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Lehrstuhl für Bodenkunde, Department für Ökologie, Wissenschaftszentrum Weihenstephan, Technische Universität München, D-85350 Freising-Weihenstephan, Germany
* Corresponding author (totsche{at}wzw.tum.de).
Received 5 July 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMODELINGNUMERICAL CASE STUDIESRESULTS AND DISCUSSIONREFERENCES |
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Abbreviations: BTC, breakthrough curve • HM, heavy metals • HOC, hydrophobic organic compounds • MOS, mobile organic sorbents • PAH, polycyclic aromatic hydrocarbons
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMODELINGNUMERICAL CASE STUDIESRESULTS AND DISCUSSIONREFERENCES |
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Due to their chemical properties (i.e., chemical diversity and high concentration of functional groups), these substances interact both with components of the immobile solid phase and with other dissolved and colloidal phase components of the liquid phase. Contaminant facilitated transport in the presence of MOS applies to such environmental conditions where MOS have to be considered a nonreactive mobile-phase constituent; that is, neither filtration nor sorption or partitioning of MOS to the immobile solid phase occurs. This is the case for porous media that is either in sorptive equilibrium with MOS or has unfavorable conditions for MOS sorption or attachment. In soils, however, MOS have to be considered reactive and are subject to immobilization due to sorptive interactions with the immobile soil (Murphy and Zachara, 1995; Kaiser et al., 1997; Weigand and Totsche, 1998). Common MOS sorbents are iron-, manganese-, and aluminum-(hydr)oxides; clay minerals; and organic matter (Kaiser et al., 1996; Jardine et al., 1989; McCarthy et al., 1993; Weigand and Totsche, 1998; Kaiser and Zech, 1998). In such environments, MOS may cause reduced overall contaminant mobility due to immobilization of MOS and thus immobilization of the MOS-associated contaminants (Lee et al., 1989; Totsche et al., 1997). The underlying process has been described as cosorption. Also, mobile organic sorbents sorption can lead to an increase of the organic C content of the bulk soil, thus increasing potential contaminant binding sites, a process referred to as cumulative sorption (Totsche et al., 1997).
In this paper, we analyze the effect of MOS on the mobility of contaminants in different environmental settings by means of numerical case studies. The objective is to find qualitative and quantitative criteria to distinguish between the effects on contaminant mobility that derive from processes which lead to MOS-mediated enhanced or reduced contaminant mobility. This knowledge is of prime importance for a reliable assessment of contaminant fate and for the interpretation of laboratory and field-scale contaminant breakthrough data. In particular, we will introduce and discuss three different scenarios of MOS-affected transport in porous media: cotransport, cosorption, and cumulative sorption. Within the cotransport scenario, the carrier MOS are considered nonreactive with respect to the immobile solid phase but are allowed to interact with the contaminants. This scenario will help to understand the phenomena of MOS-facilitated transport. In the cosorption and cumulative sorption scenarios, the MOS are allowed to interact with the immobile solid phase. These scenarios will help to understand reduced solubility and thus reduced mobility of solutes in the presence of MOS. All scenarios are based on either field data or experimental data.
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MODELING |
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TOPABSTRACTINTRODUCTIONMODELINGNUMERICAL CASE STUDIESRESULTS AND DISCUSSIONREFERENCES |
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In the following, we introduce a model that considers the transport of nutrients and contaminants in the presence of mobile and immobile sorbents. The model represents an extension of previous work (Totsche, 1995; Knabner et al., 1996; Totsche et al., 1996; Prechtel et al., 2002). The extensions comprise the consideration of multiple nonlinear sorbents for the MOS and the solutes, different additional formulations of sorption isotherms, and additional rate laws to account for kinetic interactions. Unsaturated, steady-state transport is considered by allowing the water content to be defined as a function of depth and soil materials. At present, accumulation of colloidal material at the water–air interface is not taken into account. The mobile sorbents are considered reactive; that is, they are allowed to interact with the immobile solid phase and with each other (Fig. 2) . Thus, MOS aggregation reactions can be modeled.
