visualization of particle behavior within a porous medium

Visualization of particle behavior within a porous medium:

Mechanisms for particle filtration and retardation

during downward transport

Joon Sik Yoon,1 John T. Germaine,1 and Patricia J. Culligan2

Received 17 September 2004; revised 29 December 2005; accepted 1 March 2006; published 21 June 2006.

[1] A technique for visualizing particle transport in the interior of a porous medium ispresented. The technique, which includes the construction of a translucent medium andthe use of laser-induced fluorescence for particle tracking, was used to examine thebehavior of a dilute suspension of negatively charged, micron-sized particles in the interiorof uniform glass bead packs during one-dimensional, downward flow. Particle behavior asa function of pore fluid velocity and bead surface roughness was observed at both themacroscopic and microscopic levels. Experimental results show that particle filtrationoccurred only at solid-solid contact points (contact filtration) in smooth bead packs, whileparticle filtration occurred at the top of bead surfaces (surface filtration) as well as atsolid-solid contact points in rough bead packs. Particle contact filtration was the result ofphysical straining at solid-solid contact points, while surface filtration was the result ofparticles interlocking on surface asperities. In both smooth and rough bead packs thefiltration capacity of the medium decreased with the pore fluid velocity. In smooth beadpacks the filtration capacity was approximately invariant with transport distance, while inthe rough bead packs the filtration capacity showed a decrease with transport distance.This decrease was attributed to the early surface filtration of larger particles as a result ofgravitational sedimentation. The accumulation of reversibly attached particles wasobserved even when particle pore fluid concentrations were stable.

Citation: Yoon, J. S., J. T. Germaine, and P. J. Culligan (2006), Visualization of particle behavior within a porous medium:

Mechanisms for particle filtration and retardation during downward transport, Water Resour. Res., 42, W06417,

doi:10.1029/2004WR003660.

1. Introduction

[2] Understanding particle transport in porous media isimportant to a number of problems involving subsurfaceflow and transport, water and wastewater treatment and soilpedology. For example, colloid particles, which are opera-tionally defined as particles between 1 to 10 nm and 2 to10 mm in diameter [e.g., Stumm, 1992; Buffle and Leppard,1995], are thought to facilitate the subsurface migration ofboth organic and inorganic contaminants [Penrose et al.,1990; Ryan and Elimelech, 1996; McCarthy et al., 1989].The subsurface transport of viruses, bacteria and protozoasuch as Cryptosporidium parvum, a spherical shape oocystwith an average diameter of 5 mm, also exhibit features ofparticle transport [Harter et al., 2000]. Indeed, initial studiesof particle mobilization and transport in porous media werefocused on microbial contaminants in aquifers [McCarthyand McKay, 2004]. In water and wastewater treatment,filtration through granular media is extensively used toremove micron-sized particles from liquid input streams[Aim et al., 1997]. In Europe, riverbank filtration, a process

whereby river water is drawn through adjacent soil riverbanks before extraction for drinking water, has been usedfor almost a century to remove water-borne contaminants,including pathogens and natural organic matter [Kuehn andMueller, 2000]. Riverbank filtration is now under evaluationfor water treatment in the United States [Tufenkji et al.,2002; Weiss et al., 2003]. In the field of soil pedology, theformation of argillic horizons is attributed to the transloca-tion of dilute clay suspensions [Hopkins and Franzen,2003]. Finally, ‘‘functionally intelligent’’ particles withsizes in the submicron to micron range are being consideredas possible aids to subsurface characterization and remedi-ation [Mackay and Gschwend, 2001].[3] The migration behavior of particles in porous media is

complex. Factors influencing this behavior include theparticle density, size and surface chemistry, the waterchemistry, the interstitial velocity, and the characteristicsof the porous medium [Shellenberger and Logan, 2002;Scholl and Harvey, 1992; Ryan and Gschwend, 1994;Bradford et al., 2002]. In the case of biological particles,motility, chemotaxis, growth and decay are also influential[Scheibe and Wood, 2003].[4] Conceptual models for particle behavior in a porous

medium usually assume that particles are affected by thesame physical processes that influence solute transport in aporous medium, namely advection, hydrodynamic disper-sion and mass transfer between the aqueous and solidphases within the medium [Bradford et al., 2002]. Particle

1Department of Civil and Environmental Engineering, MassachusettsInstitute of Technology, Cambridge, Massachusetts, USA.

2Department of Civil Engineering and Engineering Mechanics, Colum-bia University, New York, New York, USA.

Copyright 2006 by the American Geophysical Union.0043-1397/06/2004WR003660$09.00

W06417

WATER RESOURCES RESEARCH, VOL. 42, W06417, doi:10.1029/2004WR003660, 2006

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mac2

Placed Image

transfer from the aqueous to the solid phase in a medium iscommonly referred to as particle attachment, while particletransfer from the solid phase to the aqueous phase iscommonly referred to as particle detachment. Under cleanbed conditions, where the fraction of the solid phasecovered by particles is small, theoretical models for particlefate and transport generally adopt the so-called ‘‘clean bedfiltration theory’’ [see Yao et al., 1971] and assume thatparticle attachment and detachment obey first-order ratelaws; that is, the particle attachment rate varies with theparticle concentration in the pore fluid, while the particledetachment rate varies with the particle concentration on thesolid phase [Saiers et al., 1994a, 1994b; Yan, 1996]. Anexample of a one-dimensional, macroscopic model forparticle fate and transport that assumes first-order kineticsand both irreversible and reversible site for particle attach-ment is [Hendry et al., 1997]

@C

@tþ @S

@t¼ D

@2C

@z2� u

@C

@zð1Þ

@S

@t¼ @Sirr

@tþ @Sr

@t¼ kirr;attC þ kr;attC � kr;detSr ð2Þ

where C is the particle concentration in the pore fluid, S isthe particle concentration on the solid phase, D is thelongitudinal hydrodynamic dispersion coefficient, u is theaverage steady state pore fluid velocity, z is the distancefrom the particle injection point, Sirr is the ‘‘irreversibly’’attached particle concentration, Sr is the ‘‘reversibly’’attached particle concentration, kirr,att is the particleattachment rate at irreversible sites, kr,att is the particleattachment rate at reversible sites and kr,det is theparticle detachment rate at reversible sites. Note, S hasbeen defined as the mass of particles per pore volume. (1)and (2) assume no particle growth or decay.[5] Following the clean bed filtration theory, rate coef-

ficients, such as those presented in (2), are normallyassumed to be constants dependent upon particle-solidinteraction energies and system physics [Bergendahl andGrasso, 2000]. A common theoretical expression for kirr,attis [Logan et al., 1995]

kirr;att ¼3 1� nð Þ2d50

ahu ð3Þ

where h is the so-called collector (solid phase) efficiency, ais the particle sticking efficiency, the product ah is thefiltration capacity of the medium, n is the porosity of themedium and d50 is the average grain size of the medium. h,a parameter that accounts for the fraction of particles thatare brought into contact with the solid phase by themechanisms of diffusion, interception and gravitationalsedimentation, is frequently estimated using a modelproposed by Rajagopalan and Tien [1976],

