-
este
r
ent
for7 S
Abstract
1. Introduction
colloids from drinking water supplies (e.g.,
[42,81,114]).Microorganisms can also travel attached to abiotic
particles
(e.g., [83,24,55,61]). In addition, certainmicroorganisms
can
of the uid velocity eld and the tortuosity of the pathsthrough
the porous media. Dispersion can be more impor-tant for colloids
than for solutes, since it can lead to earlierbreakthrough of the
colloids, as presented below. In addi-tion, random interactions
among molecules and/or parti-cles result in Brownian movements
[117] that diuse the
* Corresponding author.E-mail address: [email protected]
(A.A. Keller).
Advances in Water Resources 30The transport of biocolloids
(e.g., viruses, bacteria, sporesand other microorganisms) through
saturated and unsatu-rated porous media is of signicant interest,
from the per-spective of protection of groundwater supplies
fromcontamination (e.g., [87,53,128,85,104,99]), assessment ofrisk
from pathogens in groundwater (e.g.,
[9,40,49,51,54,111,143,1,28,124,14,88,108,95,130]), natural and
enhancedbioremediation (e.g., [106,96,141,3,38,33,37,2,68]) and
forthe design of better water treatment systems to remove bio-
also facilitate the transport of metals and other
chemicals(e.g., [72,35,132,145]). Thus, it is important to
understandthe transport of colloids in general, and that of
biocolloidsin specic.
Biocolloids are aected by many of the physical andchemical
processes that inuence solute transport, i.e.,advection, diusion,
dispersion and adsorption (Fig. 1).Advection is the motion of the
biocolloids along the trajec-tories of the uid streamlines. This
mechanism can createdispersion of the biocolloids because of the
heterogeneityField and column studies of biocolloid transport in
porous media have yielded a large body of information, used to
design treatmentsystems, protect water supplies and assess the risk
of pathogen contamination. However, the inherent black-box approach
of theselarger scales has resulted in generalizations that
sometimes prove inaccurate. Over the past 1015 years, pore scale
visualization tech-niques have improved substantially, allowing the
study of biocolloid transport in saturated and unsaturated porous
media at a level thatprovides a very clear understanding of the
processes that govern biocolloid movement. For example, it is now
understood that the reduc-tion in pathways for biocolloids as a
function of their size leads to earlier breakthrough. Interception
of biocolloids by the porous mediaused to be considered independent
of uid ow velocity, but recent work indicates that there is a
relationship between them. The exis-tence of almost stagnant pore
water regions within a porous medium can lead to storage of
biocolloids, but this process is strongly col-loid-size dependent,
since larger biocolloids are focused along the central streamlines
in the owing uid. Interfaces, such as the airwaterinterface, the
soilwater interface and the soilwaterair interface, play a major
role in attachment and detachment, with signicantimplications for
risk assessment and system design. Important research questions
related to the pore-scale factors that control attach-ment and
detachment are key to furthering our understanding of the transport
of biocolloids in porous media. 2006 Elsevier Ltd. All rights
reserved.
Keywords: Colloid; Sorption; Desorption; Filtration; Straining;
GroundwaterA review of visualization techniquat the pore scale
under satura
Arturo A. Kelle
Bren School of Environmental Science and Managem
Received 15 April 2005; received in revisedAvailable
online0309-1708/$ - see front matter 2006 Elsevier Ltd. All rights
reserved.doi:10.1016/j.advwatres.2006.05.013of biocolloid transport
processesd and unsaturated conditions
*, Maria Auset
, University of California, Santa Barbara, CA, USA
m 8 November 2005; accepted 5 May 2006eptember 2006
www.elsevier.com/locate/advwatres
(2007) 13921407
-
Deposition
WaNomenclature
A Hamaker constant (J)ap particle radius (m)As soil porosity
function ()AWI airwater interface ()D1 colloid bulk diusion
coecient (m
2/s)dg eective grain diameter (m)dp particle eective diameter
(m)g gravitational acceleration (m/s2)kB Boltzmanns constant
(J/K)NA Hamaker number ()NG gravity number ()NPe Peclet number
()
Grain
A.A. Keller, M. Auset / Advances inbiocolloids. The biocolloids
can attach to the soilwaterinterface (SWI), the airwater interface
(AWI), or the triplecontact of soilwaterair (SWA).
Attachment/adsorptionto these interfaces can be reversible or
essentially irrevers-ible under certain conditions, and is perhaps
the most com-plex process, given the large number of colloid and
grainsurface characteristics that determine the probability
ofattachment, and the inuence of the dissolved chemicalspecies in
the aqueous solution on attachment and detach-ment. In addition to
those four processes, colloids are sub-ject to removal by physical
mechanisms, such as straining,interception, diusion to the wall and
gravitational deposi-tion. These physical processes are precursors
to attachment(Fig. 2).
At the level of the individual biocolloid, there are pro-cesses
that can result in the formation of clusters of biocol-loids,
either attached to an interface or mobile within theaqueous phase.