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Transport of reactive solutes in the presence of a mobile sorbent is conceptualized by assuming at least two interacting constituents, the mobile organic sorbent and the freely dissolved solute, such as a contaminant. These constituents undergo association reactions resulting in three aqueous phase components: the free solute CHf (M L–3). the free MOS CD (M L–3), and the MOS-associated solute CHb (M L–3). Solubility enhancement, or the increase of the apparent solubility of the contaminant, results from solute–MOS association in the aqueous phase. In the presence of MOS, total aqueous concentration of the solute CH (M L–3) is given by the sum of free and MOS-associated solute
 | [1] |
One may note that CH, the total aqueous concentration of the solute is much higher than predicted by the KD (KOC) or its aqueous solubility. If MOS and thus also the associate have to be considered as nonreactive with respect to the immobile solid phase, overall interactions of the solute with the immobile solid phase are reduced. Compared with the reference state (i.e., no MOS present), enhanced mobility due to cotransport is observed. In contrast, if MOS and the associate are subject to interactions with the immobile solid phase, total aqueous concentration of the solute will be smaller than predicted by the pure solid- and aqueous-phase equilibrium distribution KD (KOC) coefficient. We then observe reduced mobility.
Transport of both the solute and the MOS are modeled with the advection–dispersion equation:
 | [2] |
Here, 
denotes the differential operator, 
denotes the volumetric water content (L L–3), C (M L–3) is the mass concentration of the solute with respect to the water filled part of the pore volume, D (L2 T–1) is the coefficient of longitudinal dispersion, q (L T–1) is the volumetric flux density, and P (M L–3 T–1) is a volumetric source–sink term. In the general situation, P is the sum of both biological processes and physicochemical interactions. At present only sorptive interactions are considered within the model.
Sorptive Interactions
Sorption can be spontaneous, kinetically controlled, linear, or nonlinear. As the sorption sites are not the same for the solute, the MOS, and the associate, the bulk soil is considered to be composed of different disjoint fractions, each providing sorption sites for individual sorption reactions. Therefore, P can be written as
 | [3] |
eq and neq (M L–3) are the fractions of bulk density providing sorption sites for equilibrium and nonequilibrium sorption, and 
[C(x,t)], S(x,t) (M M–1) are the amounts of mass sorbed to equilibrium and nonequilibrium sorption sites. Transport of total solute will take place in both the free and in the MOS-associated form. The corresponding equations are
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 | [5] |
 | [6] |
For simplicity we will continue for the special case of linear contaminant–MOS association and Freundlich-type sorption reactions for both the equilibrium and the nonequilibrium interactions of the free and the MOS-bound solute. The interactions considered are partitioning or sorption following a Freundlich- or Langmuir-type Isotherm. Furthermore, a dual-mode sorption mechanism is available, which superimposes a linear sorption process with a nonlinear interaction following Polanyi-potential theory to cover sorption to microporous solids, as well. A number of lab and field studies have shown that soils provide different sorbents for MOS. Among others, the pedogenic iron oxides and the soil organic matter are important sorbents (Kaiser et al., 1996; Jardine et al., 1989; McCarthy et al., 1993; Weigand and Totsche, 1998; Kaiser and Zech, 1998). Thus, we have to consider individual soil constituents, given as mass fractions of the bulk soil mass. Sorption to an individual fraction of the bulk soil is then given by
 | [7] |
 | [8] |
Within the code, other rate laws (e.g., diffusion-limited sorption) are available as well. For the simulation scenarios presented here, we use a constant rate independent on the concentrations.