h ¼ 4A1=3s N

�2=3Pe þ AsN

�1=8Lo N

15=8R þ 0:00338 AsN

1:2G N�0:4

R ð4Þ

where As is the Happel correction factor, NPe is the Pecletnumber, NLo is the London-van der Waals attractive forcesnumber, NR is the interception number and NG is the

gravitational number. The value of a is either obtainedexperimentally [Bradford et al., 2002] or estimated usingDLVO theory [Derjaguin and Landau, 1941; Verwey andOverbeek, 1948] or extended DLVO theory [Yotsumoto andYoon, 1993].[6] Many column tests have been performed to investi-

gate particle fate and transport in porous media underdifferent conditions. A considerable body of this work hasused observations of particle concentration at a columnoutlet, namely particle breakthrough curves (BTCs), toexamine how particle behavior varies with pore fluid velocity[e.g., 2001], pore fluid chemistry [e.g., Kretzschmar andSticher, 1998; Franchi and O’Melia, 2003], particle shape,size and concentration [e.g., Elimelech and O’Melia, 1990;Bradford et al., 2002] and porous medium heterogeneity[e.g., Harvey et al., 1993; Johnson et al., 1996]. Work in thisarea has demonstrated, for example, that the concentration ofparticles that become irreversibly attached during transportthrough a porous medium decreases with the pore fluidvelocity, but increases with the pore fluid ionic strength andthe ratio of the particle size to the average grain diameter ofthe medium. Another body of work [e.g.,Harter et al., 2000]has gone further and examined spatial trends in particlebehavior within the interior of a porous medium. Here,interior concentrations of attached particles were obtainedby destructive sampling of the column at the end of anexperiment. Results acquired using this approach have de-finitively proven that irreversible particle attachment ratescan decrease with particle transport distance, contradictingtheoretical assumptions of a spatially constant attachmentrate, as described by (3). In the microbial transport literature,observations of spatially dependent particle attachment rateshave been attributed to theoretical distributions in the surfaceproperties of microbes, leading to distributions in particle-solid interaction energies, and hencea, among the population[Albinger et al., 1994; Baygents et al., 1998; Simoni et al.,1998; Bolster et al., 1999, 2000; Redman et al., 2001]. Inthe nonmicrobial literature, hypotheses put forward haveincluded distributions in interaction energies [Li et al., 2004]as well as distributions in particle size [Bradford et al., 2002].[7] Although considerable insight has been gained from

experimental programs that have monitored particle break-through concentrations at a fixed transport distance and/orprofiled particle concentrations at a given transport time,work of this nature cannot resolve, in real time, theprocesses governing particle transport in the interior of aporous medium. This limits the understanding that can begained from these experimental approaches. In order tofurther understanding of the processes governing particlefate and transport in porous media, alternative methods thatinvolve visualization studies of particle behavior within aporous medium are needed.[8] This paper presents an experimental technique that we

have developed for visualizing particle transport in theinterior of a porous medium. The technique involves theconstruction of a translucent medium and the use of laserinduced fluorescence for particle tracking. To demonstratethe utility of the technique, we used it to examine thebehavior of a dilute suspension of negatively charged,micron-size non-Brownian particles in the interior of amedium constructed from monosize 4 mm diameter glassbeads. Both macroscopic and microscopic particle behavior

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W06417 YOON ET AL.: VISUALIZATION OF PARTICLE BEHAVIOR W06417

were observed as a function of pore fluid velocity and solidsurface roughness. Our results provide clear evidence thatparticles interact with solid-solid contact points in a porousmedium as well as solid surfaces. They also showthe important influence surface roughness has on particle-surface interactions under nonfavorable electrostatic con-ditions, as well the impact of particle size distribution onspatial trends in particle concentrations. Comparison of ourresults with predictions obtained by fitting (1) and (2) toparticle breakthrough curves, also demonstrates that rateparameters obtained from fitting BTCs are not alwaysrepresentative of particle behavior in the interior of themedium.

2. Experimental Method and Materials

[9] The experimental method described in this sectionwas developed to enable direct, real-time observation ofparticle movement in a porous medium. Prior efforts todirectly visualize particle movement in a complex porespace include the use of so-called ‘‘micromodels’’, whichutilize photochemically etched glass plates to simulate aporous medium [Wan and Wilson, 1994; Wan et al., 1996;Lanning and Ford, 2002; Sirivithayapakorn and Keller,2003], and the immersion method [Ghidaglia et al.,1996a], which creates an optically transparent medium.We chose not to employ the micromodel method because,although valuable, it does not replicate the complex three-dimensional features of a pore space that we believe areimportant in determining particle behavior. Furthermore,although our initial work made use of the immersionmethod [Yoon et al., 2003], we also discarded this approachbecause it involves the use of an organic pore fluid, whichmight lead to results that are atypical for particle behavior inaqueous groundwater systems.

2.1. Visualization Technique

[10] The visualization technique involves the use of atranslucent porous medium, laser induced fluorescent par-ticles and digital image processing. The translucent porousmedium is constructed from 4 mm diameter soda-limebeads packed to an average volume porosity of 0.37 to0.38, and saturated with deionized/distilled water. Thefluorescent particles are micron sized particles with anexcitation wavelength of 511–532 nm and an emissionwavelength 570–595 nm. A 6W argon-ion laser, the Co-herent Innova 70C ion laser, is used to excite the particles,which produce fluorescent light that is well visible from

within the translucent medium. This light is captured usingthe MagnaFire digital camera, a cooled CCD digital cameraproduced by Optronics with a resolution of 10 bits per pixel.The camera’s normal lens is used for macroscopic visual-ization of particle behavior. A specially purchased micro-lens; the VZM 450i from Edmund Industrial Optics, is usedfor microscopic visualization. A filter placed over thecamera lens ensures that only the wavelength emitted bythe excited particles is passed to lens. The images taken bythe camera are captured in real time by a computer (IntelPentium II, 400 MHz) and then analyzed by the ImageProsoftware from Media Cybernetics. Each digital image con-tains 1280 � 1024 pixels, giving a maximum resolution of0.31 mm � 0.39 mm using the camera’s normal lens, and3.1 mm � 2.9 mm using the microlens.