Clusters can also be initiated via biologicalprocesses, to form
biolms (e.g., [23,76,129,21,94,126,7]).Individual or clustered
biocolloids can break o from thelm, releasing them into the owing
aqueous medium(e.g., [18,140,127]).
Biological processes such as growth, death, predation,parasitism
and other processes can result in the increase
Advectionalongcentral
streamline
Diffusion into
stagnant region
Straining
Adsorption
Flow direction
Fig. 1. Schematic of pore scale processes under saturated ow.NR
Reynolds number ()NvdW van der Waals number ()SWA soilwaterair
interface ()SWI soilwater interface ()T temperature (K)T/C pore
throat to colloid diameter (m/m)U pore water velocity (m/s)g
collision eciency ()hm soil matrix porosity ()lw viscosity of
aqueous solution (kg/m s)qp particle density (kg/m
3)qw density of aqueous solution (kg/m
3)
Flow direction(vertical)
Gravitational
ter Resources 30 (2007) 13921407 1393or removal of mobile or
attached microorganisms (e.g.,[30,36,48,91]). Many of these
biological processes are alsoinuenced by physical and chemicals
conditions, and thechanges in these conditions. Although these
processes areextremely important, they are outside the scope of
thismanuscript, which will focus on the transport of biocol-loids
through porous media.
Conventional methods to investigate biocolloid trans-port
through saturated and unsaturated porous mediaoften include column
and eld studies (e.g.,[58,67,86,30,42,53,114,130]). These
experiments are gener-ally limited to the evaluation of euent
breakthroughcurves and destructive sampling at the end of the
experi-mentation that represent some average behavior of
biocol-loids. Some studies focus on the collection ofbiogeochemical
parameters that can monitor the biologicalprocess. Unfortunately,
direct observations of the internalprocesses occurring are not
possible, and mechanisms thatcontrol biocolloid transport are
therefore poorly under-stood. A useful method to investigate pore
scale processesimplicates the use of micromodels.
In recent years, micromodels have been increasinglyemployed to
study the fate and transport of colloids and
Diffusionoff central
streamlines
Interception
Fig. 2. Schematic of processes that lead to attachment.
-
Table 1Micromodel and ow cell studies of biocolloid
transport
Conditions Reference Material Pattern Dimensions Key ndings
Saturatedporous medium
[75] Etched glass Homogeneous periodic network Pore depth 80 lm,
pore width360 lm
Dispersion of E. coli anddetermination of dispersioncoecient
[16] PDMS on glass Homogeneous network ofsquares
2 2 lm square arrays spaced1 lm apart
Particle deposition (adsorption)inheterogeneously charged
surfaces
[8] Etched silicon Homogenous network of circles,300 lm
diameter
Pore depth 50 lm, pore space173 lm, pore throat 35 lm
Transport along streamlines andattachment
[121,122] Etched silicon Realistic sand pore network Pore depth
15 lm, porediameters: 2.430 lm, porethroat 110 lm
Pathway a function of colloid size,higher dispersion for small
colloids
[4] PDMS Homogeneous network ofsquares
Pore depth 12 lm, pore throats10 and 20 lm
Inuence of colloidal size on colloidaldispersion
Saturated porousmedium withbiolm
[123] Poly(methyl methacrylate)(PMMA) and glass Parallel plate
ow cell 5.5 3.8 0.06 cm (l w h)Adhesionof
biocolloids tosolid substrata
[31] Etched silicon Network of squares; simulationof a ne
homogeneous sand;porosity 37%
Pore depth 200 lm, meanchannel width 75 lm grain sizes(0.5 mm),
pore sizes (50200 lm)
Rerouting of ow due to biomassgrowth
[32] Etched silicon Network of squares, channelwidth randomly
distributed
Pore depth 200 lm, channelwidth 75 and 123 lm
Conductivity decreases correlatedwith biolm growth
Microorganisms strongly attachingto surfaces and to each other are
themost eective at reducingpermeability Continuous, rather than
periodic,disinfection is recommended
[73] Etched glass Homogeneous triangular lattice Pore bodies 300
lm, pore throats30100 lm
Biomass accumulation causespermeability reduction Existence of a
critical shear stress
[125] Etched glass Homogeneous triangular lattice Pore bodies
300 lm, pore throats30130 lm
Exopolymer production by bacterialeads to biomass plug and
pressuredrop increase
[90] Etched silicon Homogenous network of circles 1 cm 1 cm
packed array of300 lm diameter silicon postsseparated by 35 lm pore
throats15 lm deep
Biomass growth changes water owpaths
[78] Steel and glass Flow cells packed with quartzsand
8 3 54 mm Colloidbiolm interactions haveimplications for colloid
transport andremobilizationSolution low ionic strength
(I)remobilizes attached bacterialbiomassBiomass and clay
colloidsremobilized by deplecting I orincreasing ow rate
1394A.A.Keller,
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/Advances
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Conditions
Reference
Material
Pattern
Dimensions
Key
ndings
[11]
Glass
Sandstonerock
Pore
depth
34.9lm
Biolm
developmentand
accumulationin
leadingfacesof
obstructions
Un-saturated
porousmedium
[138,139]
Etched
glass
Hexagonal,quadrilateraland
heterogeneousnetworks
Pore
sizesof20400
lm1250
pore