The Effective Isotherm
With the association reaction expressed in terms of an instantaneous linear equilibrium interaction, that is
 | [9] |
 | [10] |
Here, CD (M L–3) denotes the total solute mass concentration of the MOS, and KMOS (L3 M–1) is the partitioning coefficient or the solute between the aqueous phase and the MOS. Using Eq. [7] in combination with Eq. [10], equilibrium sorption of free and MOS-bound solute can be reformulated in terms of total mass concentration of solute CH and MOS CD:
 | [11] |
Equation [11], the effective isotherm, computes the overall equilibrium sorption of total solute due to the partial sorption of free and MOS-bound solute to the corresponding fractions of sorption sites. With Eq. [11], overall transport of total solute (Eq. [6]) can be expressed in terms of the effective isotherm:
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The transport equation for the mobile organic sorbents is given by an individual advection-dispersion equation, also. Linear steady-state movement of the MOS is then represented by
 | [13] |
Equation [12]—in combination with Eq. [13] for MOS transport and with Eq. [5] and [6], which also have to be expressed in terms of total concentrations—represents the overall transport model for reactive solutes in the presence of mobile reactive MOS. Within this paper, flow of the mobile phase is assumed to be at steady state. By doing so, we are able to analyze the effect of the physicochemical interactions on the breakthrough behavior of the solutes. We are well aware of the fact that this assumption holds only for column experiments. The effect of transient and nonhomogenous flow on MOS-affected solute transport is highly relevant for the evaluation of field transport of contaminants. Unfortunately, data on such transport conditions are currently not available, so our analysis is restricted to steady-state flow conditions.
A Priori Estimator for MOS-Affected Contaminant Transport
In the special situation of equilibrium interactions, we can estimate the effect of MOS on the transport of solutes by calculation of the ratio of the weighted isotherms of the free solute and the carrier-bound solute for the maximum observed concentration of the solute and the maximum expected concentration of the carrier:
 | [14] |
 | [15] |
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 | [16] |
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NUMERICAL CASE STUDIES |
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TOPABSTRACTINTRODUCTIONMODELINGNUMERICAL CASE STUDIESRESULTS AND DISCUSSIONREFERENCES |
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< sat). A continuous feed upper boundary condition is used for both the solutes and the MOS. All aqueous phase components are subject to the same dispersion. This assumption is based on the fact that only few data on the dispersivity of MOS are available which result from column experiments. The calculated dispersivities of the MOS did not significantly differ from the dispersivities of the conservative tracer. This assumption, however, should be checked experimentally in more detail. No sinks other than sorption-like interactions with the immobile solid phase are allowed; in particular, no chemical or biological degradation is acting on the substances. Sorption of the free solute, the MOS, and the MOS-associated solute are described by linear or nonlinear Freundlich-type interactions. The association reaction between contaminant and MOS is assumed to be fast compared with the flow velocity and with the interactions with the solid phase. Thus, an equilibrium sorption is used for the interactions between the contaminants and the MOS. Table 2 summarizes the parameter sets used for the individual scenarios.
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Hf = 0.5 m3 kg–1) and sorption to hydrophilic MOS, while the sorption of the hydrophobic contaminants is characterized by a higher partition coefficient (KHf = 50 m3 kg–1) to the bulk soil and sorption to the hydrophobic MOS. |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMODELINGNUMERICAL CASE STUDIESRESULTS AND DISCUSSIONREFERENCES |
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The most important feature is the wide range of mobilities as indicated by the breakthrough curves (BTC). The mobility of MOS or fractions of MOS can be as high as the mobility of conservative tracers or as low as hydrophobic contaminants (Table 3).
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D), and the respective sorption model (D). This product determines the retardation of MOS, as the sorption of MOS depends on both the amount of specific sorption sites and on the individual MOS sorption isotherm. The parameter values used for the simulation scenario were taken from batch and column experiments with different porous media, different MOS types, and typical MOS concentrations in soils (Kaiser et al., 1996; Weigand and Totsche, 1998; Jardine et al., 1989; McCarthy, 1998). The MOS types considered are the hydrophilic fraction, the hydrophobic fraction, and an intermediate fraction of the dissolved organic matter. The three fractions are different with respect to sorption to the components of the immobile solid phase and with respect to the association with other solution phase components. While the hydrophilic MOS fraction is more mobile and seems to relate to the transport of HM (Guggenberger et al., 1994), the hydrophobic fraction is more strongly retarded and interacts with more hydrophobic pollutants like PAH (Kukkonen et al., 1990). When these different fractions travel through soil, selective sorption results in a relative decrease of the larger and more reactive MOS fractions in favor of the smaller, less reactive and thus more mobile MOS fractions. Additionally, competitive sorption reactions are known for mobile organic sorbents (Kaiser and Zech, 1997). Thus, the passage of MOS from the source horizons down to deeper soil and groundwater results in a chromatographic separation of MOS. Weigand and Totsche (1998) showed that overall transport of MOS originating from organic C-rich soil horizons like the forest floor can be understood and modeled by superimposing the breakthrough of two fractions, which are characterized by markedly different interaction parameters, just like the hydrophilic MOS differ from the hydrophobic MOS. While one fraction, comprising approximately 30% of overall MOS, was characterized by a spontaneous and low-affinity interaction with the immobile bulk solid phase, the remaining 70% were characterized by high-affinity, nonlinear and nonequilibrium interactions with the immobile solid phase. With that approach, the authors were able to predict the breakthrough of mobile organic sorbents through goethite-coated quartz sand at different flow velocities. With this in mind, the first two BTCs (solid circles, solid rectangles) given in Fig. 3 represent hydrophilic and thus mobile fractions of MOS through soils low in MOS-specific sorbents, while the last two BTCs (open circles, inverse solid triangles) represent the hydrophobic and thus less mobile fractions of MOS in soils with a high amount of MOS-specific sorption sites. The other BTCs (solid squares, solid diamonds) represent situations of intermediate MOS in soils with either high or low content of MOS-specific sorption sites.
