Fluorescent particle image velocimetry: application to flowmeasurement in refractive index-matched porous media

M. Allen Northrup, Thomas J. Kulp, and S. Michael Angel

This paper presents results in which particle image velocimetry (PIV) is used in conjunction with refractiveindex matching to measure fluid flow velocities within complex, multiphase systems. This applicationrequired the adaptation of PIV for use with fluorescent, rather than scattering, seed particles; we refer to thetechnique as fluorescent PIV (FPIV). We applied index-matched FPIV to the measurement of low flowvelocities (tens of microns per second) at high spatial resolution (tens of microns) in a porous medium. Weproduced clear images of flowing particles in heterogeneous porous media and obtained reliable velocityvectors by a point-by-point interrogation of these images. We also found evidence of the intrapore mixing ofporous media flow.

Key words: Particle image velocimetry, PIV, fluorescence imaging, porous media flow, refractive indexmatching.

1. Introduction

The noninvasive measurement of fluid flow veloci-ties within complex, multiphase media is an importantexperimental problem in many fields of research. Ofthe methods that exist to measure fluid velocity, theleast invasive are those based on optical detection.These include laser Doppler velocimetry (LDV) andparticle image velocimetry (PIV). Optical measure-ments within a heterogeneous matrix are difficult,however, because there is usually no clear optical pathto the measurement zone. For LDV, this problem hasbeen overcome using two techniques: refractive indexmatching and fiber optic sensing. In the former ap-proach, a model of the system to be studied is con-structed of materials that have identical refractiveindices. This renders the entire system transparent,allowing direct optical probing of any internal point.In the latter approach, light used in the measurementis conducted to and from the zone of interest via anoptical fiber. That method has been applied to mea-suring blood flow.1'2 To date, there have been nosimilar efforts to apply PIV to mixed-phase media.Thus, we have undertaken an effort to adapt PIV touse in refractive index-matched media. This paperpresents the first of our results in this area.

Our motivation for this work is the need to perform

The authors are with Lawrence Livermore National Laboratory,Environmental Sciences Division, P.O. Box 5507, L-524, Livermore,California 94550.

Received 24 June 1990.0003-6935/91/213034-07$05.00/0.© 1991 Optical Society of America.

experiments that will lead to a better understanding offluid and solute flow in porous media. This knowledgeis necessary for the prediction of the movement ofchemical contaminants in soils, as well as for the eluci-dation of the behavior of other systems that can bemodeled by porous medium physics. Velocity deter-minations within these systems are central to the em-pirical verification of the theories on which these mod-els are based. Equations of bulk transport aretypically generated by spatially averaging small-scaletransport equations over representative volumes of themedium, which may include several pore regions. Be-cause of the difficulty of making measurements inporous media, there is a scarcity of experimental obser-vations of flow at subpore dimensions. Thus, in thederivation of bulk transport equations, modelers areoften forced to make assumptions regarding micro-scale processes, and there is a need for measurementsthat can be used to test these assumptions.

The nature of the microscopic flow in porous mediadictates the type of measurement method that is need-ed. To be useful, the data must be collected on thespatial scale of a fraction of a millimeter, with velocityresolutions on the order of tens of microns per second.Because a number of important processes (such asdispersion) originate from the temporal and spatialvariations of the velocity field, it is important that thevelocity be determined simultaneously at many pointswithin the flow field. Thus, although LDV has beendemonstrated in a non-refractive index matched po-rous medium; and in a number of refractive index-matched systems, including packed beds of Plexiglasspheres4 and Pyrex spheres,' and test sections of Pyrex

3034 APPLIED OPTICS / Vol. 30, No. 21 / 20 July 1991

rods,6 it does not meet the requirement for an instanta-neous snapshot of the entire flow field. Particle imagevelocimetry is well suited to this task because it can beused to measure low velocities at high spatial andtemporal resolutions.

To apply PIV to measurements in index-matchedmedia, some adaptations to the technique were re-quired. Problems with residual scattering in the me-dium were overcome through the use of fluorescent,rather than scattering, seed particles. We refer to thisadaptation as fluorescent particle image velocimetry(FPIV). In the remainder of the paper, this FPIVtechnique is described, and results of measurements offlow fields in porous media in gravitational, saturatedflow conditions are presented. This presentation in-cludes data that demonstrate the subpore level mixingof flow streams in porous media. The ramifications ofthis unsteady flow on the general PIV technique as wellas the advantages and limitations of the method arediscussed.