bodieseach
AWIisan
additionalsorbentphase
forcolloids
[46]
poly(m
ethyl
methacrylate)
(PMMA)
Parallelplateowcham
ber
7650.6mm
(lwh)
AWIdetaches
particles
from
collectorsurface
[121,122]
Etched
silicon
Realisticsandpore
network
Pore
depth
15lm,pore
diameters:2.430
lm,pore
throat
110
lm
Colloidsattached
toAWIform
acluster
withthedissolutionofair
bubble
[25]
Sem
i-translucentsilica
sand
Inltrationcham
ber
264.80.5cm
0.430.60mm
graindiameter
Colloidaltrappingat
SWAInterface
[5]
PDMS
Realisticsandpore
network
Pore
diameters:3060lm
Rem
obilizationofbiocolloidsby
interm
ittentunsaturatedow
A.A. Keller, M. Auset / Advances in Waspecically biocolloids at
the pore scale (Table 1). Micro-models are transparent physical
models of porous media,with a pore size in the range of 10100 lm,
etched in glass(e.g., [138,75]), silicon wafers (e.g.,
[69,121,122,19,8]), orpolymer substrates (e.g., [4]) like the ones
presented inFig. 3. Some recent studies have used silica particles
asthe porous media in three dimensions, visualizing the topsurface
(e.g., [25]). In addition, ow cells have also beenused to study
physical processes such as attachment,detachment and mass transfer
rates (e.g., [59,123,80,82]).Recent work by Sherwood et al., Olson
et al., [118,97] usingmagnetic resonance imaging has also served to
betterunderstand biocolloid transport at small scales. The
mainpurpose of these microscale experiments has been to visual-ize
biocolloid transport processes at the dimensions of apore or
collection of pores, validating or negating hypoth-esis that have
been put forward with regards to processesthat had not been
actually observed; a secondary objectivehas been to quantify the
importance of these processes.Although the use of micromodels has
increased, there arestill many questions that need to be answered
with regardsto attachment and detachment from interfaces, and the
roleof physical, chemical and biological heterogeneity in
suchprocesses.
In this paper, we review the most recent ndings on bio-colloid
migration and immobilization at the pore scaleusing micromodels.
The experimental details can be foundin the original papers, so
only the most relevant conditionsare discussed in this manuscript.
We begin by examiningthe processes that aect biocolloid advection
and disper-sion under saturated conditions. We then explore the
roleof interfaces on biocolloid retention in saturated and
unsat-urated porous media. We conclude with recommendationsfor
future research.
2. Biocolloid transport processes in saturated porous media
2.1. Advection, diusion, dispersion
Imposing a pressure gradient across a porous mediumrapidly
generates a stable ow eld with dened stream-lines. Even fairly
signicant changes in pressure gradienthave minimal inuence on the
streamlines that dene thepathways within the medium, although these
changes cer-tainly aect the rate of transport. Colloids and
solutesundergo advective transport moving with the pore-water,whose
velocity is governed by the hydraulic pressure gradi-ent, porosity,
and permeability distribution [44]. Solutionof the NavierStokes
equations at the pore scale (e.g.,[121]) indicates that even for
fairly complex geometries,the local velocity prole is nearly
parabolic [26,8], withthe faster streamlines in the center of the
pore throats,and slower streamlines along the solidwater
interface(Fig. 4). In the complex geometries of natural
porousmedia, there are many regions which are almost stagnant
ter Resources 30 (2007) 13921407 1395(darker blue regions in
Fig. 4), while only a few pathwaysexhibit signicant ow (lighter
blue to yellow to red regions
-
Water Resources 30 (2007) 139214071396 A.A. Keller, M. Auset /
Advances inin Fig. 4). The pressure gradient is from right to left
in thissimulation that solves the NavierStokes equations for
arealistic pore space. Thus, solutes or colloids that begintheir
transport near the central streamlines are advectedat a
considerably higher rate than those along the SWI.
Fig. 3. Scanning electron micrographs of PDMS and silicon wafer
micromodels. Typical pore size 10100 lm, pore throats 320 lm.
Fig. 4. Solution of NavierStokes equation for a complex pore
spacegeometry using FEMLAB. Flow is from right to left, and in the
laminarregime.Since diusion due to Brownian motion is inversely
pro-portional to the mass of the molecule or particle, soluteshave
a much higher probability of transferring amongstreamlines than
colloids. Even the smallest colloidsobserved to date (MS-2 viruses,
about 50 nm in diameter)exhibit very low transfer among streamlines
within thelength of a typical micromodel (a few mm). At
largerscales, with increasing transport time, transfer
amongstreamlines will eventually occur, slowing down some ofthe
faster colloids and speeding up some of the slower ones.However,
low diusion tends to focus mobile colloidsalong the certain
streamlines; slower colloids near theSWI have a higher probability
of depositing onto theSWI by a number of processes. Larger colloids
are forcedto remain near the central streamlines, while the
smallercolloids can sample a wider range of streamlines (Fig.