2.2. Properties of Materials

[11] The properties of the fluorescent micron sized par-ticles are summarized in Table 1. The particles, which weresupplied by the Laboratory for Experimental Fluid Dynam-ics, Johns Hopkins University, Baltimore, Maryland, weremanufactured by dissolving acrylic resin in ethylenedichloride, mixing the solution with the two organic dyesdichlorofluorescein and rhodamine 6G, and spraying themixture into the air, where it solidified into particles. Theparticles were then collected and sieved into different sizeranges. The particles used for the work reported here had anaverage specific gravity of 1.1 and a d50 of 7 mm, with aparticle size range of 1 to 25 mm. We measured particle sizedistribution with a Multisizer 3 Coulter Counter made byBeckman Coulter, Inc. According to (4), gravitationalsedimentation was the predominant mechanism bringingparticles to solid surfaces in our experiments.[12] The particles originally supplied by the manufacturer

were suspended in water. To prepare the particles for theexperiments, a fraction of the suspension was oven dried at110�C. The dried particles were then crushed with a ballmill using a polypropylene ball to destroy any particleclumps. Deaggregated particles were then mixed withdeionized/distilled water to make a suspension with aparticle concentration of 50 mg/L. An ionic surfactant,Alconox1 from Alconox, Inc., was mixed with the waterat a concentration of 0.05% by weight to disperse thesuspended particles and prevent them from aggregatingduring the experiments. The pH of the particle suspensionsolution was 9.1. The measured zeta potential of theparticles in the suspension solution was �110 mV.[13] The 4 mm soda-lime glass beads have a specific

gravity of 2.52. Reported values of the zeta potential ofcrushed soda-lime glass beads range from �35 mV in asolution of pH 3, to �70 mV in a solution of pH 7 [Littonand Olson, 1993]. Thus we anticipated minimal attractiveelectrostatic interactions between the particles and the beadsurfaces during the experiments. Both ‘‘rough’’ beads and‘‘smooth’’ beads were used in the experiments. Roughbeads are the glass beads as supplied by the manufacturer.SEM pictures [Yoon, 2005] suggest a bead surface rough-ness of the order of 2 mm which is in a good agreement withfindings by Smart and Leighton [1989], who report that thesurface roughness of a range of glass beads is approximately10�2 to 10�3 of the particle radii depending on the manu-facturing processes. Smooth beads are mechanically pol-ished rough beads. All beads were cleaned by

Table 1. Properties of the Fluorescent Microparticles

Value

d50, mm 7Range of particle diameter, mm 1–25Specific gravity 1.1Excitation wavelength, nm 511–532Emission wavelength, nm 570–595

V mVa �110

Settling velocity,b cm/s 1.33 � 10�4

aMeasured using a ZetaPALS instrument supplied by BrookhavenInstruments Corp. Electrophoretic mobility was converted to zeta potentialusing the Smoluchowski equation.

bMeasured using ASTM D422 sedimentation test and average values inStoke’s equation.

W06417 YOON ET AL.: VISUALIZATION OF PARTICLE BEHAVIOR

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ultrasonication and then dried in an oven at 110�C beforeeach experiment. We measured the release efficiency of thefluorescent particles from the bead surfaces by mixing50 mL of the suspension solution containing 12.5, 25,37.5, and 50 mg/L of the discrete particles, respectively,with 20 g of the smooth or rough glass beads in vials thatwe mechanically shook for 2 hours. We then measured theconcentration of the particles in the solution using theiremitted light intensity (see section 2.3). Release efficiencieswere estimated as the ratio of the final to the initial particleconcentrations in the solution [Bradford et al., 2002]. Theaverage release efficiency for the rough beads was 96.53% ±2.35%. For the smooth beads the value was 98.13% ±1.34%. Both of these efficiencies are high, suggesting littleparticle attachment to bead surfaces under agitated, fluid-ized conditions, which supports our hypothesis of minimalelectrostatic interaction between particles and the solidsurfaces. Using the Student t test, the null hypothesis thatthe difference between the two means is due to chance isaccepted. Hence we also conclude that the mechanicalpolishing of the beads does not alter, significantly, theirsurface charge.

2.3. Experimental Setup and Procedure

[14] Experiments were conducted in a box with innerdimensions 10.0 cm (width) � 27.9 cm (height) � 2.38 cm(thickness). The box was made of acrylic and all componentpieces were glued together to prevent any leakage. A 2.8 mm(1/8 inch) glass plate was placed against all inside walls ofthe box to minimize particle attachment to the walls.[15] A schematic diagram of the experimental box and

the boundary conditions is shown in Figure 1. Toward thebase of the box, a void space of 2.54 cm (width) � 3.30 cm(height) � 2.38 cm (thickness) was created to enablemeasurement of particle and tracer breakthrough curves.The glass beads were deposited by raining them from thetop of the box in 4 cm layers that were then uniformlyvibrated. The final height of the beads was approximately

16.5–17.0 cm. As noted above, the final volumetric poros-ity of the bead packs ranged from n = 0.37 to n = 0.38. Thebead packs were saturated by sealing the top of the box witha lid, applying a vacuum to the lid, and drawing water infrom the base of the box.[16] Figure 2 shows the detailed configuration of the

particle excitation system, which consists of the laser head,an optical fiber, a laser focusing lens, a spinning mirror anda traversing actuator. The laser was placed in front of the

Figure 1. Schematic diagram of the experimental setup.

Figure 2. Setup of the laser, the spinning mirror, and theactuator for scanning the front face of the experimental box.

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box. A spinning mirror was used to create a horizontal sheetof light with uniform intensity, and a traversing actuator wasused to move the sheet up and down. The actuator was set toenable the laser to scan the box either vertically up or downin a period of 6.5 s. Although not shown, the camera wasplaced next to the actuator so that it could record frontalimages of the box. The center point of the camera lens waslined up with the center point of the front face of the box. Toeliminate errors that might be introduced by anomalouslight, the entire experimental setup was covered in blackcloth and the experiments were conducted in a dark roomwhere the laser light was the only illumination. To ensurestability of the laser light during an experiment, the laserwas warmed up for at least 30 minutes before the start ofeach experiment.[17] During each experiment, inflow was introduced at

the surface of the porous medium by a multihead peristaltic

pump. The effluent was drawn at the bottom of theexperimental box using the same peristaltic pump, and itsvolume was measured with time using an electronic balanceto confirm that the fluid flow rate, Q, remained constant.Before the start of each experiment, 5 pore volumes (5 PVs)of particle suspension liquid without the particles wascirculated through the system.[18] All particle transport tests consisted of two stages,

the particle introduction stage and the particle flushingstage. About 10 PVs of the particle suspension at aconcentration of 50 mg/L were introduced as inflow duringthe particle introduction stage, while another 10 PVs of no-particle fluid with the same chemical composition wereintroduced during the flushing stage. Particle transport testswere conducted at three different pore fluid velocities,which we refer to as fast (u � 5.5 � 10�2 cm/s), medium(u � 2.7 � 10�2 cm/s), and slow (u � 1.4 � 10�2 cm/s),

Table 2. Details of the Experiments Conducted Together With Transport Parameters Obtained From the Particle BTCs