11. Particle Image Velocimetry: Background

In recent years, a number of velocity measurementtechniques have emerged that are based on the imag-ing of particle motion. These are particle image velo-cimetry (PIV), particle tracking velocimetry (PTV),and laser speckle velocimetry (LSV). The work de-scribed in this paper concerns only PIV; however, thebackground discussion includes reference to all thesemethods.

Particle image velocimetry is an imaging techniquethat allows the simultaneous measurement of instan-taneous velocities at all points with a 2-D slice througha flowing medium. To acquire PIV images, it is neces-sary that the fluid in motion be seeded with micron-sized particles. An instantaneous image of all theparticles in the measurement plane is produced byilluminating that area with a rapidly flashed sheet oflaser light. To obtain velocity information the laser ispulsed two or more times, creating a multiple exposureimage in which the positions of the moving particlesare recorded photographically where they appear onthe film as pairs or multiple spots. The separation ofthe spots is a measure of the distance traveled by theparticles between the light pulses. In regions withuniform flow, particle separations are nearly identical,and the particle images are correlated.

The multiple exposure photograph is then processedinto a high contrast transparency. Analysis is per-formed via a point-by-point interrogation of the trans-parency with a collimated laser beam. When the co-herent light of the laser strikes a correlated area, theparticle images act as point sources of light whoseillumination is projected on a screen to produce aninterference pattern (Young's fringes). The degree ofcorrelation within the interrogation area is critical toobtaining a clear fringe pattern. The angle and thedistance between the fringes are a measure of the angleand distance between an average pair of particles.This information, along with the time between film

exposures, is used to calculate the velocity vector of thefluid flow within each interrogation point. The resultis a matrix of spatially averaged measurements, each ofwhich represents flow in the region of the transparencyprobed by the spot size of the laser beam.

The first application of PIV to fluids involved theanalysis of Poiseuille flow.7-9 It has subsequentlybeen applied to Rayleigh-Benard fluid flow,'0 thermalconvection in fluids,"1 swirling fluid flow,'2 and un-steady gas flow.'3 Many recent papers on the PIVtechnique have been concerned with improving theprocessing of the images produced in the flow record-ings.'423 To obtain optimal performance of PIV in arefractive index-matched heterogeneous system, wecarefully optimize a number of experimental condi-tions, including the temperature, the purity and com-position of the index-matching fluid, and the cleanli-ness of all the surfaces in the test-bed. Temperaturecontrol is particularly important for tuning the refrac-tive index of the solid and liquid phases to match at thedesired wavelength. Optimization of these parame-ters is necessary to obtain undistorted photographicimages of the flowing particles.

Ill. Experimental Setup

A. Experimental Apparatus

The experimental apparatus is shown in Fig. 1. A 5-W Ar-ion laser (Coherent, Inc., Innova model 90) was

Mechanical shutter

cylindricalIMicrocomputer

aser beam

35 mm camera

bed

Fig. 1. Experimental apparatus used to obtain PIV photographs ina test-bed of porous media, consisting of a 5-W Ar-ion laser, mechan-ical shutter, microcomputer, beam expander, plano-cylindricallenses, and porous medium test-bed.

20 July 1991 / Vol. 30, No. 21 / APPLIED OPTICS 3035

1o-4.3 cm--4)a

_ ) _n0 LZ0

cc 0

80

60

40

20

o .,480 500 520 540 560 580

Wavelength (nm)Fig.2. Emission spectra of 10-,um fluorescent particles in water andin refractive index-matching fluid. The excitation wavelength was457 nm.

used to illuminate the fluorescent particles in the test-bed at a wavelength of 457 nm with a power output of-400 mW. A beam expander and two plano-cylindri-cal lenses were used to create a 5-cm high by 1-mmthick sheet of light within the refractive index-matched medium. Fluoresbrite particles (Polysci-ences, Inc.), 10-,Mm in diameter, with a specific gravityof 1.00 at 250C and with an excitation maximum at 458nm and an emission maximum at 518 nm were driedand resuspended in a refractive index-matching fluid[27% by weight L42 organosilicone fluid (Union Car-bide Co.) and 73% by weight 550 fluid (Dow ChemicalCo.)], previously described by Dybbs and Edwards.5The refractive index of the fluid at the sodium D linewas measured using a refractometer (Bausch & Lomb,model ABBE-3L) and was found to be 1.4905 at13.80 C. Its specific gravity (1.06 at 250 C) is onlyslightly higher than that of the fluorescent particles,resulting in a stable suspension of the particles in thefluid. It was determined that the fluorescent particleshad no effect on the refractive index of the fluid.

