SWSoil and Water: Transport of Particulate and Colloid-sorbed Contaminants through Soil, Part 2: Trapping Processes and Soil Pore Geometry

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  • Biosystems Engineering (2002) 83 (4), 387395w

    d

    E

    d

    d

    sufciently large diameter to have their movement restricted by physical straining in the soil pores when waterdrains from the soil under gravity, but if the soil is very wet (near to saturation) even these will move withoutrestriction. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved1. Introduction

    Part 1 of this paper (McGechan & Lewis, 2002)discusses some general principles governing transportthrough soil of colloid-associated contaminants such asphosphorus, pesticides and other agrochemicals,plus a range of biological microorganisms. In particular,it was noted that there appear to be two importanttypes of restrictions physically limiting the colloidmovement in soil and other porous media: straining,where the physical size of the pore is smaller thanthe particle so the particle is unable to pass, andltration, which covers a range of mechanisms bywhich particles are captured in pores with dimensionslarger than the particles. Both types of capture, butstraining in particular, are very dependent on thesizes (or the size distributions) both of colloidalparticles and of soil pores. Consideration of sizes ofcolloidal particles can refer to the sizes of free-standing

    indication of the extent of trapping of colloids bystraining.

    2. Mathematical description of soil pore space

    2.1. Requirement for description of soil pores

    Restrictions on movement of colloids through soilscaused by a range of mechanisms (but particularly dueto straining) are likely to be related to the size ofparticles in relation to the size of soil pores. Since thesizes of both colloidal particles and of the soil pores canvary over a wide range, it is necessary to consider sizedistributions for both. The geometrical shape, whichtypically is not circular or spherical, also needs to beconsidered, particularly for soil pores.The size distribution of water-lled pores in soil can

    be estimated from hydraulic properties using twodoi:10.1006/bioe.2002.0136, available online at http://wwSW}Soil and Water

    REVIEW

    Transport of Particulate and Colloid-sorTrapping Processes an

    M.B. Mc

    Environment Division, SAC, Bush Estate, Penicuik

    (Received 14 September 2001; receive

    It was established in Part 1 that potential impediments tinto straining and ltration, depending on whether aphysical trapping) or much smaller. Information abouPart 1. Owing to the dependence of colloid or particle caparticles and pores, information about pore sizeshydrological equations. Various approaches to extenparticles would be trapped by necks or irregularitiesprotozoan microorganisms (such as Cryptosporidium amicroorganisms, or of soil particles onto which con-taminants are sorbed, as discussed in Part 1. This paper(Part 2) explores a theoretical mathematical approachbased on equations of hydrology which might give an

    1537-5110/02/$35.00 387.idealibrary.com on

    PAPER

    bed Contaminants through Soil, Part 2:Soil Pore Geometry

    Gechan

    H26 0PH, UK; e-mail: m.mcgechan@ed.sac.ac.uk

    in revised form 2 September 2002)

    o movement of colloids through soil can be subdividedparticle has a dimension similar to pores (leading tot size distributions of particles was also presented inpture processes on the relative size distributions of theistributions has been derived here (Part 2) fromding this mathematical treatment to indicate whenin the pore are also presented. Results suggest thatnd Giardia) are the only colloidal contaminants withfundamental equations in uid mechanics, the capillaryrise equation and Poiseuilles Law. Later in this paper,the approach of using these equations, or adaptations ofthem, to estimate the sizes of suspended particulate or

    # 2002 Silsoe Research Institute. Published byElsevier Science Ltd. All rights reserved

  • M.B. MCGECHAN388so h=15 10 /rm.Poiseuilles law is stated as

    Q pr4DP8Lm

    2

    where: Q is the water ux in m3 s1 due to a pressuredrop DP in Pa along length of tube L in m and m is thedynamic viscosity of water in Pa s. For water at 108C,m=1312 103 Pa s. From Eqn (2), the mean owvelocity %uu in m s1 through the tube can be derived:

    %uu r2DP8Lm

    3

    2.3. Capillary bundle model

    There have been a number of theoretical studies ofsoil and other porous media using these equations,

    integral of the pore size distribution curve, or converselythat the pore size distribution is the slope of the waterrelease curve (Payne, 1988). Ball (1981) pointed out thatthis model is inaccurate in soils where pores ofcontrasting radius are joined together, since larger porescan drain only at the same time as the smaller pores thatthey link, and consequently the volume of small pores isoverestimated. However, in the absence of a satisfactoryalternative, the simple model is widely assumed. Itappears to be preferable to the approach adopted byNicholson et al. (1988), Kosugi and Hopmans (1998)and Kosugi (1999), who based similar analyses onvarious alternative standard frequency distributionequations for soil pore radius, rather than basing it onthe measured water release curve. Brooks and Corey(1966) derived an equation for a curve to be tted toexperimental water release data, based on an assumeddistribution of pore sizes. This equation includes a porecolloidal material which will either pass freely throughthe soil prole or be prevented from passing, is explored.

