Release of colloidal particles in natural porous media by monovalent and divalent cations

Journal of Contaminant Hydrology 87 (2006) 155 – 175 www.elsevier.com/locate/jconhyd

Release of colloidal particles in natural porous media by monovalent and divalent cations Daniel Grolimund a,⁎, Michal Borkovec b a

Nuclear Energy and Safety Department, Waste Management Laboratory, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland b Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Sciences II, 30, Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland Received 4 May 2005; received in revised form 19 April 2006; accepted 5 May 2006 Available online 17 July 2006

Abstract We study mobilization of colloidal particles from natural porous media, such as soils and groundwater aquifers. Extensive laboratory scale column experiments of particle release from four different subsurface materials are presented. The important characteristics of the release process are (i) its non-exponential kinetics, (ii) the finite supply of colloidal particles and (iii) the strong dependence of the release kinetic on the nature of the adsorbed cations. Particle release depends most sensitively on the relative saturation of the medium with divalent cations. We propose a mathematic model, which captures all these aspects quantitatively, and can be used to describe the coupling between transport of major cations and the release of colloidal particles. The present experimental investigations as well as the developed modeling framework represent an important step towards the understanding of colloid-facilitated transport phenomena in natural porous media. © 2006 Elsevier B.V. All rights reserved. Keywords: Release of natural colloids; Reactive transport; Subsurface porous media; Cation exchange; Colloid-facilitated transport; Modeling colloid release and transport; Monovalent and divalent cations

1. Introduction Naturally occurring colloidal particles are involved in many important processes in the subsurface zone. Their mobilization, generation and subsequent transport represent a possible mechanism for structure formation, clogging and structural changes of subsurface porous media, or enhanced ⁎ Corresponding author. Tel.: +41 56 310 4782; fax: +41 56 310 45 51. E-mail address: [email protected] (D. Grolimund). 0169-7722/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jconhyd.2006.05.002

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mobilization of contaminants induced by mobile colloidal particles. Due to the importance of these processes in the subsurface environment, the transport of colloidal particles has been studied in several disciplines, including soil sciences (Quirk and Schofield, 1955; Birkeland, 1984), petrology (Jones, 1964; Mungan, 1965; Reed, 1972; Muecke, 1979), hydrology (Goldenberg et al., 1983) or environmental engineering (Champlin and Eichholz, 1968; McCarthy and Zachara, 1989; Bates et al., 1992). Mobilization of the fine clay fraction from the solid matrix is considered to be the major source of mobile colloidal particles in subsurface systems (McCarthy and Degueldre, 1993; Ryan and Elimelech, 1996; Kretzschmar et al., 1999). The understanding of particle release is therefore of fundamental importance in order to judge the susceptibility of subsurface porous media to physical alteration induced by mobile colloidal particles or the significance of colloid facilitated contaminant transport. Despite the potential importance of the particle mobilization, experimental investigations of particle release in natural porous media are scarce, and the detailed mechanisms of release and re-deposition of colloidal particles within natural porous media are poorly understood. Numerous studies are available on particle deposition and release in model systems. Release of colloidal particles has been studied in model porous media made of glass or steel beads or quartz grains with colloidal particles, such as metal oxides (Kolawoski and Matijevic, 1979; Kuo and Matijevic, 1979, 1980; Kallay and Matijevic, 1981; Kallay et al., 1983; Thompson et al., 1984; Kallay et al., 1986, 1987; Ryan and Gschwend, 1994) or polystyrene latex (McDowell-Boyer et al., 1986; Hahn, 1995; Yan et al., 1995; Nocito-Gobel and Tobiason, 1996; Roy and Dzombak, 1996; Yan, 1996). Release of colloidal particles is controlled by particle–surface interactions and hydrodynamics of the flow field. The interaction forces have been modeled within the framework of the theory by Derjaguin, Landau, Verwey and Overbeek (DLVO) by adding the short-ranged Born repulsion force. Within this framework, particle release can be described as a simple kinetic escape process, which can often be expressed by a first-order rate law (Dahneke, 1975; Ruckenstein and Prieve, 1976) Aq ¼ −kq At