Testa Input BeadsAverage Pore WaterVelocity u,b cm/s Porosity nb

Medium depthL,b cm

kirr, att,10�4 s�1

kr, att,c

10�3 s�1kr, det,

c

10-3 s-1 ahd

RF-1 particles rough fast5.31 (±0.14) � 10�2

0.378 (±0.002) 16.90 (±0.08) 1.48 4.60 7.47 1.2 � 10-3

RF-2 particles rough fast5.31 (±0.14) � 10�2

0.378 (±0.002) 16.90 (±0.08) 1.48 4.60 7.47 1.2 � 10-3

RM-1 particles rough medium2.73 (±0.24) � 10�2

0.376 (±0.004) 16.87 (±0.18) 2.25 5.29 5.19 3.5 � 10-3


0.376 (±0.004) 16.87 (±0.18) 2.25 5.29 5.19 3.5 � 10-3


0.376 (±0.004) 16.87 (±0.18) 2.25 5.29 5.19 3.5 � 10-3


0.376 (±0.004) 16.87 (±0.18) 2.25 5.29 5.19 3.5 � 10-3

RS-1 particles rough slow1.36 (±0.13) � 10�2

0.367 (±0.007) 16.60 (±0.20) 2.36 1.97 1.34 7.4 � 10-3


0.367 (±0.007) 16.60 (±0.20) 2.36 1.97 1.34 7.4 � 10-3


0.367 (±0.007) 16.60 (±0.20) 2.36 1.97 1.34 7.4 � 10-3

RS-micro particles rough 1.27 � 10�2 0.367 16.53 not measured not measured not measured not measuredSF-1 particles smooth fast

5.49 (±0.16) � 10�20.379 (±0.003) 17.06 (±0.08) 0.75 12.1 14.0 0.6 � 10-3

SF-2 particles smooth fast5.49 (±0.16) � 10�2

0.379 (±0.003) 17.06 (±0.08) 0.75 12.1 14.0 0.6 � 10-3

SF-3 particles smooth fast5.49 (±0.16) � 10�2

0.379 (±0.003) 17.06 (±0.08) 0.75 12.1 14.0 0.6 � 10-3

SM-1 particles smooth medium2.76 (±0.08) � 10�2

0.373 (±0.002) 17.04 (±0.06) 0.83 3.56 3.66 1.3 � 10-3


0.373 (±0.002) 17.04 (±0.06) 0.83 3.56 3.66 1.3 � 10-3


0.373 (±0.002) 17.04 (±0.06) 0.83 3.56 3.66 1.3 � 10-3


0.373 (±0.002) 17.04 (±0.06) 0.83 3.56 3.66 1.3 � 10-3


0.373 (±0.002) 17.04 (±0.06) 0.83 3.56 3.66 1.3 � 10-3

SS-1 particles smooth slow1.38 (±0.15) � 10�2

0.374 (±0.002) 17.04 (±0.09) 0.85 2.39 2.11 2.6 � 10-3


0.374 (±0.002) 17.04 (±0.09) 0.85 2.39 2.11 2.6 � 10-3


0.374 (±0.002) 17.04 (±0.09) 0.85 2.39 2.11 2.6 � 10-3

D-1 dye N/A 4.24 � 10�2 0.381 16.60 not measured not measured not measured not measuredD-2 dye N/A 9.88 � 10�3 0.381 16.60 not measured not measured not measured not measured

aR and S represent rough and smooth beads, respectively. F, M, and S represent fast, medium, and slow pore fluid velocities, respectively.bThe numbers in the parentheses are the standard deviations.cR2 values for least squares error method fits �0.99.dHere ah was calculated from (3) using kirr,att.


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respectively. Flow velocities were calculated from u = Q/An,where A was the known cross-sectional area of flow. Toexamine solute transport in the medium, two experimentswere also performed using an organic dye, fluorescein, inplace of the particle suspension liquid. Table 2 providesdetails of the experiments that were conducted. Betweentwo and five particle transport experiments were conducted ateach flow velocity to quantify the repeatability of the results.[19] The macroscopic particle concentration during an

experiment conducted with the normal camera lens wascalculated from the intensity of the light captured within animage. The intensity of captured light at each pixel within animage was a function of (1) the intensity of light emitted fromfluorescing particles within the pixel, (2) the magnitude oflight scattering from neighboring pixels and (3) the imagedistortion produced by the camera lens. To reduce measure-ment errors associated with light scattering, the number ofpixels illuminated during image capture was constrained bythe following, fully automated, procedure: At three to fiveminute intervals during each experiment, the horizontal lasersheet was moved to a predefined measurement location,paused to illuminate a 1.5 cm high portion of the medium,the light emitted from the illuminated portion was capturedover an exposure time of 400 ms, the image was stored, andthe laser sheet was then moved to the next location[20] During experiments with the normal camera lens,

images were captured at the ponded source area at the top ofthe medium, seven interior locations within the medium andthe breakthrough monitoring area at its base. The averagelight intensity captured in each image was calculated usingthe Image Pro software. To enable captured light intensitiesto be converted to particle concentrations, calibrations wereperformed in the experimental box, either with or withoutthe glass beads, using particle suspensions of 50, 37.5, 25and 12.5 mg/L, as well as particle-free suspension liquid. Toquantify the image distortion produced by the camera lens,profiles of average horizontal light intensity versus verticallocation were obtained for each calibration liquid. Forcalibrations performed without the glass beads, thirteen,replicate profiles were obtained for each liquid. For cali-brations with the glass beads, 26 replicate profiles were

obtained for each liquid. As expected, the maximum hori-zontal light intensity in each profile coincided with thevertical location of the center point of the camera lens. Aunique parabolic relationship between vertical location, andthe average horizontal light intensity normalized by themaximum light intensity in a profile, was used to correctfor camera distortion [Yoon, 2005]. Figure 3 provides a plotof normalized, corrected light intensity versus normalizedparticle concentration. The error bars in Figure 3 represent thestandard deviation of all replicate measurements. As seen, thecorrected light intensity exhibits a linear relationship withparticle concentration, with or without the presence of theglass beads. Predictably, emitted light intensities were lowerin the saturated glass beads than the pure liquid at the sameparticle concentration. Separate calibrations, which followeda similar procedure, were performed for the fluorescein dye.[21] The method described above for translating captured

light intensity into particle or dye concentration used aver-aged horizontal light intensities, and thus neglected horizon-tal variations in concentration. We believe this approach isreasonable for the one-dimensional flow conditions of theexperiments reported here. However, an alternative calibra-tion approach using the same equipment could enable hori-zontal, as well as vertical, resolution of particle and dyeconcentrations, thereby permitting investigations of particletransport under two-dimensional flow conditions.[22] Experiments performed using the microscopic lens

enabled direct visualization of particle behavior in themedium’s pore space during the particle introduction andflushing stages of the experiments. The microscopic obser-vation tests were intended to provide qualitative insight andnot quantitative measurements, so no attempt was made toperform calibrations at this scale. In addition to microscopicvisualization during particle transport, microscopic picturesof some areas of the porous medium were taken after eachmacroscopic visualization experiment to see how particleswere locally distributed at the end of the experiment.