Effect of Mobile Organic Sorbents on the Transport of Solutes in Soils
In the following, the effect of MOS on the transport of solutes will be discussed based on the results of numerical case studies of three different scenarios. Scenario A combines typical conditions for MOS-facilitated transport, while Scenarios B and C have the conditions for reduced mobility of contaminants in the presence of MOS.
Scenario A: Enhanced Mobility
The assumptions for Scenario A are as follows (conditions for the respective model parameters for this and all other scenarios are given in brackets):
Hf > 0). D = 0). D = KHb = 0). This set of assumptions applies for soil horizons that are either equilibrated and saturated with MOS or low in MOS sorbents, such as pedogenic oxides or clay minerals (e.g., eluvial [E] horizons). Soil horizons that are potentially sorbing MOS but partially saturated with MOS were found to be the A horizons, and Bh horizons of spodosols (Kaiser et al., 1996). Similar conditions may also be found in aquifers (McCarthy, 1998) and sediments with high input of MOS. Such conditions also prevail in those sediments and aquifer environments where MOS is mainly composed of low molecular weight, hydrophilic and therefore more mobile constituents. This nonreactive property of MOS is the result of a combination of several processes—filtering, sorption, ion exchange, flocculation, microbial transformation, and mineralization—acting on MOS during its passage from forest floor and organic-rich surface horizons to aquifers (Jardine et al., 1990; McCarthy et al., 1993; Weigand and Totsche, 1998). Although even low-molecular weight MOS undergoes association with HOC, the sorptive capacity of this type of MOS for HOC is considerably lower (Raber and Kögel-Knabner, 1997).
In Fig. 4 the BTCs obtained for this scenario with both contaminant types, the heavy metal (a,b) and the dummy HOC (c,d) are given. For the contaminant, the total (CH; a,c) and the free concentration (CHf; b,d) are shown. All concentrations are normalized to the inflow concentration C0 of the respective solute.
The presence of MOS results in a progressively earlier breakthrough of the two different contaminants. First arrival and complete breakthrough is affected by the MOS in solution. With increasing MOS concentration CD, from 0 to 0.100 kg MOS m–3, breakthrough of the total solute is shifted to smaller porevolumes (Fig. 4a and 4c). The breakthrough of the free solute CHf is also faster at higher MOS concentrations. The effluent concentration of the free solute (Fig. 4b and 4d) reduces from CHf = 0.9CH for CD = 5 to CHf = 0.5CH for CD = 100.0. The reduced effluent concentration of the free solute is due to the higher proportion of MOS-associated contaminant at higher MOS concentration (Eq. [11]). The increasing amount of MOS-associated solute leads also to increased mobility of the total solute, as the overall interactions of the total solute are more and more dominated by the interactions with the (nonreactive) MOS. Such situations have been observed in column experiments for HM and hydrophobic organic pollutants (Dunnivant et al., 1992; Kan and Tomson, 1990) where the solid phase materials were preequilibrated with MOS. Thus MOS-facilitated transport of the contaminants was to be observed. The relative effect of MOS on contaminant mobility is similar for both types of contaminants. Because of the difference in the affinity to the bulk solid phase of HM and HOC, the breakthrough times for HM are generally much shorter than for HOC (Tables 4 and 5).