ð1Þ

where q denotes the surface particle concentration and k the release rate coefficient. Based on such an extended DLVO theory, one predicts that the release rate coefficient increases with increasing ionic strength for constant potential boundary conditions. The opposite trend is predicted for constant charge boundary conditions. On the basis of DLVO theory, a non-exponential release process has been proposed as well (Barouch et al., 1987). However, such results must be interpreted cautiously, since the release process is dominated by forces at separation distances below a few nanometers. In this regime, the DLVO description is known to break down (Israelachvili, 1992). Changes in the hydrodynamic conditions, such as fluid flow velocity or flow geometry, affect the hydrodynamic shear forces and the extension of the diffusion boundary layer (Ryan and Elimelech, 1996). For sub-micron particles, hydrodynamic shear forces are considered to be negligible within the range of the DLVO potential (Kolawoski and Matijevic, 1979; Khilar and Fogler, 1984; Cerda, 1987). However, under conditions, which result in the disappearance of the energy barrier, diffusion processes across the diffusion boundary layer affect the release of colloidal particles. Additionally, in fractured media and other systems dominated by a macroporous structure, hydrodynamic effects may more important. General conclusions based on the investigation of model systems can be summarized as follows: (i) particle release is usually enhanced by lowering the ionic strength; (ii) the release process strongly depends on the solution composition, whereby monovalent counter ions promote this process most effectively; (iii) in systems with pH dependent surface charge, release is influenced by pH; (iv) the

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kinetic of the release process is strongly non-exponential; and (iv) in some cases, aging effects are important. Thereby, the likelihood for particle release becomes smaller the longer the particle was attached to the surface. In contrast to the large number of studies on colloidal particles release in model systems, systematic investigations in natural porous media, such as soil or aquifer materials, are scarce. Most studies in natural systems focus on permeability changes due to particle release and subsequent pore clogging or structure damage (Quirk and Schofield, 1955; Jones, 1964; Khilar and Fogler, 1984; Khilar and Fogler, 1987). Loss in permeability has been used as an indirect indicator for the mobilization of colloidal particles. In a limited number of studies, colloidal particles released from natural porous media have been detected directly (Frenkel et al., 1978; Shainberg et al., 1980; Ryan and Gschwend, 1994; Seaman et al., 1995; Grolimund et al., 1996; Roy and Dzombak, 1996; Grolimund and Borkovec, 1999; Grolimund et al., 2001a). These observations are mostly in qualitative agreement with the findings from model systems. Thereby, solution composition turns out to be an important variable. One usually observes particle release in systems saturated with a monovalent counter ion by decreasing the ionic strength. For divalent counter ions mobilization of colloidal particles is strongly impaired. The ubiquitous presence of mobile colloidal particles in subsurface systems is also demonstrated by several field studies (Nightingale and Bianchi, 1977; Saltelli et al., 1984; Gschwend and Reynolds, 1987; Degueldre et al., 1989; McCarthy and Degueldre, 1993). Several authors have observed facilitated transport of contaminants by mobile colloidal particles (Champ et al., 1984; Buddemeier and Hunt, 1988; Penrose et al., 1990; Kersting et al., 1999) or changes in hydraulic properties due to mobilization phenomena (Wiesner et al., 1996; Saripalli et al., 2001). This paper emphasizes in situ mobilization of colloidal particles from natural porous media. Four natural subsurface materials including topsoil and groundwater aquifer materials have been investigated. We shall demonstrate that release of colloidal particles is intimately linked to variations of solution chemistry, particularly to the presence of monovalent versus divalent cations. Since the transport of these ions is governed by the formation of non-linear chromatographic fronts, the mobilization of colloidal particles is expected to be strongly linked to the migration of these fronts. This interplay between particle release and non-linear chromatography represents the major focus of the present study. 2. Experimental 2.1. Soil and aquifer materials Particle mobilization studies were performed by using four different soil or aquifer materials. Major characteristics of these materials can be found in Table 1. Prior to experiments, each sample was thoroughly mixed to generate a homogeneous batch, sieved to pass a 2 mm screen, air dried and stored at 4 °C. 2.2. Column experiments Aggregates were dry packed in chromatographic glass columns (Omni), and depending on the structure of the material, different aggregate size fractions and various column dimensions were employed. The feed solutions were pumped by a HPLC pump (Jasco) through a degasser (Erma) into the column upwards until the columns were completely water-saturated. The columns were further preconditioned with leaching of about 200 pore volumes of 500 mM CaCl2 and, if required, subsequently leached calcium free with up to 1000 pore volumes of 500 mM NaCl solution until

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Table 1 Characterization of the subsurface materials Riedhof Soila

Norfolk Soilb

Location

Non-calcareous aquic dystric Eutrochrept; (E)B-horizon Northern Switzerland

Texture Corg [g kg− 1]e pHf CEC [mmol/g]g

Silt loamy 6 4.1 0.07

Siliceous, thermic Typic Kandiudult; Ap-horizon Middle Coastal Plain region, NC, USA Fine loamy 3.6 6.1 0.02

Type

a b c d e f g

Eng Ground Soilc

Aquifer Materiald Calcareous aquifer

Wageningen, NL

Northern Switzerland

Sandy 11 4.1 0.01

Coarse sandy n.d. 8 n.d.