2.4. Mass Balance Errors

[23] Pretests with the experimental setup indicated thatthe captured images of fluorescing particles represented anaveraged signal from particles located within the first 3 or 4bead grains from the front face of the experimental box[Yoon, 2005]. To confirm that the particle concentrationestimated from this signal was representative of conditionsthroughout the entire porous medium thickness, evaluate thereliability of the experimental method, and verify that hori-zontal variations in particle concentration could reasonablybe neglected, mass balance calculations were performed forall of the particle transport experiments. Figure 4 comparesthe (known) cumulative mass of particles introduced into theporous medium with the cumulative particle mass calculatedusing the emitted light intensity for one of the experiments.The error in estimated mass balance was within ±3% of theintroduced mass over the entire experimental series, lendingconfidence to the accuracy of the test results.

3. Results and Discussion

3.1. Solute Behavior

[24] Figure 5 shows the breakthrough curves obtainedfrom the dye tests D-1 and D-2. Both BTCs indicate anormalized concentration of C/Co = 0.5 after 1 PV of

Figure 3. Calibration relationship between corrected,normalized light intensity and particle concentration withand without the presence of the glass beads.

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elution, suggesting that mechanisms of advection and dis-persion controlled the dye’s behavior. A modified version of(1) with S = 0 was fit to the BTCs to estimate D, and hencethe longitudinal dispersivity, aL = D/u, of the porousmedium. For D-1, the estimated value aL was 7.9 mm,while for D-2, we obtained aL = 8.1 mm. These values arereasonable given that the medium composed of 4 mmdiameter uniformly packed particles. For subsequent calcu-lations that we will present later in the paper, we assumethat aL = 8.0 mm, even for the particle suspensions.

3.2. Particle Behavior at the Macroscopic Level

[25] The particle breakthrough behavior is illustrated inFigure 6, where we plot particle breakthrough concentra-tions versus time for the three pore fluid velocities for boththe rough (Figure 6a) and the smooth beads (Figure 6b).Note, that the data points presented in Figure 6 are theaverage of all measurements from the duplicate tests at eachflow rate. For the purpose of discussion, predictions ofbreakthrough concentration using (1) and (2) are alsoplotted in Figure 6. The predictions were generated by afinite difference analysis using the Crank-Nicholson scheme.For each test condition, D was estimated using aL = 8.0 mm,kirr,att was acquired from the plateau concentration of theBTC, and kr,att and kr,det were obtained by curve fitting theBTC data obtained from the particle introduction stage of anexperiment using the least squares error method. Values ofkirr,att, kr,att and kr,det are reported in Table 2, together withvalues of ah which were estimated using (3). We found thatalternative models to (2), which involved a lower number ofrate coefficients [e.g., Harvey and Garabedian, 1991], couldnot be well fit to the data.[26] Two main characteristics of the particle breakthrough

are different from the dye breakthrough. First, a normalizedparticle concentration of C/C0 = 0.5 occurred after 1 PV ofelution indicating ‘‘retardation’’ of particles within themedium. Second the plateau concentration was lower thanthe input concentration, meaning that a fraction of theparticles were filtered (i.e., retained) by the porous medium.The fraction of retarded and filtered particles was high forall experiments considering the highly unfavorable electro-

static conditions, suggesting that there must have beenphysical mechanisms for particle retardation and filtration.Despite unfavorable electrostatic conditions we saw noevidence that a measurable fraction of the particles traveledfaster than the dye. Comparison of the data for the differentpore fluid velocities confirms observations by others [e.g.,Compere et al., 2001] that particle retardation and filtrationincreased as the pore fluid velocity decreased. Comparisonof the results for the rough and the smooth beads alsoconfirms that particle retardation and filtration increasedwith medium roughness [Shellenberger and Logan, 2002].Finally, we note that predictions by (1) and (2) do not matchthe descending portion of the BTCs. This is because, likeothers [e.g., Harter et al., 2000], our observations provideevidence of the slow elution of particles from the porousmedium at the end of the particle flushing stage, a phenom-enon that is not accounted for by transport models like (1)and (2).[27] Figure 7 shows the size distribution of particles in

the effluent during the particle introduction stage of anexperiment conducted at the slow pore fluid velocity in therough beads (RS-3). The size distribution of particles in theinfluent is also provided. The size distribution curves showthat smaller particles eluted earlier, and that the sizedistribution of particles in the effluent stabilized after about4 to 6 PVs. The particle effluent concentration normalizedby the particle influent concentration is plotted versus PV inFigure 8. As seen, particle retardation and filtration in-creased with particle size, although particles less than 2 mmin diameter appeared to be neither retarded nor filtered bythe medium. According to (4), Brownian motion wouldhave been the predominant mechanism for bringing par-ticles less than 2 mm in diameter into contact with themedium’s solid phase during RS-3. Hence we speculate thatthese smaller particles generally remained suspended infaster moving streamlines within the medium’s pore space[Brenner and Edwards, 1993], while all other particlesinteracted with the medium’s solid phase as a result ofgravitational sedimentation.

Figure 5. Breakthrough curves for the dye tests. D-1, u =4.26 � 10�2 cm/s; D-2, u = 9.88 � 10�3 cm/s. Dotted curveillustrates predicted breakthrough using (1) with S = 0, D =aLu, and aL = 8.0 mm.

Figure 4. Comparison of introduced particle mass withestimated particle mass for RM-3, an experiment conductedin a rough bead pack at the slow pore fluid velocity.


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[28] Table 3 reports estimated values of kirr,att, ah, h anda for each particle size fraction. As seen, kirr,att and ahincrease with particle size. However, a appeared to peak foran average particle size of 12 mm. The reason for this trendis currently not clear. Of note, is the fact that kirr,att, for theaverage particle size is similar to the average kirr,att valuereported in Table 2 for the slow velocity tests in roughbeads. This leads us to speculate that the parametersobtained from our particle BTCs might reflect the behaviorof the d50 particle.[29] Figure 9 is an example of particle concentrations

observed within the interior of the porous medium duringanother experiment, RS-2, conducted at a slow velocity inrough beads. Note, the vertical axis is the sum of the particlefluid concentration and the particle concentration on thesolid phase, (C + S) normalized by the input concentrationC0. This is because our macroscopic visualization techniquecannot currently distinguish between particle fluorescenceoriginating from the pore fluid and that originating fromsolid surfaces. Predicted interior concentrations using theparameters obtained by fitting the BTC are also displayedon Figure 9. It is clear that, for the conditions of thisexperiment, use of the breakthrough curve to infer what ishappening in the interior of the medium is not appropriate.[30] All interior concentrations exhibited similar features,

as illustrated by Figure 10. During phase A, when local

particle concentrations in the pore fluid were still increasing,the increase in total concentration versus time was nonlin-ear. During phase B, when local pore fluid concentrationsreach a steady state concentration of Cs-s, a linear increase in

Figure 7. Particle size distribution in the influent andeffluent at different pore volumes for RS-3, an experimentconducted in a rough bead pack at the slow pore fluidvelocity.

Figure 6. Breakthrough curves for the particle transport tests at the three pore fluid velocities: (a) roughbead tests (left) ALL TEST and (right) PV 0 TO 5; (b) smooth bead tests (left) ALL TEST and (right) PV0 TO 5. The solid lines represent the fitted predictions using (1) and (2) with the parameters listed inTable 2.