5).The schematic shows two sizes of colloids (2 and 7 lm
indiameter) in two dierent pore throats (10 and 20 lm indiameter)
and the range of streamlines they can travelthrough as indicated by
the black rectangles. For a smallerpore throat to colloid diameter
ratio (T/C ratio), the col-loid is severely constrained to the
central streamlines.
Under controlled conditions, Auset and Keller [4]showed that
some colloids follow these streamlines evenFig. 5. Schematic of
possible distribution of small (2 lm) and largecolloids (7 lm)
within pore throats of dierent diameters (10 and 20 lm).
-
Waalong sharp turns into perpendicular pore throats at theend of
pore bodies. Smaller colloids can easily follow alongthe pore
walls, making many detours along their path,while the larger
colloids tend to stay on the central stream-lines and in general
have fewer detours (Fig. 6). For thesame size of colloids, travel
through narrower pore throatsresults in shorter average residence
time and a narrower
Fig. 6. Schematic of dierential colloid transport along
streamlinescalculated using the solution to the NavierStokes
equation for a simplepore geometry.
A.A. Keller, M. Auset / Advances indistribution of residence
times, relative to a wider pore net-work (Fig. 7a,b). Travel
through a more complex network,closer to real pore spaces, results
in longer average resi-dence time and a broader distribution than
those of simplepore networks (Fig. 7c). Colloid residence time is
also afunction of the pressure gradient (Fig. 8); large
gradientsresult in wider dierences in residence time between
col-loids of dierent sizes, while small gradients tend to reducethe
dierences. Torquato [131] also discusses the eect ofheterogeneity
on colloid dispersion.
For complex pore geometries such as that shown inFig. 4, the
dierence in colloid size has increasing impor-tance. Smaller
colloids sample many of the pathways avail-able to them, traveling
though both narrow and wide porethroats, and are thus more likely
to move into regionswhere ow is almost stagnant (Fig. 4). Larger
colloidsare excluded from many regions and pathways, in partbecause
they remain in the central streamlines, as shownby
Sirivithayapakorn and Keller [121]. This dierentialbehavior can
have a signicant eect on the average resi-dence time of dierent
colloid sizes, since the larger colloidscan travel at signicant
faster velocities through the porousmedium compared to the smaller
colloids. At the porescale, this phenomenon can result in colloid
velocities thatare 1.53 times greater than the average water
velocity(Fig. 9). This eect has been designated as a velocityter
Resources 30 (2007) 13921407 1397enhancement (e.g., [52,4,70]).
Mathematically, it has beenproposed that this could be handled as a
retardation factorless than unity or a lower eective porosity [43].
Due to col-loid removal processes the magnitude of this
eectdecreases with travel distance, as shown by Keller et al.[70],
but can nevertheless result in earlier breakthrough ofcolloids
moving through a porous medium, as seen in lar-ger scale studies
(Table 2).
An important result from these studies is that dispersiv-ity,
which is generally considered an intrinsic property ofthe porous
medium [10], is a function of colloid size [4];it may be more
appropriate to denominate it apparent dis-persivity when discussing
colloid transport. The eect had
Fig. 7. Experimentally measured residence time distributions for
2 lmcolloids in dierent pore geometries, with a pressure gradient
of 500 Paacross the micromodel (visualization method as presented
in [4]).
-
Wa1398 A.A. Keller, M. Auset / Advances inbeen observed at
larger scales. For example, Shonnardet al.,Pang et al. [119,98],
analyzing earlier breakthroughof microbes relative to a tracer,
assigned a lower dispersiv-ity for microbes than for solutes. They
noted dierences indispersion that led to faster breakthrough,
although theywere unable to pinpoint the mechanism that caused
thesedierences. Sinton et al. [120] reported reductions in
thedispersivity when modeling migration of dierent sized
Fig. 8. Comparison between geometries at dierent pressure
gradients. Mean rmodel (circles), 20 lm-channel model (squares),
zig-zag model (triangle). (a) 1
Fig. 9. Ratio of ensemble mean velocity and the straight path
meanvelocity for four colloid sizes, at the highest-pressure
gradient (1500 Pa) ineach pore geometry.esidence time as a function
of colloidal diameter. Ten micrometer-channel500 Pa; (b) 1000 Pa;
(c) 500 Pa and (d) 100 Pa.
ter Resources 30 (2007) 13921407microorganisms in an alluvial
gravel aquifer. Schulze-Mak-uch et al. [116] also found variable
longitudinal dispersivi-ties between bromide and MS2 virus in a
model aquifer andshowed that vertical dispersion of MS2 is actually
less thanthat of bromide. The micromodel studies have provided
thevisual explanation for these macroscale observations.