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Scenario B: Reduced Mobility due to Cosorption
The assumptions for Scenario B are:
Hf > 0). D > 0). D = KHb > 0). These assumptions hold for soil horizons with an excess sorption capacity for MOS. Such situations are found in B horizons of Inceptisols, Alfisols, and illuvial B horizons of Spodosols, rich in MOS-sorbing minerals and low in organic C (Kaiser et al., 1996; Weigand and Totsche, 1998).
Figure 5 shows the MOS-mediated breakthrough of the two different dummy solutes at increasing MOS concentrations. The respective transport scenario for the MOS breakthrough is indicated by the dashed line within Fig. 5a and 5b (Fig. 3, solid rectangles). With progressing time, the amount of MOS sorbed to the immobile solid phase increases until the MOS-specific sorption sites are completely occupied by the MOS molecules. From then on, the amount of MOS entering the soil equals the amount of MOS leaving the soil. For HOC and HM we observe the expected reduction of the free concentration CHf as the consequence of the association with the MOS. In the case of the dummy HM, the BTCs for the different MOS concentrations are congruent in the beginning of the breakthrough and start to diverge markedly after the effluent concentration level of the contaminant exceeds C/C0 = 0.2. This breakthrough behavior is seen for the free CHf (Fig. 5a) and the total concentration CH (Fig. 5b). With progressing time, the divergence grows because the amount of MOS in the mobile phase increases. With that, the amount of MOS providing sorption sites for the HM in the mobile phase also increases. While in the beginning of the breakthrough almost all MOS are consumed by the solid phase, the progressing saturation of the solid phase with the MOS results in an increase of the liquid-phase MOS concentration. With that, the extent of the association reaction grows until the equilibrium is established.
According to the difference in affinity to the immobile solid phase between the two contaminants (HM and HOC), and especially because of the difference in the affinity contrast to the MOS, the effects on the contaminant breakthrough are different. While we observe reduced mobility for the heavy metal, the mobility of the HOC is still increased. In case of the HM, the breakthrough time increases from pvBTC = 44 for the reference situation with no MOS present to pvBTC = 54 for 0.100 kg MOS m–3 (Tables 4 and 5). With the MOS present in the mobile phase, the breakthrough of the heavy metal is delayed. The presence of MOS results in reduced mobility.
Reduced mobility, however, is not observed for the hydrophobic contaminant. The breakthrough time decreases from pvBTC = 4286 for the reference situation with no MOS present to pvBTC = 2175 for 0.1 kg MOS m–3 present in the mobile phase (Table 3). The difference compared with the heavy metal solute is due to the fact that the equilibration of the immobile solid phase with the inflowing MOS is accomplished much faster than the equilibration with the HOC. This results in a quasi-nonsorbing situation for the MOS and thus for the MOS-bound contaminant at the onset of the contaminant breakthrough. The solid phase is no longer an effective sorbent for the MOS. The cosorption conditions prevail only at the beginning of the breakthrough. The soil column is completely saturated with MOS after about 120 pore volumes (see also Fig. 3, solid rectangles). Because of the high affinity of HOC to the organic matter of the bulk phase, first breakthrough of HOC compounds occurs after about 1000 pore volumes have been exchanged. Thus, the conditions of cotransport dominate this scenario for most of the duration of the breakthrough.
This is also reflected in ß (Eq. [14] and [15]), which is a measure to estimate the effect of MOS on the mobility of a solute. If ß < 1, the mobility is enhanced compared with the reference situation without MOS. If ß > 1, the mobility is reduced compared with the reference situation. In the HOC transport scenario ß = 0.0147, which is an indication of mobility enhancement. Compared with Scenario A, the enhanced mobility scenario, where no sorption of the MOS and the MOS-bound HOC occurs, the breakthrough is delayed. The difference in the breakthrough times for the two scenarios increases with the MOS concentration, starting from virtually no difference at low concentrations (
pvBTC = 0 at 0.001 kg MOS m–3) to approximately 30 pv at 0.100 kg MOS m–3 (Tables 4 and 5). It is therefore important to note that the presence of reactive MOS does not result in all cases in reduced mobility. Whether or not increased or reduced mobility is observed depends at first on the extent of the ratio between the affinity of the free contaminant (HfKHf) to that of the MOS-bound contaminant (HbKHb), that is, the ß value. As the sorption, and therefore retardation, of the MOS-bound contaminants is predominantly controlled by the type and moieties of the MOS itself, the characterization of the MOS properties and moieties is a crucial step for the estimation of the effect of MOS on the mobility of contaminants.