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total concentration versus time was observed, implying thatany process responsible for retaining particles within themedium had a linear rate. Of significance, is the fact that theexperimental measurements can be used to directly resolvethis rate at different spatial locations within the medium.During phase C local particle concentrations in the porefluid were decreasing, and particles reversibly attached tothe medium’s solid phase, represented by the concentrationSr, were reentrained into the pore fluid and flushed out ofthe medium. During the final phase D, particle pore fluidconcentrations were negligible. Hence (C + S) is theconcentration of particles that remained filtered by theporous medium, namely Sirr. Because the concentration ofthese particles showed a very slow decline with time theyare not strictly ‘‘irreversibly’’ attached to the solid phase.However, in what follows, we will continue to use the term‘‘irreversible’’ when discussing this particle fraction to beconsistent with the literature.[31] As illustrated by Figure 10, our macroscopic mea-

surements of particle concentration at different locations inthe interior of a porous medium can be used to directlyresolve spatial variations in Sirr at the end of an experiment,and thus spatial variations in kirr,att and ah. Spatialvariations in Sr at the end of an experiment can also beresolved if the distribution of Cs-s in the medium is known.Because our experimental technique does not directly mea-sure Cs-s in the interior of the medium, we estimated itsdistribution by assuming a linear drop in Cs-s, from C0 at thetop of the medium to the Cs-s measured in the BTC at thebase of the medium. We acknowledge that, in reality, thisdecrease would not have been linear. However, since wefound our estimated spatial variations in Sr changed littlewhen we adopted more complex distributions in Cs-s, weused a linear relationship for simplicity. Finally, by assum-ing that the observed slope during phase B = @Sirr

�@t (i.e., by

assuming that there was no accumulation of reversiblyattached particles during phase B, when C = Cs-s), the slopecan be used in conjunction with our estimated distributionin Cs-s to obtain a second prediction for kirr,att (see (2)and (3)).

3.3. Particle Behavior at the Microscopic Level

[32] Microscopic images obtained of particle behaviorclose to the front face of the experimental box during a slowvelocity experiment with the rough beads are provided inFigure 11. Note, as previously stated, microscopic imageswere only used for qualitative evaluation of particle behaviorwithin a medium; they were not used to estimate particleconcentrations. Figures 11a–11c show particle behaviorduring the particle introduction stage, and Figures 11d–11fduring the flushing stage. It is clear from Figures 11a–11cthat particle interactions with the solid phase, which involvedboth the retardation and filtration of particles, occurred overmost of the bead surfaces and at the solid-solid contact points.However, from Figures 11d–11f it becomes apparent thatparticle filtration, i.e., ‘‘irreversible’’ particle attachment tothe medium’s solid phase, occurs only at the top surfaces ofthe beads and at the solid-solid contact points.[33] Figure 12 is a microscopic image of the porous

medium at its mid-depth after the end of a slow velocityexperiment using the smooth beads. In contrast to theobservations made in the rough bead packs (e.g.,Figure 11f), particle filtration in the smooth bead packsoccurred only at the solid-solid contact points, where crescentshaped particle clusters that are concave downward are

Table 3. Estimated Filtration Properties of Particle Fractions

During RS-3, an Experiment. Conducted in a Rough Bead Pack at

the Slow Pore Fluid Velocity

Average ParticleSize, mm

kirr,att,a

10�4 s�1 hb ahc a

1.5 0 1.64 � 10�3 0 03 0.17 3.16 � 10�3 5.15 � 10�4 0.147 2.5 17 � 10�3 7.68 � 10�3 0.4512 8.6 49 � 10�3 2.68 � 10�2 0.5518 15.5 110 � 10�3 4.84 � 10�2 0.44

aEstimated from the plateau concentrations shown in Figure 8.bCalculated from (4).cCalculated from kirr,att using (3).

Figure 8. Particle breakthrough behavior for the different particle sizes during RS-3. The breakthroughconcentration for each particle size is normalized by the inlet concentration for that particular particlesize.


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clearly visible. Cushing and Lawler [1998] first claimed thatcontact points collected particles by ‘‘funneling effects’’,which they simulated using three dimensional particle tra-jectory modeling. Our experimental work provides directevidence to support this claim. As noted by Cushing andLawler [1998], the clean bed filtration theory, upon whichmany particle transport models are founded, does not accountfor contact filtration.

4. Mechanisms for Irreversible andReversible Particle Attachment

[34] Our macroscopic data and microscopic pictures ofparticle behavior in the glass beads lead us to hypothesize

that, for the conditions of our experiments, the ‘‘irrevers-ible’’ attachment of particles to the medium’s solid phaseoccurred at solid-solid contact points (contact filtration ofparticles) and on rough solid surfaces (surface filtration ofparticles). Likewise, the reversible attachment of particlesoccurred as a result of particle interaction at solid-solidcontact points (contact retardation of particles) and on solidsurfaces (surface retardation of particles).

4.1. Particle Filtration

[35] Contact filtration of particles, sometimes referred toas contact straining [e.g., Bradford et al., 2002], isexplained by the physical capture of particles in the smallpendular pore space surrounding solid-solid contact points.

Figure 9. Interior concentration change with time for RS-2, an experiment conducted in the rough beadpack at the medium pore fluid velocity: (a) 1.8 cm from the surface where particles are introduced, (b) 3.6cm, (c) 5.8 cm, (d) 8.0 cm, (e) 12.4 cm, and (f) 15.0 cm. The solid lines represent predictions by (1) and(2) using parameters obtained from the BTC.

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We believe that the surface filtration of particles under theunfavorable electrostatic conditions in our experiments isexplained by the physical interlocking of particles withasperities on the rough particle surfaces (Figure 13). Forceand torque balance calculations that used DLVO theory toestimate the double layer force [Hogg et al., 1966] and theVan der Waals force [Elimelech et al., 1995], and Happel’ssphere-in-cell model [Happel, 1958] to calculate the dragforce, show that surface roughness can hold particles on thetop of bead surfaces provided that q is less than a criticalangle. Calculations performed for a d50 particle, an assumedgap distance between the particle and the bead surface of1 mm, and a 2 mm high asperity, show that is q isapproximately 6.6� at the slow pore fluid velocity, 3.5� atthe medium pore fluid velocity and 1.8� at the fast pore fluidvelocity [Yoon, 2005]. As seen in Figure 11f, observedvalues of q during an experiment performed at the slow porefluid velocity agree with our estimated value of 6.6�,supporting our argument that medium roughness was re-sponsible for the surface filtration of particles during theexperiments.[36] Figure 14a is a plot of the average value of Sirr/C0 as

