Biosystems Engineering (2002) 83 (4), 387–395doi:10.1006/bioe.2002.0136, available online at http://www.idealibrary.com onSW}Soil and Water

REVIEW PAPER

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

M.B. McGechan

Environment Division, SAC, Bush Estate, Penicuik EH26 0PH, UK; e-mail: m.mcgechan@ed.sac.ac.uk

(Received 14 September 2001; received in revised form 2 September 2002)

It was established in Part 1 that potential impediments to movement of colloids through soil can be subdividedinto straining and filtration, depending on whether a particle has a dimension similar to pores (leading tophysical trapping) or much smaller. Information about size distributions of particles was also presented inPart 1. Owing to the dependence of colloid or particle capture processes on the relative size distributions of theparticles and pores, information about pore sizes distributions has been derived here (Part 2) fromhydrological equations. Various approaches to extending this mathematical treatment to indicate whenparticles would be trapped by necks or irregularities in the pore are also presented. Results suggest thatprotozoan microorganisms (such as Cryptosporidium and Giardia) are the only colloidal contaminants withsufficiently 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 reserved

1. 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, andfiltration, 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-standingmicroorganisms, 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

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-filled pores in soil canbe estimated from hydraulic properties using twofundamental equations in fluid mechanics, the capillaryrise equation and Poiseuille’s 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 by

Elsevier Science Ltd. All rights reserved

M.B. MCGECHAN388

A matching parameterd diameter of filtrate particle, md85 85% percentile of filtrate particle diametersD diameter of filter particle, mD15 15% percentile of filter particle diametersg acceleration due to gravity, m s�1

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

the wetted surface (‘hydraulic radius’), mDP pressure drop along length L of tube, PaQ water flux due to a pressure drop Dp, m3 s�1

r radius of tube with circular cross-section, mS surface area per unit volume, m�1

%uu mean flow velocity through tube, m s�1

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 s�2

j soil water tension, Pa

Notation

colloidal material which will either pass freely throughthe soil profile or be prevented from passing, is explored.

2.2. Fundamental equations

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

h ¼2srwgr

ð1Þ

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 s�2; rw is the density in kgm�3; and g is theacceleration due to gravity in m s�2. For water at 108C,s=0�0727 kg s�2, rw=1000 kg m�3 and g=9�81m s�2,so h=15� 10�6/rm.

Poiseuille’s law is stated as

Q ¼pr4DP

8Lmð2Þ

where: Q is the water flux in m3 s�1 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=1�312� 10�3 Pa s. From Eqn (2), the mean flowvelocity %uu in m s�1 through the tube can be derived:

%uu ¼r2DP

8Lmð3Þ

2.3. Capillary bundle model

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

based 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 tubediameters is derived from a measured water releasecurve assuming that tension is related to the radius ofthe largest water-filled pore according to Eqn (1). Thisrelationship implies that the water release curve is theintegral 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 fitted toexperimental water release data, based on an assumeddistribution of pore sizes. This equation includes a ‘pore

TRANSPORT OF CONTAMINANTS THROUGH SOIL 389

size 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 1�38. 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 hydraulic

conductivity

2.4.1. Conductivity based on capillary bundle approach

Hydraulic conductivity is related to the whole poresize distribution rather than the largest water-filled pore,since at a given soil water content all continuous water-filled pores contribute to the total flow of water throughthe soil. The electrical analogy for this is the currentscalculated by Ohm’s law for resisters in parallel. Thesimplest treatment of this is described by Jury et al.(1991), by summing the contributions from each water-filled 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 ‘tortuosity’term 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 to

non-circular cross-sections

A number of researchers (Kozeny, 1927; Fair &Hatch, 1933; Carman, 1937; Wyllie & Spangler, 1952)have modified the flow 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 m�1), andk0 is a component of the ‘Kozeny constant’ k where

k ¼ k0 Le=L� �2 ð4Þ

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/3�33for 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 2�5 for most irregular shapes,compared to theoretical values for regular cross-sectionsreported by Carman (1937) such as 2�0 for a circle and3�0 for a rectangle of infinite width. Similarly, values ofaround 5�0 have been measured experimentally for k,implying a tortuosity (Le/L)

2 of around 2�0. 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 approach

Another complexity in deriving the conductivity curvewas first introduced by Childs and Collis-George (1950),but later modified 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 flow isdetermined by the smaller pore at the join, whichrequires a summation for tension (pore size) class groupsof an equation of the form

K yð Þi¼ AXn

j¼i

½ð2j þ 1� 2iÞj�2j ; i � 1; 2; :::; n ð5Þ

where: KðyÞ 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 simplified 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-called‘Kozeny-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 fit 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. MCGECHAN390

measured 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 to

pore 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 2�3)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 complicationsspecific to macropores, which require an extension tothe approach based on Eqn (2), are described by Chenand Wagenet (1992).