Special Case. A special scenario was simulated for the transport of contaminants in porous media low in sorbed MOS and low in specific immobile sorbents for the contaminants. Under such conditions the sorption of the MOS to the immobile bulk soil is even higher than the sorption of the contaminants.
Figures 6a and 6b show the breakthrough of HM in the presence of intermediate MOS with high amount of specific sorption sites for this type of MOS while Fig. 6c and 6d show the breakthrough of HOC in the presence of hydrophobic MOS with a high amount of MOS-specific sorption sites.
For both cases, the effect of the reduced amount of specific contaminant sorption sites is dramatic. For the reference situation (i.e., no MOS present in the liquid phase) the breakthrough time drops from pv = 44 to pv = 3.1 for the heavy metal and from pv = 4286 to pv = 215 for the HOC (Table 3). This reflects the well known but often neglected fact that the retardation is both the result of the sorption isotherm and of the amount of accessible sorption sites. The observed breakthrough time and as such the retardation are affected if one or the other is varied.
The effect of the special case scenario on the breakthrough of the solutes is minor as long as ß is close to 1. Figure 6a and 6b show this situation exemplarily for the breakthrough of the heavy metal. The sigmoidal shape of the BTCs is conserved and the heavy metal mobility is still reduced with ß = 2.4 (ß = 1.47, high amount of specific heavy metal–sorption or HOC–sorption sites), while the HOC mobility is still enhanced with ß = 0.024 (ß = 0.0147, Tables 4 and 5).
However, the effect on the breakthrough markedly changes for the HOC (Fig. 6c, 6d). The most prominent feature of the total HOC breakthrough behavior is the change of the graph from sigmoidal shape (Fig. 5c, KD = KHb = 15) to the shoulder shape (two changes in curvature from convex to concave back to convex and finally to concave) for the high affinity case (Fig. 6c, KD = KHb = 1870). The shoulder is observed exclusively for the breakthrough of total solute. The free solute and the MOS still exhibit a sigmoidal BTC. Because the breakthrough of the total solute is the consequence of the superposition of the BTC of the free solute and the MOS-associated solute, the initial breakthrough observed for the total solute is essentially the breakthrough of the free solute in the high affinity MOS-sorption case. This is revealed by the congruence of the BTC for the free and the total solute for about 1000 exchanged pore volumes. Then the BTC for the free and the total solute deviate because the breakthrough of the free solute is completed. The BTC for total solute asymptotically approaches the BTC of the MOS, which also represents the breakthrough of the MOS-associated solute. The delay in the breakthrough of the MOS and thus the MOS-associated HOC is determined by (i) the affinity of the solute to the MOS, (ii) the total concentration of the MOS, and (iii) the affinity of the MOS to the immobile solid phase. The limiting situations of the formation of a shoulder as a consequence of the increase of the concentration are depicted in Fig. 7
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The evolution of a shoulder or even a plateau will be more pronounced the stronger the differences are between the affinity of the MOS-bound solute and the free solute with respect to sorption to the immobile phase. Therefore the formation of the shoulder for the total solute is a strong indication for reduced mobility and for the fact that the MOS affect the sorption of the solute to the immobile phase. In soil horizons high in specific sorption site for MOS, such as the iron- and manganese oxide–rich subsoil horizons of spodosols or the sesquioxide enriched horizons of gleysols, such a transport scenario will result in an enrichment of contaminants only in the MOS-sorption layers. This scenario might help us understand the depth profiles found at rural and forested sites, which are affected solely by atmospheric imissions of hydrophobic organic contaminants like polycyclic aromatic hydrocarbons (PAH). Hartmann (1995) and Pichler (1995) found enriched PAH concentrations in subsoil horizons high in organic matter content. Large amounts of PAH were found particularly in soil horizons rich in iron or manganese oxides. These soil minerals are known to be specific sorbents for the MOS and thus for the MOS-bound PAHs. The process of cosorption is thus an effective process for the reduction of contaminant concentration in the seepage water and as such adds to the filter function of soils.