a function of pore fluid velocity and depth in the mediumfor the experiments conducted in the smooth bead packs.The error bars show the range of measurements for theduplicate tests. Because there appeared to be no surfacefiltration of particles during the smooth bead tests, we haveassumed that Sirr is the concentration of particles filtered atsolid-solid contact points, Sirr(contact). We note that thenormalized concentration of contact filtered particles de-creased with pore fluid velocity but showed little changewith depth, and hence transport distance. Values of(ah)contact versus depth are shown on Figure 14b. Thesevalues generally agree well with those estimated from theexperimental BTCs (see Table 2), although the BTCs valuesare higher than the averaged interior values at the mediumand slow pore fluid velocity. The data presented in Figure 14bshow a decrease in particle removal capacity by contactfiltration with pore fluid velocity, but little variation in(ah)contact, and hence kirr,att(contact), with transport distance.[37] Figure 15a is a plot of the average value of Sirr/C0 as

a function of pore fluid velocity and depth in the medium

for the experiments conducted in the rough bead packs.Again, the error bars show the range of measurements forthe duplicate tests. During experiments in the rough beadpacks, the total particle filtration, Sirr(total), was the sum ofthe particle contact filtration, Sirr(contact), and the particlesurface filtration, Sirr(surface). To estimate trends in particlesurface filtration with depth, we have assumed that at eachpore fluid velocity, the variation in Sirr(contact) with depthwas the same in the rough and the smooth bead packs. Inother words, that the magnitude of contact filtration was afunction of pore fluid velocity and depth but not mediumroughness. Estimated average values of Sirr(surface) as afunction of pore fluid velocity and depth are also providedon Figure 15a. These values were obtained by subtractingthe profiles of average Sirr(contact) versus depth at a givenpore fluid velocity (see Figure 14a) from the profiles ofaverage Sirr (total) versus depth at the same pore fluid

Figure 10. Typical profile of measured interior concentra-tion change with time.

Figure 11. Microscopic observations of particle attach-ment and detachment during RS-micro, an experimentconducted in the rough bead pack at the slow pore fluidvelocity. Figures 11a–11c were taken during particleinjection while Figures 11d–11f were taken during particleflushing. (a) The 0.9 pore volume passed, (b) 2.8 porevolumes passed, (c) 9.2 pore volumes passed, (d) 1.8 porevolumes flushed after the end of particle injection, (e) 4.6pore volumes flushed, and (f) 8.3 pore volumes flushed (theend of phase D).


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velocity. As per the contact filtration, the surface filtrationof particles decreased with the pore fluid velocity. However,in contrast to the contact filtration, Sirr(total), and henceSirr(surface), decreased notably with depth at the medium andslow pore fluid velocities. A comparison of Figures 15a and14a reveals that particle filtration was dominated by contactfiltration at the fast pore fluid velocity, and by surfacefiltration at the medium and slow pore fluid velocities.[38] Values of Sirr(total) and Sirr(surface) were used to calcu-

late (ah)total and (ah)surface as a function of pore fluidvelocity and depth (Figure 15b). For the fast pore fluidvelocity (ah)total, and hence (ah)surface, were approximately

constant with depth. Furthermore, the average value of(ah)total agrees well with the average value obtained fromthe BTCs of the experiments conducted at the fast pore fluidvelocity in the rough bead packs (see Table 2). In contrast,for both the medium and the slow pore fluid velocities, therewas a clear trend of (ah)total, and hence irreversible particleattachment rates, decreasing with particle transport distance.Comparison of the average (ah) values obtained from theBTCs (see Table 2) with the (ah)total values plotted inFigure 15b, show that close to the particle source, (ah)values obtained from the BTCs underestimate the (ah)totalvalues obtained from the interior concentration measure-ments, while further away from the particle source the BTC(ahs) overestimate those obtained from the interior mea-surements. However, on average the (ah) values from theBTCs at the medium and slow pore fluid velocities arehigher than the averaged interior values.[39] We believe that our observed trends in (ah)total

versus depth in the rough bead packs are the result of theFigure 12. Microscopic picture taken in the middle of themedium after SS-3, an experiment conducted in the smoothbead pack at the slow pore fluid velocity.

Figure 13. Model for surface filtration of particles inrough bead packs. Up to an angle q, particles brought tobead surfaces are held by asperities because momentsresisting particle overturning at the particle-asperity contactpoint (resulting from the gravitational and Van der Waalsforces) exceed the overturning moments (resulting from thedrag and double layer forces).

Figure 14. Observed particle filtration behavior at the endof experiments in the smooth bead packs where it is assumedthat contact filtration was preeminent: (a) Sirr(contact)/C0 asa function of pore fluid velocity and depth from theparticle injection point; (b) (ah)contact as a function ofpore fluid velocity and depth from the particle injectionpoint.

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distribution of particle sizes in the influent liquid. Forexperiments conducted at the slow velocity, the averageobserved (ah)total ranged from 8.2 � 10�3 at the top of themedium to 6.6 � 10�3 at the base of the medium(Figure 15b). According to the data presented in Table 3,this range can be explained by the removal of >d50 sizedparticles close to the particle source <d50 sized particlesfurther away from the particle source. Hence the change in(ah)total with transport distance is a result of the earliercollection of larger particles by the medium, which reducedthe average size of the mobile particle fraction with depth.Because our observed values of (ah)contact were approxi-mately constant with depth, we believe that selectiveparticle size filtration in our experiments was only associ-ated with the mechanism of surface filtration. To explainwhy variations in (ah)surface with particle transport distancewere observed at the medium and slow pore fluid velocitiesbut not at the high pore fluid velocity, we plot the h valuesobtained from (4) versus particle size for each pore fluidvelocity in Figure 16. As seen, the variation in h with dincreases as the pore fluid velocity decreases. Thus changes

in (ah) with transport distance that will arise as a result ofthe polydisperse particle population, will be more apparentat slower pore fluid velocities.

4.2. Particle Retardation

[40] Retarded particles are particles that were reversiblycollected at solid-solid contact points or on solid surfaces inthe porous medium, and then reentrained back into the porefluid during any of the stages A to C of our experiments.Explanations for surface retardation include insufficientsurface roughness to ‘‘irreversibly’’ hold particles broughtto the surface of glass beads, temporary ‘‘hydrodynamiccapture’’ of particles in slow moving and stagnant regionsof pore fluid [Lee and Koplik, 1999; Ghidaglia et al.,1996b], and particle-particle interactions on or close to solidsurfaces that perturb local viscous forces to either favorparticle attachment [e.g., Biggs et al., 2003] or detachment[e.g., Meinders and Busscher, 1995]. Explanations forcontact retardation include inadequate geometric captureof particles (i.e., inadequate straining) as well as theperturbations in local viscous forces caused by particle-particle interactions. We do not have the data to distinguishbetween the concentrations of particles experiencing contactretardation and surface retardation, so we will present theconcentrations of retarded particles, Sr, as a whole. Note, theSr values that we report refer to the concentration ofparticles washed out of the medium during Stage C of ourexperiments (see Figure 10).[41] Figures 17a and 17b are plots of average values of