2.2. Exclusion
A number of colloid exclusion processes have been dis-cussed in
the literature (e.g., [43,44,13,12]). The most evi-dent exclusion
process occurs when the colloid diameteris larger or equal to the
pore throat to be entered, resultingin either exclusion (the
colloid does not enter the downgra-dient pore space) or straining,
with attachment of the col-loid to the SWI. A more subtle exclusion
process wasobserved in the micromodel experiments conducted by
Sir-ivithayapakorn and Keller [121,122] which revealed thatthe pore
T/C ratio threshold for entering a pore throatwas about 1.5, due to
the hydrodynamics of the system.Since colloids are focused towards
the central streamlines,they rarely enter small pore throats. In
these studies, morethan 100 colloids were tracked through various
pores, andthe T/C threshold seemed to hold for various sizes
andtypes of colloids, including viruses [121,122]. The
pressuregradient was seen not to have a signicant eect on theT/C
threshold. Although the exact T/C ratio thresholdwas not
determined, one can use this value to consider thatbiocolloids
larger than about 15 lm can be excluded from
-
Table 2Column and eld studies of colloid velocity
enhancement
Reference Travel distance Medium, particle size Colloids, size
(lm) Velocity enhancement Velocity (m/d)
Colloid transport through laboratory columns
[153] 110 cm Particles, 18, 40, 58 lm Microspheres,1, 2, 3, 5,
7, 10 lm 1.031.09 3.27
[150] 30 cm Quartz powder, 30 lm Microspheres 0.04 lm 1.06
0.1440.17 lm 1.110.31 lm 1.13
[147] 60 cm Column sediments, 0.51 mm 0.2 lm 1.9 1.40.7 lm
1.71.3 lm 1.6
[50] 46 cm Soil aggregates 12 mm Microspheres 0.11 lm 1.4 10
[52] 10 cm Coarse sand, 1.42.4 mm Medium sand, 0.40.5 mm
Cryptosporidium parvum oocysts, 4.55.5 lm 11.38 0.7Fine sand,
0.180.25 mm 7
[29] 40 cm 50 cm Sand sediments Comamonas sp., 0.6 1.1 lm
1.11.551.8 0.5
[149] 120 cm Crushed int gravel,1.53 mm Aeolian quartz silt, 260
lm 0.751.08 10.4432
[116] 109 cm Sieved play sand Phage MS2 = 0.024 lm 0.88 (pH 6.1)
2301.03 (pH 7.5)1.14 (pH 8.1)
[70] 60 cm Medium sand Microspheres, 3 and 0.05 1.051.09
1.4Phage MS2 = 0.025 lm 1.111.14 14
Field studies of colloid transport
[152] Aquifer Escherichia coli 1.161.2
[148] 0.57 m Sand aquifer 1.001.3 0.431.081.62 m Fulvic acid, 1
nm 1.12.3 0.360.624
Polystyrene sulphonate, 20 nm 1.041.11 0.61.31.01.4 0.431.08
[146] 6.9 m downgradient Sandy aquifer, 0.5 mm Carboxylated
microspheres 0.23 lm 1.4 0.330.53 lm 1.40.91 lm 1.41.35 lm 1.1
[151] 385 m Alluvial gravel aquifer Fecal coliforms 1.29
160F-RNA coliphages 1.88Escherichia coli,J6-2 1.05Phage MS2
1.25
[98] 61.63 m Alluvial gravel aquifer Bacillus subtilis
endospores 1.16 64
[120] 1218 m Alluvial gravel aquifer Escherichia coli, 1.56 lm
1.3 and 2 94Endospores, 0.81.5 lm 1.22 94Phage MS2, 0.026 lm 1.21
72
[144] 0.30 m Colluvial aquifer,silt to gravel size particles
Microsphere, 0.98 lm 1.810.55 m 1.51.81 m 1.1
A.A.Keller,
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-
most small pore throats on the order of a few lm [121,122].A
third exclusion process can occur for higher pressure gra-dients,
since the colloids will tend to by-pass relatively stag-nant
regions, traveling along the central streamlines. Inaddition,
larger colloids are excluded from some of thestreamlines near the
pore body and pore throat walls[121,122]. Finally, biocolloids may
have surface chargesthat result in repulsion from the grain
surfaces, thusexcluding them from certain pore regions (e.g.,
[113]).
The size of the microbe had previously been observed tobe an
important factor in bacterial transport in porousmedia (e.g.,
[41,39,29]). Variation on the macroscopictransport behavior of
dierent sized biocolloids can benow explained by mechanisms that
occur at the scale ofpores and pore networks. All four exclusion
processesresult in selectively faster transport of larger colloids,
rela-tive to smaller colloids.