A schematic of the porous medium test bed is shownin Fig. 2. The test-bed consists of a polymethyl meth-acrylate (PMMA) cell that has a cylindrical 4.3-cm i.d.internal cavity and a 5.2-cm square outer shape. Theflat outer walls of the cell allow the normal incidencelaser sheet to enter the system without being refracted.The cylindrical inner volume of the cell is randomlypacked with 9.4-mm diam PMMA balls (Spex Indus-tries), having a refractive index of 1.4905. The inter-nal cylindrical portion of the cell was extended 20 cmbeyond the top of the test-bed to form a reservoir thatwas filled with enough fluid to create a sufficient gravi-tational head pressure to cause flow. Optimal indexmatching was accomplished by immersing the test-bedin a water bath that was maintained at 13.8° 4 0.10 Cusing a recirculating water cooler (model C750, LineLite Laser Corp.).

All the photographs were taken with a Nikon N200035-mm camera with an f/2.8,55-mm Micronikkor lens.The fluorescent emission was isolated from the excita-

5.2 cm -.1

Fluidreservoir

20.0 cm

10.9 cm

l::: - ::::: :

,- _ Nt i Planar laserbeam

3i

7-4 T

DrainFig. 3. Schematic of a porous medium test-bed including 9.4-mmdiam PMMA beads, PMMA flow cell, refractive index-matchingfluid seeded with fluorescent particles, and a planar laser beam.

tion light using a 5-cm round, narrow bandpass filter(515 + 1 nm) mounted on the front of the camera. Asshown in Fig. 3, the emission band of the fluorescentparticles is broad (over 70 nm). Thus, only a smallfraction (passing through the narrow bandpass filter)of the emission is utilized in forming an image. It canalso be seen from Fig. 3 that the fluorescent propertiesof the particles remained unchanged after the particleswere dried and resuspended in the refractive index-matching fluid. The camera shutter was left openduring the exposure of the film while the laser beamwas gated with a computer-controlled shutter. KodakTMAX 3200 ASA, black-and-white film was used torecord the images. The film was developed (TMAXdeveloper) for 8.5 min at 240 C. The transparencieswere made using an automatic Jobo drum processor,and contact printed on high contrast black-and-whitefilm with a continuous tone processor. The 514-nmline of an air-cooled Ar-ion laser (model 530, Omnich-rome) was used to probe the images using a power of<10 mW. The interrogation area was -1 mm2 with aparticle density of -8-10 particles/mm2 within thearea of the film. Young's fringes produced by the laserinterrogation beam were projected on a screen. Thefringe distances and angles were measured directlyfrom the projected fringe images. The resultant vec-tor fields were compared to projected images of theFPIV photograph to identify any errors in the record-ing process.

3036 APPLIED OPTICS / Vol. 30, No. 21 / 20 July 1991

ax-

1 0 0

L

B. Index-Matching Optimization

The use of fluorescent particles along with properrefractive index matching in the present work allowedus to obtain clear PIV images of the flowing fluid in theporous medium test-bed. In our first attempts atmaking PIV measurements in the index-matched sys-tem, nonfluorescent tracer particles were used. Inthese tests we found that scattering from the materialswithin the cell was comparable to the intensity ofparticle scattering, making it difficult to obtain clearPIV images. It is probable that the index matchingdid not fully eliminate scattering due to inhomogenei-ties within the PMMA material that was used. It islikely that the use of higher grade materials (i.e., opti-cal glass) would reduce scattering. However, insteadof using higher grade materials, we decided to usefluorescent particles and wavelength selective filters.The filters allow rejection of the scattered laser light,resulting in an image of the wavelength-shifted parti-cle fluorescence. In this method, an efficient band-pass filter centered at the particle emission band isplaced over the camera lens to transmit the particlefluorescence signal and reject unwanted scatter.