The specific situation of a low amount of specific sorption sites for the solute was further modified by assuming a nonlinear, convex shaped Freundlich-sorption isotherm (p > 1) of the solutes to the immobile solid phase. Without any MOS present, such an isotherm results in increased tailing as small concentrations travel much faster than high concentrations (Fig. 8a, 8b) .
This is still the case for the onset of the breakthrough of the solute in the presence of MOS, as long as the liquid concentration of MOS is small due to MOS sorption to the immobile solid phase. As soon as the sorption sites for MOS are equilibrated with MOS and the liquid phase MOS concentration starts to increase, the formation of the MOS-bound contaminant fraction dominates the overall breakthrough of the contaminant. This results in an abrupt change of the increase of the effluent concentration of the total solute (Fig. 8a). The slope of the BTC diminishes, and the breakthrough is delayed to high pore volumes. Thus, the sorption of the MOS-bound solute enforces the effect of the nonlinear convex sorption characteristic. For the breakthrough of the free solute, the development of a maximal export concentration is observed. The maximum peaks just in front of the onset of the breakthrough of the MOS. This maximum is the consequence of the fact that the sorption sites for the free solute are already at equilibrium, resulting in maximal free solute concentration, while the formation of the MOS-bound fraction has not started so far. A peak effluent concentration is the marked consequence of the cosorption scenario under nonlinear sorption conditions. The necessary requirement for the formation of the shoulder or a plateau is a much higher affinity of the MOS, and thus of the MOS-bound solute, compared with the affinity of the free solute.
In a qualitative manner, the same holds for concave-shaped Freundlich-type with p < 1.0 or Langmuir- or saturation-type sorption isotherms. In fact, the effect of MOS and the formation of a shoulder or a peak effluent concentration are even more pronounced. Concave-shaped sorption isotherms result in a self-sharpening concentration front, as the low concentrations travel slower than the high concentrations. This results in a steeper and narrower peak than the convex-shaped sorption isotherms (data not shown).
Based on the experimental finding and on the field evidence, reduced contaminant concentrations due to the dynamics of MOS might also be observed without the requirement of the formation of a MOS-bound fraction of the contaminant. One may assume that first MOS are sorbed to specific sorption sites. The sorbed MOS then adds to the soil organic matter and thus to the sorption sites for the free contaminants. This scenario is studied next.
Scenario C: Reduced Mobility due to Cumulative Sorption
The assumptions for Scenario C are:
Hf > 0; KHf > 0). D > 0; KD > 0). For the following discussion, we will focus on the consequences of the sorption of MOS for the solid phase organic matter and for the sorption of subsequent solutes.
In Fig. 9
, the depth profiles of the bulk density Hf of the organic matter fraction is plotted for a sequence of MOS concentrations (0, 5, 10, 50, and 100 g MOS m–3, Fig. 9a) and for a sequence of exchanged pore volumes (10, 100, 200, 280, 400, and 700). These profiles were obtained by assuming that the sorption of MOS leads to an increase of the soil organic matter content. This assumption may apply to illuvial horizons of spodosols, where the continuous sorption of humic substances to iron, aluminum and manganese (hydr)oxides leads to the formation of C-rich spodic horizons. More general, the release of MOS from organic materials, the transport from organic C-rich surface soil horizons to deeper soil horizons and the subsequent sorption, precipitation or flocculation within the subsurface is one of the major soil forming processes. Besides the direct input of organic materials by flora and fauna, transport from organic C-rich horizons is the dominant process which results in enrichment of organic matter in the subsurface. Given a fixed amount of MOS-specific sorption sites, the successive import of MOS results in the progressive saturation of these sites and such in an increase of the overall amount of organic matter in the subsurface. The organic matter content is controlled by the total concentration level and the type and properties of the MOS. Figure 9a shows the course of the depth profiles for different mean MOS concentrations calculated for the fixed time of 280 exchanged pore volumes. With respect to the sorbed MOS concentration, the system is still not completely equilibrated. Figure 9b shows the course of the depth profiles for a fixed concentration of 50 g MOS m–3 and different snapshots in time. The sorption of MOS results in the propagation of the solid phase organic matter front. The specific bulk density of organic matter increases from Hf = 0.0300, which resembles the initial condition, to Hf = 0.0254, the final condition after 1000 pore volumes have been exchanged.