stant (m/s2), lw = viscosity of aqueous solution (kg/m s),U =
pore water velocity (m/s), dp = particle eective diam-eter (m), dg
= eective grain diameter (m), As = soil specicconstant related to
hm = soil matrix porosity (),kB = Boltzmanns constant (J/K), and T
= temperature(K). Recently, Tufenkji and Elimelech [133] have
proposedthe following rened correlation based on
experimentalevidence:
g 2:4A1=3S N0:081R N0:715Pe N 0:052vdW 0:55ASN 1:675R N 0:125A
0:22N0:24R N 1:11G N 0:053vdW 3
where NR dpdg ; NPe UdpD1
; N vdW AkBT ;
NA A12plwa2pU
; NG 29
a2pqp qfglU
;
D1 = colloid bulk diusion coecient (m2/s), A = Hamaker
21 20
1400 A.A. Keller, M. Auset / Advances in Water Resources 30
(2007) 139214072.3. Collision with SWI
From a theoretical perspective, colloids are thought toreach the
SWI based on three mechanisms: interception,diusion and
gravitational deposition. The theoreticalframework was put forward
by Yao et al. [142] and Rajag-opalan and Tien [102], and has since
been rened by severalauthors, in particular by Rajagopalan et al.,
Ryan andElimelech [103,109]. Based on this theoretical approach,the
probability of a collision can be estimated from:
g 0:897As
3p kBT
lwdpdgU
2=3 32As
dpdg
2 qp qwg
18lwUdp
1As 21 p5=2 3p 3p5 2p6; p 1 hm1=3 2
where qp = particle density (kg/m3), qw = density of aque-
ous solution (kg/m3), g = gravitational acceleration con-Fig.
10. Estimate of relative importance of interception, diusion and
gravitavelocities, for colloids of (a) 50 nm; (b) 1.0 lm; (c) 2.5
lm and (d) 5.0 lm.constant (3 10 4 10 J), and ap = particle
radius(m). The three terms correspond to interception, diusionand
gravitational deposition.
Using general values for biocolloids, such as a particledensity
of 1050 kg/m3 (ref) and particle size ranging from50 nm to 5 lm,
the relative importance of these three pro-cesses as a function of
velocity can be estimated using Eq.(3) (Fig. 10), considering a
porosity of 30% and an eectivegrain diameter of 100 lm (ne sand).
The range of owvelocities corresponds to a few cm/d to about 100
m/d,which is the range of interest for transport in porous
media.From Eq. (1), interception is considered to be mostly
afunction of the relative size ratio between the colloid andthe
grains of the porous medium, as well as the porosityvia As,
independent of U. Interception is expected to bestrongly inuenced
by matrix porosity, particularly asporosity decreases below 10%.
However, the empirical evi-dence used to parameterize Eq. (3)
indicates that intercep-tion is in fact a function of ow velocity,
decreasing withtional deposition, and total collision probability
(Eq. (3)) at dierent ow
-
increasing velocity. This was recently observed in micro-model
studies by Baumann and Werth [8]. These experi-ments show that at
high ow velocities interception is lessprobable, since the colloids
follow along the streamlinesand are generally diverted from the
grain surfaces.
For small biocolloids such as viruses and microorgan-isms up to
about 1 lm, interception is thought to be negli-gible, while
diusion dominates over gravitationaldeposition at all ow velocities
of interest (Fig. 10a,b).From the micromodel studies and
calculation of the veloc-ity eld within a complex pore network,
there are regionsof stagnant water which are shielded from the main
owdirection by the grains, are in crevasses or dead end pores,or
along the walls of wide pore bodies (Fig. 11). Small bio-colloids
are likely to accumulate initially in these regions,since they are
more likely to be traveling along thesestreamlines and can more
easily diuse into stagnantregions. For larger biocolloids,
interception should domi-nate, followed by diusion (Fig. 10d).
Gravitational depo-sition becomes important only for ow velocities
less than1 106 m/s, or on the order of mm/day, since
biocolloidsthat are almost buoyancy neutral.
2.4. Attachment
stability [62]. Recently, work by Tufenkji and Elimelech,Redman
et al. [134,105] suggests that additional aspectsneed to be
considered. Grain surface composition andcharge have been shown to
be important (e.g.,[135,89,56]), as well as the biocolloid surface
proteinsand other charged chemical species (e.g., [74,136]).
Basedon theoretical calculations, Baumann and Werth [8] esti-mated
that the probability of attachment for their colloidsis in the
range of 104106. Schijven et al. [115] reportedvalues for a of
0.000270.0014 for MS2 viruses in dunesand. Keller et al. [70]
reported values of 0.0080.0026for MS2 viruses in medium sand at ow
velocities of1.414 m/day. For Cryptosporidium, Harter et al.
[52]reported values from 0.37 to 1.1 in sand. In Sedimentcores,
Dong et al. [29] measured values of 0.0030.025for Comamonas sp.
Most of the experimental evidence isfrom column studies, leaving
this as an area of openresearch at the microscale.
A number of studies have addressed the mechanisms ofbiocolloid
attachment to the SWI and/or a growing bio-lm. A biolm may include
cells as well as exopolymericsubstances that serve as a substrate
modier for a numberof reasons (e.g., [22,17,47]). Dierent bacterial
strains mayexhibit dierential attachment (e.g., [6]). Surface
physico-
A.A. Keller, M. Auset / Advances in Water Resources 30 (2007)
13921407 1401Once the biocolloid collides with the SWI, the
proba-bility of attaching to the surface, also denominated
theattachment eciency, a, is thought to be controlled
byelectrostatic and van der Waals interactions [84].
