image throughDoppler(1997)polystyrenehighly scatteringtomographybeadsmedia(ODT)Optical flow Hitt et al.5m blood20 20 20In vivo study ofusing video(1996)cellsblood flowmicroscopyOptical flow Lanzillotto1 20m 20 40Can image withoutusing X-ray et al.(1996)emulsionoptical accessimagingdropletsUncagedPaul et al.Molecular100 20 20Resolution limited byfluorescent(1997)Dyemolecular diffusiondyesParticleBrody et al.0.9m 10Particle streakstreak(1996)polystyrenevelocimetryvelocimetrybeadsPIVUrushihara et al.1m oil280 280 200Turbulent flows(1993)dropletsSuper-Keane et al.1m oil50 50 200Particle trackingresolution(1995)dropletsvelocimetryPIVPIVSantiago et al.300nm6.9 6.9 1.5Hele-Shaw Flow(1998)polystyreneparticlesPIVMeinhart et al.200nm5.0 1.3 2.8Microchannel flow(1999)polystyreneparticlesPIVWesterweel500nm0.5 05 2.0Siliconet al.(2004)polystyrenemicrochannelparticlesflow2448 Micro-PIVin a 30m 300m(hightwidth)rectangular channel,with a flow rateof 50l/h,equivalent to a centerline velocity of 10mm/s.The experimentalapparatus,shown in figure 8.1,images the flow with a 60,NA=1.4,oil-immersion lens.The 200nm-diameter polystyrene flow-tracing particles werechosen small enough so that they faithfully followed the flow and were 150times smaller than the smallest channel dimension.A subsequent investigationby Meinhart&Zhang 291 of the flow inside a microfabricated inkjetprinter head yielded the highest speed measurements made with PIV.Usinga slightly lower magnification(40)and consequently lower spatial resolution,measurements of velocities as high as 8 m/s were made.Here,we will givean overview of PIV techniques and provide several application examples insection 9.8.2 Overview of Micro-PIVThree fundamental problems differentiate PIV from conventional macro-scopic PIV:The particles are small compared to the wavelength of the il-luminating light;the illumination source is typically not a light sheet butrather an illuminated volume of the flow;and the particles are small enoughthat the effects of Brownian motion must be considered.Three-Dimensional Diffraction Pattern.Following Born&Wolf 3,the intensity distribution of the three-dimensional diffraction pattern of apoint source imaged through a circular aperture of radius a can be written interms of the dimensionless diffraction variables(u,v)I(u,v)=?2u?2,U21(u,v)+U22(u,v)-I0(8.1)I(u,v)=?2n?2?1+V20(u,v)+V21(u,v)2V0(u,v)cos?12?u+v2u?2V1(u,v)sin?12?u+v2u?I0(8.2)where Un(u,v)and Vn(u,v)are called Lommel functions,which may beexpressed as an infinite series of Bessel functions of the first kind:Un(u,v)=+s=0(1)s?uv?n+2sJn+2s(v)Vn(u,v)=+s=0(1)s?vu?n+2sJn+2s(v)(8.3)8.2 Overview of Micro-PIV2452afzrLensParticledpGeometricShadowFig.8.2.Geometry of a particle with a di-ameter dp,being imaged through a circu-lar aperture of radius a,by a lens of focallength f(after 408).The dimensionless diffraction variables are defined as:u=2z?af?2,v=2r?af2(8.4)where f is the radius of the spherical wave as it approaches the aperture(whichcan be approximated as the focal length of the lens),is the wavelength oflight,and r and z are the in-plane radius and the out-of-plane coordinate,respectively,with the origin located at the point source(Figure 8.2).Although both,equation(8.2)and(8.2)are valid in the region near thepoint of focus,it is computationally convenient to use equation(8.2)withinthe geometric shadow,where|u/v|1 3.Within the focal plane,the intensity distribution reduces to the expectedresultI(0,v)=?2J1(v)v?2I0(8.5)which is the Airy function for Fraunhofer diffraction through a circular aper-ture.Along the optical axis,the intensity distribution reduces toI(u,0)=?sinu/4u/4?2I0.(8.6)The three-dimensional intensity distribution calculated from equation(8.2)and(8.2)is shown in figure 8.3.The focal point is located at the origin,theoptical axis is located at v=0,and the focal plane is located at u=0.The maximum intensity,I0,occurs at the focal point.Along the optical axis,the intensity distribution reduces to zero at u=4,8,while a localmaximum occurs at u=6.Depth of field.The depth of field of a standard microscope objectivelens is given by Inou e and Spring 14 as:z=n0NA2+neNA M(8.7)2468 Micro-PIVFig.8.3.Three-dimensional intensity distribution pattern expressed in diffractionunits(u,v),following Born&Wolf 3.The focal point is located at the origin,the optical axis is located along v=0,and the focal plane is located along u=0(after 3).where n is the refractive index of the fluid between the microfluidic device andthe objective lens,0is the wavelength of light in a vacuum being imaged bythe optical system,NA is the numerical aperture of the objective lens,M isthe total magnification of the system,and e is the smallest distance that canbe resolved by a detector located in the image plane of the microscope(forthe case of a CCD sensor,e is the spacing between pixels).Equation(8.7)is the summation of the depths of field resulting from diffraction(first termon the right-hand side)and geometric effects(second term on the right-handside).The cutofffor the depth