    2.2. Fundamental equations

    The equation for capillary rise (which is mostsignicant for a tube with small radius) can be statedfor a liquid in a tube with circular cross-section as

    h 2srwgr

    1

    where: h is the height in m that water will rise in acapillary tube of radius r in m with which it forms a zerocontact angle; s is the surface tension of the liquid waterin kg s2; rw is the density in kgm

    3; and g is theacceleration due to gravity in m s2. For water at 108C,s=00727 kg s2, rw=1000 kg m

    3 and g=981m s2,6

    A matching parameterd diameter of ltrate particle, md85 85% percentile of ltrate particle diametersD diameter of lter particle, mD15 15% percentile of lter particle diametersg acceleration due to gravity, m s1

    h capillary rise, mi, j, n summation limitsk Kozeny constantk0 shape factorK(y) hydraulic conductivity of soil at volumetric

    water content yL length of straight tube or porous medium, mLe actual path length through length L of

    medium taking account of tortuosity, mm ratio of the pore space volume to the area of

    Notabased on the analogy with a bundle of capillary tubes ofvarious diameters, e.g. that of Jury et al. (1991), who usethe term capillary bundle model. Analysis would bevery straightforward for a bundle of tubes all of thesame diameter, but this is not the case for soil, andvarious approaches have been taken to take account ofthe distribution of tube (or pore) diameters. Thisdistribution of pore diameters, along with other featuresof pore geometry such as shape and continuity, accountsfor the important hydraulic characteristics of a real soil,the water release curve (tension against water content)and the hydraulic conductivity (which declines withdecrease in water content or increase in tension).In the capillary bundle model, the distribution of tube

    diameters is derived from a measured water releasecurve assuming that tension is related to the radius ofthe largest water-lled pore according to Eqn (1). Thisrelationship implies that the water release curve is the

    the wetted surface (hydraulic radius), mDP pressure drop along length L of tube, PaQ water ux due to a pressure drop Dp, m3 s1

    r radius of tube with circular cross-section, mS surface area per unit volume, m1

    %uu mean ow velocity through tube, m s1

    a scaling parametery volumetric soil water content, fractionys porosity, fractionl pore size distribution index (Brooks & Corey,

    1966)m dynamic viscosity of water, Pa srw density of water , kg m

    3

    s surface tension of liquid water, kg s2

    j soil water tension, Pa

    tion

  • TRANSPORT OF CONTAMINANTS THROUGH SOIL 389size distribution index parameter l, such that a largevalue of l indicates a narrow range of pore sizes and asmall value of l indicates a wide range of pore sizes.Arya and Paris (1981) present a model for predicting thesoil water characteristic from the particle size distribu-tion and bulk density, based on the similarity betweenthe particle size distribution and the water retentioncurve. Pore lengths based on spherical particles werescaled to natural pore lengths using a scaling parametera, taking an average value of 138. Later, Arya et al.(1999a) determined different values of a for different soiltypes by summing properties in particle size classes.

    2.4. Theoretical basis for variation in hydraulicconductivity

    2.4.1. Conductivity based on capillary bundle approachHydraulic conductivity is related to the whole pore

    size distribution rather than the largest water-lled pore,since at a given soil water content all continuous water-lled pores contribute to the total ow of water throughthe soil. The electrical analogy for this is the currentscalculated by Ohms law for resisters in parallel. Thesimplest treatment of this is described by Jury et al.(1991), by summing the contributions from each water-lled tube in the bundle as given by the tube radiusdistribution derived from the water release curve. Thecontribution from tubes of a particular range of radii isderived from Eqn (2), with an additional tortuosityterm based on the assumption that each tube isconvoluted, so its length Le is longer than the wholebundle L, as discussed by Fatt and Dykstra (1951),Burdine (1953) and by Wyllie and Gardner (1958).