Theseinteractions have been estimated using
DerjaguinLan-dauVerweyOverbeek (DLVO) theory of biocolloidalFig.
11. Images of collision via interception and diusion into dead-end
pores fwithin a PDMS micromodel. Clusters of colloids form even at
very low ionicchemical properties inuence the ability of
biocolloids toform biolms (e.g., [15,79,63,92]). These biolms
caninduce changes in hydrodynamic properties that inuencethe
transport of subsequent biocolloids (e.g., [107]).Detachment of
biocolloids from these biolms is a sourcefor downgradient sites,
and may be inuenced by a varietyof processes including ow velocity
and associated shearor 5 lm latex microspheres at an average
velocity of 143 lm/s = 12 m/day,strength (deionized water)
(visualization method as presented in [4]).
-
stress, chemical conditions or biolm thickness
(e.g.,[57,45,140,60]).
Particleparticle interactions may lead to attachmentand
clustering (Fig. 11e,f, Fig. 12). Attached biocolloidscan also form
large clusters up to a certain thickness
matrix, and will also inuence the pathways of
subsequentcolloids, modifying the dispersivity of the matrix.
Clustersof colloids can also form at the AWI (discussed in thenext
section), which upon release from the interface canlead to a
collision with the SWI and subsequentattachment.
3. Biocolloid transport processes in unsaturated porous
media
Flow and transport mechanisms in the unsaturated zonebecome more
complicated than those in the saturated zonebecause of the presence
of the AWI, ow discontinuitiesand wetting history [93,110].
Investigations at larger scaleshave shown that volumetric moisture
content and porewater velocity play a key role in biocolloid
transport inthe vadose zone (e.g., [101]). Biocolloid sorption at
theAWI has been recognized as an important process for sev-eral
years [138,139,100].
Pore scale studies in unsaturated conditions [139,122]have shown
that, like the SWI, the AWI serves as collectorof biocolloids (Fig.
13). Some of the colloids might also betrapped at the triple
junction, the SWA. These interfaces(AWI and SWA) are therefore
important barriers for bio-colloid transport. Colloids can interact
with the AWI
Fig. 12. Clustering of colloids that results in signicant
modication ofpermeability and colloid transport pathways
(visualization method aspresented in [4]).
1402 A.A. Keller, M. Auset / Advances in Water Resources 30
(2007) 13921407(i.e., biolms, aggregates and laments, biowebs),
untilsome of the cells in the interior become starved of a
par-ticular chemical (e.g., electron acceptor, nutrients), lead-ing
to rupture of the biolm and subsequent release(biosloughing) (e.g.,
[32]). These clusters can result in sig-nicant modication of the
permeability of the porousFig. 13. Sequence showing the imbibition
process that displaces the air phase, eEventually the air bubble
dissolves, leading to the formation of clusters of colbreak up
(visualization method as presented in [4]).through the same
collision processes described before.However, in part due to the
hydrophobicity of the AWIand the proliferation of these interfaces
as the porousmatrix drains, the probability of attachment
increasessignicantly.
ventually leading to a detached air bubble with several colloids
at the AWI.
loids. The clusters can then be transported through the pore
space, or can
-
WaThe earlier work visualizing colloid sorption at the AWIwas
done under steady pore water ow [138], and it led tothe conclusion
that colloids were sorbed irreversibly at theAWI. Increasing air
saturation increased retention at theAWI [139]. These observations
were supported by resultsof experiments on mass balance of
breakthrough colloidconcentrations in sand columns [112,6466,77]
where moreparticles were retained at lower water contents.
Calcula-tions by Sirivithayapakorn and Keller [122] using
DLVOtheory and evaluating the electrostatic and capillary
forcesindicated that colloids, including MS2 viruses, should beheld
almost irreversible at the AWI, once they cross overthe energy
barrier for attachment. The energy barrierincreases with particle
size, but is on the scale of 115 nmmeasured from the AWI into the
bulk solution. Thus, col-loids can migrate slowly very near the AWI
along stream-lines perpendicular to the interface and not be
capturedunless they cross the energy barrier due to some
mechanism(diusion or interception). On the other hand, water
owaround entrapped air bubbles decreases substantially, sincethe
dimensions of the water lms through which water owis on the order
of a few lm2 at most [69].
As with attachment to the SWI, biocolloid attachmentto the AWI
is a function of ionic strength and the surfaceproperties of the
biocolloid, such as hydrophobicity andsurface charge [138].
Increases in ionic strength will reducethe magnitude of the
repulsive energy barrier between thenegatively charged airwater
interface and the biocolloids,leading to progressively more
favorable conditions forattachment and faster rates of airwater
interface capture.