Sr/C0 as a function of depth and velocity for the testsconducted in the smooth and rough bead packs, respectively.Error bars show the range of measurements for all duplicatetests. As per Sirr, Sr generally decreased with pore fluidvelocity; the exception being Sr values below 5 cm in therough bead packs at the slow pore fluid velocity, whichappeared to be lower than those in the rough bead packs atthe medium pore fluid velocity. For the experimentalconditions investigated, the range of Sr/C0 lay betweenapproximately 0.4 and 1.4. Thus the concentration ofretarded particles showed much less variability with porefluid velocity and surface roughness than the concentrationof filtered particles.[42] The data presented in Figure 17 show that at the slow

and medium pore fluid velocities, Sr/C0 > 1 close to theparticle source. This indicates an accumulation of reversiblyattached particles on the medium’s solid phase close to thecolumn inlet. To examine whether some of this accumulationoccurred during phase B of an experiment, we comparedkirr,att obtained from the phase B slope, with kirr,att obtainedfrom the end of experiment Sirr values (see Figure 10).Figure 18 shows the ratio of kirr,att(slope)/kirr,att(Sirr) for experi-ments in the smooth bead packs; trends in the rough beadpack were similar. As seen, this ratio was greater than unity atthe medium and slow pore fluid velocities, indicating that@Sr�@t > 0 during phase B for these flow conditions. An

accumulation of reversibly attached particles with timeduring phase B, would explain why (ah) values obtainedfrom the BTC curves at the medium and slow velocities, werefractionally higher than those obtained from the interiormeasurements of Sirr. For the fast pore fluid velocity, theaverage ratio of kirr,att(slope)/kirr,att(Sirr) appears to be close tounity, although the trend is quite scattered.

Figure 15. Observed particle filtration behavior at the endof experiments in the rough bead packs: (a) Sirr (total)/C0 andSirr(surface)/C0 as a function of pore fluid velocity and depthfrom the particle injection point; (b) (ah)total and (ah)surfaceas a function of pore fluid velocity and depth from theparticle injection point.


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[43] We believe that particle retardation as a result ofreversible particle interactions with the solid phase of amedium is both complex and dynamic and deserves furtherinvestigation. Our microscopic images of particle behaviorshowed, for example, particle heaps building up on the topof bead surfaces, collapsing and then rebuilding again.Models that assume retarded particles behave as a singlefraction that can be described by one attachment and onedetachment rate, are unlikely to capture the true complexityof particle fate and transport.

5. Conclusions

[44] We have presented a technique for directly observingparticle transport in the interior of a porous medium thatinvolves the construction of a translucent medium, and theuse of laser induced fluorescence for the analysis of soluteand particle concentrations. The technique allows the quan-titative evaluation of macroscopic images of particle behav-ior in the porous medium and the qualitative evaluation ofmicroscopic images. We used the technique to examine thebehavior of a dilute suspension of negatively charged,micron-size non-Brownian particles in the interior of a17 cm high medium constructed from monosize 4 mmdiameter glass beads. The particles had specific gravity of1.1., a d50 of 7 mm and a size range of 1–25 mm. One-dimensional, downward transport experiments were con-ducted in both smooth and rough bead packs at threedifferent pore fluid velocities; namely, fast (u � 5.5 �10�2 cm/s), medium (u � 2.7 � 10�2 cm/s), and slow (u �1.4 � 10�2 cm/s). Each experiment involved 10 PVs ofparticle injection at a constant concentration C0 = 50 mg/L,followed by 10 PVs of particle flushing.[45] The macroscopic images collected during the experi-

ments enabled us to resolve particle concentrations versustime at the inlet of the medium, the outlet of the mediumand seven locations in the interior of the medium. Themicroscopic images enabled us to observe particle behavior

Figure 16. Theoretical variation in h with particle size and pore fluid velocity.

Figure 17. Observed particle retardation behavior at theend of experiments: (a) Sr/C0 as a function of pore fluidvelocity and depth from the particle injection point in thesmooth bead packs; (b) Sr/C0 as a function of pore fluidvelocity and depth from the particle injection point in therough bead packs.

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at a fixed location in a medium over time, or observe howparticles were distributed in a medium at the end of anexperiment. Data collected from the experiments were usedto resolve spatial variations in: Sirr, the concentration ofparticles ‘‘irreversibly’’ attached to the solid phase of themedium at the end of an experiment (filtered particles); Sr,the concentration of particles reversibly attached to the solidphase of the medium at the end of an experiment (retardedparticles), and @S

�@t, the rate of accumulation of particles on

the medium’s solid phase when local pore fluid concen-trations reach a steady state, Cs-s. Values of Sirr and

@S�@t were

used in conjunction with the clean bed filtration theory toestimate values of ah, the medium’s filtration capacity, andkirr,att, the irreversible attachment rate of particles on thesolid phase.[46] Our experimental results show that, in the smooth

bead packs, particle filtration occurred predominately atsolid-solid contact points (contact filtration) with a filtrationcapacity that decreased with pore fluid velocity. However,our results indicated little change in the contact filtrationcapacity of a medium, and hence kirr,att, with particletransport distance. In the rough bead packs our results showthat particle filtration occurred at the top of bead surfaces(surface filtration) as well as at solid-solid contact points,with contact filtration dominating at the fast pore fluidvelocity and surface filtration dominating at the mediumand slow pore fluid velocities. We believe that surfaceroughness was responsible for the surface filtration ofparticles under the highly unfavorable electrostatic condi-tions of our experiments. As for the smooth bead tests, therough medium’s filtration capacity decreased with the porefluid velocity. However, for experiments conducted at theslow and medium flow velocities, the filtration capacity alsodecreased with particle transport distance. We attribute thisobservation to the preferential surface filtration of largerparticles close to the particle source as a result of gravita-tional sedimentation. Because the slow pore fluid velocityused in our experiments is higher than the average naturalpore fluid velocity in many groundwater systems, we

believe that changes in kirr,att with distance, as a result ofthe preferential filtration of larger particles, is likely to bethe norm for non-Brownian particle transport in the field.With respect to particle retardation; our macroscopic mea-surements suggest the accumulation of reversibly attachedparticles with time even under constant pore fluid concen-trations, while our microscopic measurements indicate thatmechanisms for particle retardation during porous mediatransport are both complex and dynamic. Hence the as-sumption that particle retardation can be described by onesingle attachment and one single detachment rate is prob-ably over simplistic in many cases.[47] Our visualization technique has enabled us to pro-

vide clearer insight into the physical behavior of non-Brownian particles in the interior of a uniform porousmedium. Because the use of the technique is not restrictedto the experimental conditions presented here, it has greatpotential for advancing understanding of particle behaviorin more complex systems and under a range of differentenvironmental conditions.

[48] Acknowledgments. The authors gratefully acknowledge thefunding for this work provided by the National Science FoundationCareer grant CMS-9875883 and Bechtel BWXT Idaho. In addition, thetechnical and machining assistance provided by Stephen Rudolph is highlyappreciated.

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��P. J. Culligan, Department of Civil Engineering and Engineering

Mechanics, Columbia University, 626 S.W. Mudd Building, New York,NY 10027, USA. ([email protected])

J. T. Germaine and J. S. Yoon, Department of Civil and EnvironmentalEngineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA.

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