In performing PIV using fluorescent particles, thedegree of index matching at both the excitation andemission wavelengths must be considered. For thisstudy, the dispersion of the PMMA/silicone fluid mix-ture precluded the possibility of creating an optimalmatch at both wavelengths, making it necessary toselect between the two. We decided in favor of match-ing for the emission to eliminate distortion of the parti-cle images. As a result, nonmatched conditions at theexcitation wavelength caused some minor scatteringand distortion of the planar laser beam. This would bedetrimental if it caused the illumination of particlesoutside the intended measurement plane or the cre-ation of excess background light. No significant evi-dence of the former problem was found. The effects ofthe latter were eliminated by the narrow bandpassfilter on the camera, which passed only the fluores-cence wavelength. The filter also eliminated scatter-ing that was generated within the beads by refractiveindex inhomogeneities of the PMMA itself. However,the use of the narrow (1-nm bandpass) filter caused asignificant loss of fluorescence signal; the emissionbandwidth of the particles is over 70 nm. This narrowbandpass was necessary because the filter also servedto reject a uniform background emission that was gen-erated by fluorescence in the index-matching fluid.Trials with a 10-nm bandpass filter resulted in lowerimage contrast because of the collection of more back-ground fluorescence.

The optimal index-matching conditions at the emis-sion wavelength were determined by adjusting thetemperature of the medium. The degree of matchingwas estimated by observing the distortion of a planarlaser beam using the 514-nm Ar-ion laser line as itpassed through the test bed (514 nm is approximatelythe wavelength of the particle emission). The tem-perature of the water bath was adjusted until the mostuniform profile was obtained. To confirm that subtle

image distortions did not affect the PIV data, a gridcomposed of a mesh of fine wires (70-nm diameter) wasphotographed through the medium under 514-nm la-ser illumination. No evidence of distortions to thegrid pattern was detected. Once the system was set atthe proper temperature, the laser was retuned to theexcitation wavelength (457 nm) for the subsequentPIV experiments.

IV. Results and Discussion

Figure 4 shows a double exposure photograph of theflowing fluorescent particles in the porous media testbed. The flow direction in this and all other photo-graphs is from top to bottom. The dark round areascorrespond to the location of the PMMA beads. Evi-dence of flow as indicated by correlated particle imagesis readily observable within the pore spaces. Thisphotograph was taken with a shutter delay time of 10 sand an exposure time of 50 ms. The volumetric flowrate of the fluid in the column was 11,liter/s. Figure 5shows the corresponding velocity vectors obtainedfrom an analysis of Fig. 4. Attempts to measureYoung's fringes were performed at each point in a gridof locations that were spaced at 1-mm intervals in thehorizontal and vertical directions spanning the 35-mmtransparency. It was not, however, possible to obtainusable fringes at every position in this grid. This canbe attributed to a number of factors, including locallyinsufficient particle density, the lack of appreciableparticle movement during the delay time, or the lack ofsufficiently correlated flow. For the data shown inFig. 4, it may be noted that the particle density in thisexperiment was somewhat low (10 particles/mm 2 )

Fig. 4. Double exposure PIV photograph of 10-,um fluorescentparticles in a test-bed of porous medium: shutter delay time 10 s,exposure time 50 ms, excitation wavelength 457 nm, volumetric flowrate 11 uliter/s.

20 July 1991 / Vol. 30, No. 21 / APPLIED OPTICS 3037

9 mmSpatial scale: -i Spaia scle

Velocity scale: (i = 50.0 pm/sec

Fig. 5. Vector field diagram obtained from Young's fringe methodof analysis of transparency in Fig. 4. The analysis pattern consistedof a 20-mm by 20-mm grid interrogated at 1-mm intervals by acollimated laser beam at a wavelength of 514 nm.

but is within the range that allows the use of theYoung's fringe method of analysis. 2 4 However, as wewill discuss, the complexity of the flow in this systemmay also lead to a reduction in local correlation at theprobe dimension used in this study.

Over 100 vectors were obtained from Fig. 4, rangingin magnitude from 5 to 70 Mm/s. Given the 10-s shut-ter delay time and the 25-um apparent particle diame-ter, the minimum flow velocity that could be measuredwas -2.5,Mm/s. The minimum and maximum measur-able vectors can, of course, be modified by changingthe delay time between illumination pulses. Figure 6contains a vector field that was generated by a higherresolution interrogation of the area within the squareshown in Fig. 5. Here, over seventy-five vectors wereproduced by measurements spaced in 0.5-mm incre-ments across the same transparency used to generateFig. 5. These vectors spanned a range of 8-60 Mm/s inmagnitude. The vector flow field results (Figs. 5 and6) were compared directly to the projected image ofFig. 4. From these comparisons, <10% of the vectorsobtained appeared to result from erroneous Young'sfringes. They were subsequently eliminated from thediagram of the flow field.