    2.4.2. Adaptation of capillary bundle model tonon-circular cross-sections

    A number of researchers (Kozeny, 1927; Fair &Hatch, 1933; Carman, 1937; Wyllie & Spangler, 1952)have modied the ow velocity equation further to takeaccount of non-circular cross-sections as well as thetortuosity effect, replacing r2/8 in Eqn (3) by m2/k0,where m is the ratio of the pore space volume to the areaof the wetted surface (called the hydraulic radius, inm), and k0 is a shape factor; m is describedmathematically as ys/S where ys is the porosity (frac-tion), S is the surface area per unit volume (in m1), andk0 is a component of the Kozeny constant k where

    k k0 Le=L 2 4

    Values of m can be calculated for regular-shaped pores,e.g. r/2 for a cylindrical tube, r/3 for a sphere and r/333for the space surrounding uniform diameter spherespacked with their centres in line in three dimensions.Values of k0 have been measured experimentally asbeing in the region of 25 for most irregular shapes,compared to theoretical values for regular cross-sectionsreported by Carman (1937) such as 20 for a circle and30 for a rectangle of innite width. Similarly, values ofaround 50 have been measured experimentally for k,implying a tortuosity (Le/L)

    2 of around 20. Thehydraulic radius and shape factor have been incorpo-rated by Brooks and Corey (1966) into a procedure forderiving the decrease in hydraulic conductivity withdecrease in water content, from the pore size distribu-tion indicated by l in their equation for the water releasecurve.

    2.4.3. Random joining of pores approachAnother complexity in deriving the conductivity curve

    was rst introduced by Childs and Collis-George (1950),but later modied by Marshall (1958), and Millingtonand Quirk (1959, 1961), and further discussed by Greenand Corey (1971), Jackson (1972), Campbell (1974) andGavalas (1980). This treatment takes account of varioussequences of pores of different sizes when pores arerandomly arranged in a porous system. Mathematically,they assume that the bundle of tubes of various sizes iscut and randomly rejoined in a different position sosmall pores meet up with large ones and the ow isdetermined by the smaller pore at the join, whichrequires a summation for tension (pore size) class groupsof an equation of the form

    K y i AXn

    ji

    2j 1 2ij2j ; i 1; 2; :::; n 5

    where: Ky is the hydraulic conductivity of soil atvolumetric water content y; i; j and n are summationlimits; A is a matching parameter; and j is the soil watertension in Pa.Equation (5) is similar to that presented by Marshall

    (1958) who simplied the procedure by dividing up thepore size distribution into equal porosity intervals,unlike Childs and Collis-George (1950) who subdividedtension into class intervals which made the procedureeven more complex. Some authors have attempted topredict absolute values of conductivities taking accountof estimates of m, k0 andy (the subject of much of theongoing discussion by Marshall, 1958; Millington &Quirk, 1959, 1961; Green & Corey, 1971), the so-calledKozeny-Carmen equation. However, this equation hasbeen applied mainly to fairly uniform porous mediasuch as microscopic glass beads or sand beds rather thanagricultural soils. Other authors including Childs andCollis-George (1950), Brooks and Corey (1966) andJackson (1972) only predict the variation of conductivitywith water content, choosing a value of the matchingparameter A in Eqn (5) to t the relationship to the

  • Fig. 1. Water release characteristics, measured data points andBrooks and Corey (1964) fitted relationships for three soils:(a) clay loam tilled soil; (b) sandy loam tilled soil; (c) siltyclay loam grassland soil; (from McGechan et al., 1997). Radiusof largest water-filled pore according to Eqn (1) also indicated:&, 0.05 m depth (upper topsoil);}m}, 0.15 m depth (lowertopsoil); }*}, 0.5 m depth (subsoil); }^}, 0.8 m depth(lower subsoil, tilled sandy loam soil only); . . ... . ., below

    0.95 m (C horizon, tilled sandy loam soil only)

    M.B. MCGECHAN390measured conductivity at one particular water content,and this is the procedure which has been adopted herefor agricultural soils.

    2.4.4. Other approaches to relating conductivity topore sizes from hydraulic equations

    An alternative set of equations for determining thehydraulic conductivity curve from water retention datais presented by Campbell (1994). Vucovi!cc and Soro(1992) compared and assessed ten alternative theoreticalor empirical equations relating conductivities of porousmedia to grain size composition. Arya et al. (1999b)apply a similar approach to that which they used for thewater retention curve (determining a by summing inparticle size classes, Arya et al., 1999a, see Section 23)to determine the hydraulic conductivity function fromthe particle size distribution. Beven and Germann (1981)describe a two-domain adaptation of the capillarybundle model approach for separate representation ofmacropores and micropores. Further complicationsspecic to macropores, which require an extension tothe approach based on Eqn (2), are described by Chenand Wagenet (1992).