of field due to diffraction(first term on the right-hand side of equation(8.7)is chosen by convention to be one-quarter of theout-of-plane distance between the first two minima in the three-dimensionalpoint spread function,that is,u=in figure 8.3 and equation(8.2)and8.2.Substituting NA=nsin=n a/f,and 0=n yields the first term onthe right-hand side of equation(8.7).If a CCD sensor is used to record particle images,the geometric termin equation(8.7)can be derived by projecting the CCD array into the flowfield,and then,considering the out-of-plane distance,the CCD sensor can bemoved before the geometric shadow of the point source occupies more thana single pixel.This derivation is valid for small light collection angles,wheretan sin=NA/n.Depth of correlation.The depth of correlation is defined as twice thedistance that a particle can be positioned from the object plane so that theintensity along the optical axis is an arbitrarily specified fraction of its focused8.2 Overview of Micro-PIV247intensity,denoted by.Beyond this distance,the particles intensity is suffi-ciently low that it will not influence the velocity measurement.While the depth of correlation is related to the depth of field of the op-tical system,it is important to distinguish between them.The depth of fieldis defined as twice the distance from the object plane in which the objectis considered unfocused in terms of image quality.In the case of volume-illuminated PIV,the depth of field does not define precisely the thickness ofthe measurement plane.The theoretical contribution of an unfocused particleto the correlation function is estimated by considering(1)the effect due todiffraction,(2)the effect due to geometric optics,and(3)the finite size of theparticle.For the current discussion,we shall choose the cutofffor the on-axisimage intensity,to be arbitrarily one-tenth of the in-focus intensity.Thereason for this choice is that the correlation function varies like the intensitysquared so a particle image that with one-tenth the intensity of a focusedimage can be expected to contribute less than 1%to the correlation function.The effect of diffraction can be evaluated by considering the intensity of thepoint spread function along the optical axis in equation(8.6).If?=0.1,thenthe intensity cutoffwill occur at u 3.Using equation(8.4),substitutingz=2z,and using the definition of numerical aperture,NA nsin=na/f,one can estimate the depth of correlation due to diffraction as:cg=3n0NA2(8.8)The effect of geometric optics upon the depth of correlation can be esti-mated by considering the distance from the object plane in which the intensityalong the optical axis of a particle with a diameter,dp,decreases an amount,=0.1,due to the spread in the geometric shadow,that is,the lens col-lection cone.If the light flux within the geometric shadow remains constant,the intensity along the optical axis will vary as z2.From figure 8.3,if thegeometric particle image is sufficiently resolved by the CCD array,the depthof correlation due to geometric optics can be written for an arbitrary valueof?as:zcd=(1?)dp?tanfor dpeM(8.9)Following the analysis of Olsen&Adrian 294,295 and using equa-tion(2.22),the effective image diameter of a particle displaced a distance zfrom the objective plane can be approximated by combining the effective im-age diameter dwith a geometric approximation to account for the particleimage spreading due to displacement from the focal plane to yieldd=?M2d2p+1.49(M+1)22?nNA?2 1?+?MDazso+z?2?12(8.10)where sois the object distance and Dais the diameter of the recording lensaperture.2488 Micro-PIVThe relative contribution of a particle displaced a distance z from thefocal plane,compared to a similar particle located at the focal plane can beexpressed in terms of the ratio of the effective particle image diameters raisedto the fourth power=?d(0)d(zcorr)?4(8.11)Approximating D2a/(so+z)2 D2a/s2o=4(n/NA)2 11,combining equa-tion(8.10)and(8.11),and solving for zcorryields an expression for the depthof correlationzcorr=?1?d2p(n/NA)214+1.49(M+1)22(n/NA)2124M2?.12(8.12)From equation(8.12)it is evident that the depth of correlation zcorrisstrongly dependent on numerical aperture NA and particle size dpand isweakly dependent upon magnification M.Table 8.2 gives the thickness ofthe measurement plane,2zcorr,for various microscope objective lenses andparticle sizes.The highest out of plane resolution for these parameters is2zcorr=0.36m for a NA=1.4,M=60 oil-immersion lens and particlesizes dp/2 from the object plane as being completely unfocused andcontributing uniformly to background intensity,while particles located withina distance|z|/2 as being completely focused,the total flux of backgroundlight JBcan be approximated byJB=AvC?2aJ(z)dz+?La2J(z)dz?,(8.18)where C is the number of particles per unit volume of fluid,L is the depthof the device,and Avis the average cross sectional area contained within thefield of view.Combining equation(8.14)and(8.18),correcting for the effect ofmagnification,and assuming so?/2,the intens