2.5. Measured and derived hydraulic conductivities

for 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 field capacity (Jansson, 1996; Jarvis,1994) are superimposed in Fig. 1. The radius of thelargest water-filled 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 first of these soils are plotted in Fig. 2.The first curve is that of the Brooks and Corey (1964)equation with a linear relationship near to saturation,fitted to experimental data (McGechan et al., 1997)measured using a tension infiltrometer 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

Fig. 2. Variation in hydraulic conductivity of clay loam tilledsoil in the surface layer (0–0.1 m) predicted by various models:– – – –, Jury et al. (1991); }}, Childs and Collis George

(1950); , Brooks and Corey (1964)

TRANSPORT OF CONTAMINANTS THROUGH SOIL 391

data 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 benefit 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).

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 waterflow 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 into‘arterial 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 quantified 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 and

colloids

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

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

in the surface layer (0–0.1 m) at various tension values

M.B. MCGECHAN392

through 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 flow through ashort neck in a pore of diameter smaller than theparticle. Physical filtration (‘straining’) is therefore verydependent on the size distributions of both colloidalparticles and water filled 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 filtration) process.

3.2. Water flows in relation to pore size distribution

When considering filtration of particulate pollutants,the size of the largest water-filled 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 flows out of soil through fielddrains by gravity if the soil is wetter than the ‘fieldcapacity’ water content, and field capacity is commonlydefined as a tension of 5 kPa. Although field capacity asa steady-state situation is rarely reached in practice, theconcept is useful here to indicate the limiting size of awater-filled pore in which water can just move undergravity. Equation (1) gives a diameter of 60.5� 10�6 mat 5 kPa tension for the largest water-filled pore. This isthe diameter of the largest water-filled 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-filled 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 flow rate through each pore can beconstructed for a particular water content (Fig. 3). Thissuggests that 50% of the water in a soil at field capacityis conducted through pores of more than 42.8� 10�6 mand 90% through pores of more than 19.1� 10�6 mdiameter.

3.3. Straining estimated by relating sizes of pollutant

particles to soil pore sizes

Since both particle sizes and pore sizes are representedby distributions rather than fixed values, it is difficult todefine size parameters which will indicate straining orfree movement of particles. Also there are variations inthe diameter of a pore along any flowpath in the form of

necks which are liable to cause straining. In theliterature on deep bed filtration where straining is ofno practical significance, there is only a brief referenceby Tien and Payatakes (1979) who present an equationfor ‘collection efficiency’ 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 aflowpath in either the gas- or the water-filled 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 filtration of water-borne soilparticles using filters of fairly uniform sand or gravelthat for most soils there was a critical value of D15/d8545 (15% of filter particles having diameter 4D15

and 85% of filtrate particles diameter 4d85) belowwhich particles would be strained and above which theywould not. They also made a rough attempt atmeasuring flow channel dimensions, showing that allflow channels had roughly the same maximum andminimum dimensions normal to the direction of flow,with the minimum dimensions ranging between 0�09D15

and 0�18D15. However, they found a higher critical D15/d85 ratio when filtering 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 particleand pore sizes (considering both soil matrix pores andmacropores) than the filters tested by Sherard et al.

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 constriction

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 filter, and theflow-related pore size mean or decile (see Section 3.2)may be relevant parameters. At field capacity, the flow-related mean pore size is 42�8 mm and 90% of the flow isthrough pores of more than 19�1� 10�6m diameter;allowing for a further factor of 10 to take account ofvariations in pore dimensions along a flowpath. Thissuggests that particles with diameter greater than1�91� 10�6m 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 thanfield capacity so that water moves under gravity, themain flow 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 flowing to fielddrains or deep percolation, and even these will be mobilewhen soil is markedly wetter than field capacity.Straining may limit movement of colloid carriedcontaminants under dry conditions when only soilmatrix pores are water-filled, but under these conditionssuch contaminants are not released to the environmentas no liquid water leaves the soil profile. 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 called‘physical filtration’ or ‘mechanical filtration’) where aparticle has a dimension larger than the pore throughwhich it is trying to pass, and true filtration (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-filled 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 suffi-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 colloidcapture 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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