    2.5. Measured and derived hydraulic conductivitiesfor real soils

    Measured water release data for three layers each ofthree agricultural soils, as reported by McGechan et al.(1997), are shown in Fig. 1. Fitted water release curvesaccording to the Brooks and Corey (1964) equation witha transition to a linear relationship in the macroporousregion near to eld capacity (Jansson, 1996; Jarvis,1994) are superimposed in Fig. 1. The radius of thelargest water-lled pore corresponding to each of thesecurves estimated from Eqn (1) is also indicated in Fig. 1.Curves representing hydraulic conductivities at a rangeof low tension values given by various equations for theupper layer of the rst of these soils are plotted in Fig. 2.The rst curve is that of the Brooks and Corey (1964)equation with a linear relationship near to saturation,tted to experimental data (McGechan et al., 1997)measured using a tension inltrometer technique (Jarviset al., 1987; Ankeny et al., 1988). The other curves arefrom the equations described by Jury et al. (1991),Childs and Collis-George (1950), Marshall (1958), andMillington and Quirk (1959, 1961) each adjusted by thefactor A to give the Brooks and Corey conductivityvalue at 6 kPa tension. Although both Marshall (1958),and Millington and Quirk (1959, 1961) attempt tocalculate the conductivity without an adjustment factor(Section 2.4.3), in both cases the results calculated in thisway were so much at variance with the experimental

  • TRANSPORT OF CONTAMINANTS THROUGH SOIL 391data and values predicted by the other equations thatthey are not shown in Fig. 2. When the adjustmentfactor is applied, all the equations are in reasonablyclose agreement. The biggest discrepancy (but not large)is shown by the simple Jury et al. (1991) equation,suggesting that there is a small benet in taking accountof the pore surface area to cross-sectional area ratio asdone by Childs and Collis-George (1950), Marshall(1958), and Millington and Quirk (1959, 1961).

    Fig. 2. Variation in hydraulic conductivity of clay loam tilledsoil in the surface layer (00.1 m) predicted by various models: , Jury et al. (1991); }}, Childs and Collis George

    (1950); , Brooks and Corey (1964)2.6. Fractal geometry as a description of soil pore space

    Further to the above descriptions of soil pore space interms of the mathematics of standard hydrologicalequations, there is also a very extensive use of theconcept of fractals to describe soil porosity and shapesof pores. Fractal mathematics is used to describe particlesize distributions and soil aggregate structures by Rieuand Sposito (1991a, 1991b), Perfect and Kay (1991),Young and Crawford (1991), Crawford et al. (1993,1997), Hallett et al. (1998) and Castrignan "oo and Stelluti(1999). Water release characteristics and/or hydraulicconductivities of soils have been related to fractalgeometry and particle size distributions by Tyler andWheatcraft (1990), Rieu and Sposito (1991a, 1991b),Crawford (1994), Crawford et al. (1995), Perrier et al.(1995), Bird et al. (1996), Perfect et al. (1996), Bird andDexter (1997) and Bird et al. (2000). The fractalapproach may have the potential to indicate irregula-rities in pore shape which will restrict colloid movement,but such a procedure has not so far been attempted.2.7. Further descriptions of soil pore space

    The foregoing descriptions of soil pore space all comefrom hydrological sources, where the interest has beenthe passage of liquid water (or in some cases gases)through pores, but these give only limited informationabout the variation in pore dimensions along a waterow streamline. However, such variations in poredimensions are important when considering colloidtransport since short constrictions are liable to trapparticles as they pass. Some papers considering poredimensions or descriptions but not directly concernedwith hydrological processes are discussed in this section.Farrell and Larson (1972) describe a physicoma-