Figure 7 contains a 2.5-X enlargement of an FPIVphotograph that was obtained under conditions simi-lar to those previously described. Given this enlarge-ment factor and the fact that the particle density wasincreased by a factor of -3 over that in Fig. 4, the

Velocity scale: ( = 54.0 pm/sec

Fig. 6. Vector field diagram obtained from Young's fringe methodof analysis of the section of the Fig. 4 transparency outlined in Fig. 5.The analysis pattern consisted of a 5-mm by 5-mm grid interrogatedat 0.5-mm intervals by a collimated laser beam at a wavelength of 514nm.

Fig. 7. Enlargement (2.5X) of the double exposure PIV photographof 10-/im fluorescent particles in a test-bed of porous media withshutter delay time 11 s, exposure time 50 ms, excitation wavelength457 nm, and volumetric flow rate 10 uliter/s.

3038 APPLIED OPTICS / Vol. 30, No. 21 / 20 July 1991

5 mmSpatial scale: | - i

Velocity scale: = 50.0 pm/sec

Fig. 8. Vector field diagram obtained from Young's fringe methodof analysis of the Fig. 7 transparency. The analysis pattern consist-ed of a 20-mm by 20-mm grid interrogated at 0.5-mm intervals by acollimated laser beam at a wavelength of 514 nm.

resultant particle density is about the same in bothanalyses. Over 130 vectors were obtained from thephotograph in Fig. 7. In areas of clearly visibleYoung's fringes, the same range of velocity vector mag-nitudes was obtained as in Fig. 6. These data are ofinterest because they illustrate the complex flow pat-terns that are encountered within a porous medium.From the measured vector field (Fig. 8), it is readilyapparent that, in some locations, the direction of flowvaries greatly from one point to another. The lack ofparticle correlation in certain sections of this FPIVexperiment may be attributed to the mixing of theintrapore flow streams that is evident in Fig. 7. As aresult of this complicated behavior, some difficultieswere encountered in analyzing this slide by theYoung's fringe method. In certain regions, so muchvariation in flow direction and magnitude occurredwithin the area of the probe laser spot that the result-ing fringe pattern was unreadable. It should be possi-ble to reduce this problem by careful optimization ofthe particle density and laser spot size (or image mag-nification) so that only well-correlated particle imagesare present within the probe area. Alternatively, itmay be possible to analyze the degraded fringe pat-terns to obtain some quantification of the variation ofvelocity within a region. This is of particular interestbecause it is an important factor in porous mediumdispersion. A statistical method to extract this type of

information has been developed by Hinsch et al.2 1,22 intheir attempts to analyze data obtained in unsteady orturbulent gas flows. We anticipate the use of thismethod in our further investigations. Also, applica-tion of velocity ambiguity removal techniques23 mayhelp to increase spatial resolution and provide resultsin areas of turbulent flow. Other future work willinclude reducing the dimensions of the porous mediato closer approach true groundwater flow regimes,higher resolution flow analyses, and specific chemicalspecies flow studies.

V. Conclusions

The results of the experiments described above aresignificant because they demonstrate that the combi-nation of refractive index matching and the FPIVmethod can be used to quantitatively image velocityfields in the interstitial regions of complex media. Inapplications to porous media flow, this methodologywill allow the instantaneous determination of intersti-tial velocity fields and the subsequent direct spatialaveraging of these fields. This will be an importanttool for the verification of fundamental equations oftransport in multiphase systems.

Some of the challenges facing the further use of theFPIV methodology include determining the optimalparticle density to obtain velocity vectors in areas ofhighly mixed flows, and the application of statisticalmethods to determine the degree of spatial correlationin small areas. Combining large area interrogationtechniques21 22 with the FPIV method or using otherimaging techniques, such as particle streak imaging,25

may provide solutions to the challenges encounteredwhen trying to measure flow in porous systems. Theauthors are presently exploring these techniques toresolve the mixed nature of the flow in heterogeneousporous media.

The authors would like to recognize John Blunden ofthe LLNL Technical Information Department for hisexpertise in film processing. This research was fund-ed by the Subsurface Science Program, Office ofHealth and Environmental Research, U.S. Depart-ment of Energy, under the direction of Frank Wobber.The work was performed under the auspices of the U.S.Department of Energy at Lawrence Livermore Na-tional Laboratory under contract W-7405-Eng-48.

When this work was done M. A. Northrup was aPh.D. candidate in the Biomedical Engineering Groupof the University of California at Davis.

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