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Hf), but also in an increase of the sorption sites for hydrophobic organic contaminants. Thus, Fig. 9a and 9b can be interpreted in terms of an increase of specific HOC sorption sites in time. This increase should affect the transport of solutes with particular affinity to soil organic matter. This effect is shown in Fig. 10
. We study two different scenarios with respect to the properties of the MOS and the soil. Figure 10a shows the effect on solute breakthrough for intermediate MOS in a soil with a high amount of MOS-specific sorption sites while Fig. 10b shows the effect on solute breakthrough for hydrophobic MOS in a soil with a high amount of MOS-specific sorption sites. For both cases the breakthrough is delayed. This is the consequence of the increase of the organic matter due to the sorption of MOS. In general, the onset of the breakthrough is neither affected by the intermediate nor by the hydrophobic MOS. This reflects the important fact that the cumulative-sorption scenario does not require a formation of MOS-bound solute. As the sorption of MOS has to persist for a very long time to result in an increase of the solid phase organic matter, the initial breakthrough of the solute remains unchanged compared with the reference situation.
With progressing time the individual BTCs for the different MOS concentrations deviate from the reference state (without any MOS present). For both cases, the effect on the breakthrough of the solute is marked. But only the hydrophobic MOS result in an effect on the shape and curvature of the solute BTC. The long-lasting increase of the specific bulk density (i.e., the organic matter content) as a result of the sorption of MOS results in a dramatically prolonged breakthrough behavior of the solute. The BTCs exhibit a plateau much smaller than the respective equilibrium contaminant-effluent concentration. During the ongoing MOS sorption process, the contaminant sorption has to be considered a transient process. Under natural MOS release and transport conditions this reduced contaminant concentration may last for very long times (years to decades). Once the MOS-sorption sites are equilibrated, the effluent concentration of the contaminants will dramatically increase as soon as the contaminant sorption sites are saturated. This can be seen in Fig. 10b after approximately 1600 pore volumes have been exchanged.
The cumulative-MOS sorption scenario has important consequences for contaminant fate in porous media. First of all, this scenario causes transient sorbent properties (i.e., a time-dependent solid phase composition). Contaminant sorption parameters obtained for such situations may hold just for the moment. The sorption isotherm will prove time dependent as long as the MOS sorption equilibrium is not established. Soil materials with a high content of MOS-specific sorption sites should therefore be tested for prevailing conditions favorable for cumulative sorption. The estimation of the contaminant sorption parameters can then be constrained by the sorption behavior of the MOS.
The increase of the soil organic matter content due to cumulative MOS sorption can reduce the porosity and as such the permeability of the porous media (e.g., Abadzic and Ryan, 2001). Thus, cumulative sorption will also affect the flow of water and other liquid and gaseous phases through soils high in MOS-specific sorbents.
The concentration of the contaminants in the seepage water of soils subject to cumulative MOS sorption is reduced as long as the cumulative MOS sorption persists. Once completed, the contaminant concentration will increase markedly. With that, soil and groundwater protective values may be violated. Risk assessment studies aimed at groundwater protection have to consider such transient MOS sorption conditions when estimating the long-term contaminant concentration within the liquid phase.
Up to now, we studied the effect of increased contaminant specific sorption sites by considering the effect of cumulative MOS sorption. In principle, the same holds for the opposite case, that is, a time-dependent decrease of organic matter and consequent loss in contaminant-specific sorption sites. Such a decrease could be the result of microbial degradation of organic matter due to changed environmental and climatic conditions. This would result in increased release of MOS and contaminants as well. Such conditions have to be addressed in future work on the fate of contaminants affected by mobile organic sorbents.
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