    thematical alternative to capillaric modelling of thepore structure of a porous medium. Fi"ees and Bruand(1998) discuss pore space in relation to packing of clay,silt and sand particles. They examined such pore spacesby electron microscopy and using a mercury porosime-try method described by Fi"ees (1992). Moutier et al.(1998) also discuss pore space and particle packingformations, in connection with swelling in clay soilsreducing porosity and hydraulic conductivity. In con-nection with the work on gas diffusion through soil,Arah and Ball (1994) describe a model of a soil coredivided into slices with pore space subdivided intoarterial porosity, marginal porosity and (not alwayspresent), remote porosity. Eggleston and Peirce (1995)extended this concept into a dynamic programminganalysis of effective pore space (i.e. not including dead-end pores), to describe pore space and shapes, pathlengths, etc. A Boolean model of soil pores (Glasbeyet al., 1991) has been applied to simulate gas diffusion byHorgan and Ball (1994), while Ewing and Gupta (1993a,1993b) described the pore structure as a domainnetwork. Vogel and Roth (1998) describe a pore-scalenetwork model in which pore space is quantied interms of the pore size distribution and pore connectivity.This is further developed by Vogel (2000) and Kasteelet al. (2000) to derive the water release and hydraulicconductivity relationships, as well as to indicate solutetransport. A similar approach using a network modelentitled Pore-Cor has been described by Peat et al.(2000). Aitkenhead et al. (1999) describe a cellularautomaton method using an array of three-dimensionalpixels to describe soil pore space.

    3. Colloid capture by straining

    3.1. General principles of straining of particulates andcolloids

    For colloidal or particulate pollutants to pass freelythrough the soil, particles must be smaller than the pores

  • which particles would be strained and above which theywould not. They also made a rough attempt atmeasuring ow channel dimensions, showing that allow channels had roughly the same maximum andminimum dimensions normal to the direction of ow,with the minimum dimensions ranging between 009D15and 018D15. However, they found a higher critical D15/d85 ratio when ltering clay soil material with very fewsand or silt size particles (Sherard et al., 1984b). Sahimiand Jue (1988) discuss various concepts and equations(including a fractal description of pore space) represent-ing the hindering of transport of large solute moleculesthrough pores in a medium with dimensions of similarorder of magnitude to the solute molecules.Agricultural soils have a much wider range of particle

    and pore sizes (considering both soil matrix pores andmacropores) than the lters tested by Sherard et al.

    M.B. MCGECHAN392through which soil water is moving. A particle largerthan a pore is unable to move, so is captured, and thiswill also occur if a particle attempts to ow through ashort neck in a pore of diameter smaller than theparticle. Physical ltration (straining) is therefore verydependent on the size distributions of both colloidalparticles and water lled soil pores. Information aboutcolloidal particle size distributions has already beendiscussed in Part 1 and theoretical derivations of soilpore size distributions have been presented in Section 2.In this section, pore size and colloidal particle sizedistributions are compared to estimate the likely extentof the straining (physical ltration) process.

    3.2. Water flows in relation to pore size distribution

    When considering ltration of particulate pollutants,the size of the largest water-lled pore and thedistribution of pore sizes are estimated initially fromthe water release curve, but conductivity curves providea means of checking the assumptions about sizedistribution. Water only ows out of soil through elddrains by gravity if the soil is wetter than the eldcapacity water content, and eld capacity is commonlydened as a tension of 5 kPa. Although eld capacity asa steady-state situation is rarely reached in practice, theconcept is useful here to indicate the limiting size of awater-lled pore in which water can just move undergravity. Equation (1) gives a diameter of 60.5 106 mat 5 kPa tension for the largest water-lled pore. This isthe diameter of the largest water-lled pore, so mostpores which are conducting water are somewhat smaller.However, due to the power relationship in Eqn (2), mostof the water is conducted through pores only slightlysmaller than the largest water-lled pore (see also, Jury,1982; Jury & Stolzy, 1982; White, 1985). For a typicalwater release curve (Fig. 1), which represents the simplecumulative pore size distribution, a distributionweighted by the ow rate through each pore can beconstructed for a particular water content (Fig. 3). Thissuggests that 50% of the water in a soil at eld capacityis conducted through pores of more than 42.8 106 mand 90% through pores of more than 19.1 106 mdiameter.