Wan and Tokunaga [137] introduced an additionalmechanism of
colloid immobilization in partially saturatedporous media. They
used the concept of lm straining tosuggest that the transport of
suspended colloids could beretarded due to physical restrictions
imposed when thethickness of water lms is smaller than the diameter
ofthe colloids. Wan and Tokunaga [137] estimated that theselms
should be on the order of 2040 nm, which is consid-erably thinner
than a 1 lm Escherichia coli, but may notcompletely immobilize a 25
nm virus. Chu et al. [20] esti-mated a lm thickness in the range of
1521 nm for dier-ent soils, at a water content of 0.170.29 cm3 cm3.
In theircolumn studies, Keller et al. [70] estimated a thickness
forthe water lms of 3060 nm in a medium sand and averagewater
content of 0.110.18 cm3 cm3.
According to Wan and Tokunaga [137], colloid reten-tion by lm
straining depends on the existence of pendularring discontinuity,
on the ratio of biocolloid size to lmwidth and on ow velocity. A
pendular ring is dened aswater retained by capillarity around the
adjacent grains.The possibility of pendular ring discontinuity
augmentsas the capillary pressure decreases [27]. When the
biocol-loid diameter is smaller than lm thickness, strainingremains
ineective. When the biocolloid diameter is similaror bigger than lm
thickness than surface tension forces
A.A. Keller, M. Auset / Advances inretain biocolloids against
grain surfaces. Crist et al. [25]provided visual evidence that
biocolloid retention can alsooccur via trapping at the
solidwaterair (SWA) interface.These thin water lms serve as storage
locations for biocol-loids under unsaturated conditions, but may
also serve toplace the biocolloid in direct contact with the SWI if
thewater lm thickness decreases even more.
Transient ow, generated by rainfall and snowmeltevents
interspersed between dry periods or due to articialaquifer recharge
or other anthropogenic actions, can pro-mote very rapid biocolloid
mobilization (e.g., [34]). Undertransient conditions it has been
observed that the move-ment of biocolloids is aected by the
movement of air bub-bles and AWI (e.g., [46,45,71]).
Sirivithayapakorn andKeller, Auset et al. [122,5] observed in
micromodels howinltration events can mobilize the AWI, thicken the
waterlms where colloids are immobilized, dissolve some of thegas
phase and mobilize air bubbles (Fig. 13). First, theAWI is
displaced as the water re-imbibes into the porousmedia. Colloids
trapped in stagnant water regions are ableto remobilize. At some
point, an air bubble breaks o fromthe main air phase. Colloids
which were attached to theAWI remain attached until the AWI
disappears. Eventu-ally, these rewetting processes lead to the
remobilizationof all colloids trapped at the AWI or in thin water
lms.
Depending on colloid surface properties, the colloidsmay tend to
cluster even in solution. However, in manycases surface charges are
similar, creating an electrostaticbarrier that reduces the
likelihood of clustering, as calcu-lated by Sirivithayapakorn and
Keller [122] for MS2viruses and latex microspheres in a weak ionic
solution.Nevertheless, colloid clusters can form at the AWI as
thesize of the AWI shrinks, as observed in Fig. 13gh. Theseclusters
might be stable enough to travel as a single body,or they might
break up while traveling (Fig. 13i). Theseobservations suggest that
coagulation at the AWI mayincrease the overall ltration for
biocolloids transportedthrough the vadose zone.
Whether all colloids on the AWI are actually at theSWA interface
is an open question. In most micromodelvisualizations, the pore
space being observed reects a thin(1050 lm) wedge between the top
and bottom surfaces(see for example the diagram in [25]). Colloids
whichappear to be at the AWI could in fact be at the SWA.
Cer-tainly, some of the colloids observed in these experimentsare
at the SWA, as suggested by Crist et al. [25]. Even asthe imbibing
water front displaces the air phase in Figs.13bg, some of the
colloids remain in place, suggestingattachment to the SWI at the
same time that the colloidswere in contact with the AWI. However,
in other sequences(e.g., [5,122]; and Fig. 13), some colloids are
seen to rapidlytravel through the porous media as soon as the AWI
disap-pears, suggesting no attachment to the SWI.
Rewetting processes and intermittent wetting and dryingevents
thus can result in signicant mobilization of biocol-loids that had
been considered irreversibly retained at theAWI. Colloid
remobilization appears to be a strong function
ter Resources 30 (2007) 13921407 1403of particle size [71].
Although intermittent ltration providessignicant pathogen removal
capacity, it is important to
-
unanswered. The conditions that result in attachment to
ter and the UCSB Academic Senate. M. Auset thank the
Wapostdoctoral fellowship support from the Secretara de Es-tado
de Educacion y Universidades (Spain). Jose Saletaperformed the ESEM
at MEIAF/UCSB (NSF 9977772).
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A review of visualization techniques of biocolloid transport
processes at the pore scale under saturated and unsaturated
conditionsIntroductionBiocolloid transport processes in saturated
porous mediaAdvection, diffusion, dispersionExclusionCollision with
SWIAttachment
Biocolloid transport processes in unsaturated porous mediaFuture
research directionsAcknowledgementsReferences