    3.3. Straining estimated by relating sizes of pollutantparticles to soil pore sizes

    Since both particle sizes and pore sizes are representedby distributions rather than xed values, it is difcult todene size parameters which will indicate straining orfree movement of particles. Also there are variations inthe diameter of a pore along any owpath in the form ofnecks which are liable to cause straining. In theliterature on deep bed ltration where straining is ofno practical signicance, there is only a brief referenceby Tien and Payatakes (1979) who present an equationfor collection efciency based on geometrical consid-erations and constriction size distribution data fromPayatakes (1973). The work of Ball (1981) also gives anindication of the variation in pore diameter along aowpath in either the gas- or the water-lled porosityfor soils of varying water content. McDowell-Boyer et al.(1986) quote Herzig et al. (1970) that geometricalanalysis (Fig. 4) suggests that there will be little or nostraining where the pore size is more than 12 times theparticle size, but this takes no account of the distribu-tions of pore and particle sizes. Sherard et al. (1984a)found in experiments on ltration of water-borne soilparticles using lters of fairly uniform sand or gravelthat for most soils there was a critical value of D15/d8545 (15% of lter particles having diameter 4D15and 85% of ltrate particles diameter 4d85) below

    Fig. 3. Cumulative distributions of water flows through soilpores of different diameters, for unsaturated clay loam tilled soil

    in the surface layer (00.1 m) at various tension values

  • TRANSPORT OF CONTAMINANTS THROUGH SOIL 393(1984a, 1984b). A criterion for straining is thereforerequired based on the pore size distribution rather thanthe particle size distribution of soil as a lter, and theow-related pore size mean or decile (see Section 3.2)may be relevant parameters. At eld capacity, the ow-related mean pore size is 428 mm and 90% of the ow is

    Fig. 4. Straining in triangular constrictions (Herzig et al.,1970): (d/D)lim largest value of ratio of filtrate particle diameter

    d to filter particle D for filtrate particle to pass constrictionthrough pores of more than 191 106m diameter;allowing for a further factor of 10 to take account ofvariations in pore dimensions along a owpath. Thissuggests that particles with diameter greater than191 106m will be subject to some capture bystraining. Out of all the colloidal substances consideredin Part 1, only protozoan microorganisms fall into thissize category. Under conditions when soil is wetter thaneld capacity so that water moves under gravity, themain ow of water is through pores which aresubstantially larger than all colloidal particles otherthan protozoa. This suggests that protozoa may be theonly colloidal contaminants for which straining is arestriction on the movement in water owing to elddrains or deep percolation, and even these will be mobilewhen soil is markedly wetter than eld capacity.Straining may limit movement of colloid carriedcontaminants under dry conditions when only soilmatrix pores are water-lled, but under these conditionssuch contaminants are not released to the environmentas no liquid water leaves the soil prole. There may besome restriction on phosphate nutrients reaching plantroots other than in dissolved form, but this is not thesubject of this paper.4. Conclusions

    There are potential impediments to movement ofcolloids and colloidal contaminants through soil, andthese can be subdivided into straining (sometimes calledphysical ltration or mechanical ltration) where aparticle has a dimension larger than the pore throughwhich it is trying to pass, and true ltration (as discussedin Part 1) where the particle dimensions are muchsmaller than the pores. The extent of particle capture bystraining is very dependent on the relative dimensions(or size distributions) of the particles and pores. There isadequate information about size distributions for theimportant classes of colloidal particles (described in Part1), and it has been shown that pore size distributions(for water-lled pores) can be derived mathematicallyfrom the equations of hydrology. Supporting informa-tion about variations and irregularities in pores whichplay a part in particle trapping can also be gleaned fromliterature sources. These suggest that free-standing proto-zoan microorganisms (such as Cryptosporidium andGiardia) are the only colloidal contaminants with suf-ciently large diameter to have their movement restrictedby physical straining in the soil pores when water drainsfrom the soil under gravity, but if the soil is very wet(near to saturation) even these will move withoutrestriction. There may be capture in the soil of conta-minants such as chemicals, viruses and bacteria sorbedonto colloids in the clay particle size range (where theextent of capture is dependent on the size of the colloidalcarrier particle). Capture is likely to be at a low level innearly saturated soil, so carrier colloids can be assumedto move freely with soil water (like a solute), and theonly restriction on movement of the contaminant is bysorption mechanisms, with competition from sorptionsites on the mobile colloid and on the static soil matrix.The theoretical and mathematical analysis of colloid

    capture processes described in this paper has beencarried out to support and complement experimentaldetermination of capture process parameters. However,this approach is based purely on physical size con-siderations, whereas experimental results may differ dueto other physical or chemical factors or effects, asdiscussed in Part 1.

    Acknowledgements

    The Scottish Executive Environment and Rural AffairsDepartment provided funds to carry out the work.

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    Notation1. Introduction2. Mathematical description of soil pore spaceFigure 1Figure 2

    3. Colloid capture by strainingFigure 3Figure 4

    4. ConclusionsAcknowledgementsReferences

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