Grolimund et al. (1996). Kretzschmar et al. (1993). Boekhold et al. (1993). Kretzschmar et al. (1997). Organic carbon determined by a combustion technique (Nelson and Sommers, 1982). Measured in water according to McLean (1982). Cation exchange capacity measured by column technique (Sardin et al., 1986; Cernik et al., 1994).

the calcium concentration was below 10− 7 M. Typical flow rates employed during the preconditioning procedures were 0.5 mL/min. All solutions were prepared by dissolving appropriate amounts of corresponding chloride salts (p.a., Merck) in water from a Barnstead Nanopure apparatus. Column characteristics such as pore volume and dispersivities were determined with pulse tracer experiments. Solutions of Ca(NO3)2 were injected with a sample loop into the CaCl2 background. The nitrate breakthrough was measured on-line with a HPLC UV/VIS detector (linear, operated at 220 nm), which was connected to a PC for data acquisition. By evaluating the first and second moments of the breakthrough, the mean travel time and the dispersion coefficient were obtained (Villermaux, 1981). Typical column characteristics are reported in Table 2. The column experiments were carried out by leaching different solutions through the column. At the column outlet, the pH was measured with a flow-through combination electrode (Hamilton, microelectrode), and the outflow was collected by a fraction collector (Gilson).

Table 2 Characteristic column properties

Column-diameter [cm] Length [cm] Aggregate size [mm] Pore volumes [cm3]e Porosity [%]f Density [kg/L]e Peclet number a b c d e f

Riedhof Soila

Norfolk Soilb

Eng Ground Soilc

Aquifer Materiald

1.0–2.5 10–40 1.0–2.0 7.5–30.0 65 1.6 30–150

1.0 15–40 1.0–2.0 8.0–10.0 60 1.7 50–75

0.6–1.0 10–20 0.063–0.63 2.5–7.0 50 2.8 60–80

1.0 37.5 0.1–2.0 12.5 45 3.5 300

Grolimund et al. (1996). Kretzschmar et al. (1993). Boekhold et al. (1993). Kretzschmar et al. (1997). The average relative error of these quantities is ∼5%. The average relative error of these quantities is ∼10%.

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2.3. Sample analysis and particle characterization Samples collected with the fraction collector were split into several parts. The first part was acidified with distilled HNO3 to pH b 2, sonicated and analyzed for total concentration of Na, Ca, Si, Al, Fe, Mg, Mn and Ti by inductively coupled plasma atomic emission spectroscopy (ICP-AES, Varian Liberty 200) coupled to ultrasonic nebularization (Cetac U-5000AT). Comparison with results from microwave digestion (MLS 1200, Microwaves Laboratory Systems MLS GmbH) with a mixture of 40% HNO3 (65%, Merck p.a.), 40% HF (48%, Merck p.a.) and 20% HClO4 (70%, Merck p.a.) of the colloidal suspension confirmed the complete atomization of the particles in the plasma. The second part of the sample was centrifuged for 2 h at 2 ×105g (40,000 rpm) resulting in supernatant solutions, which were effectively free of colloidal particles (i.e., particle size b 10 nm and particle concentrations b 0.07 mg/L). The supernatant was subsequently analyzed by ICP-AES for the same elements as above leading to dissolved concentrations of the corresponding elements. The final part of the collected sample was used to measure the average particle size with dynamic light scattering with an ALV goniometer (ALV/SP-125 S/N 30) equipped with a krypton laser (Innova 300, Coherent) operating at a wavelength of 647 nm. To avoid multiple scattering, concentration of colloidal particles was kept below 5 mg/L. The hydrodynamic radius was measured at 90° from second cumulant fits. Particle concentrations were calculated from the difference between total and dissolved concentrations of indicator elements Fe, Al and Si. The elemental contents of the colloidal particles were converted to particle concentrations (mass per unit volume) based on the expected elemental compositions, or by means of calibration with isolated particles obtained with flocculation, ultra-centrifugation, and freezedrying (Grolimund et al., 1996). 3. Modelling colloid release, deposition and transport Transport of a dissolved species i of molar concentration ci(x, t) has been modeled by classical convection–dispersion equation Aci Aqi A2 ci Aci þq ¼ D 2 −v At At Ax Ax

ð2Þ

where D is the dispersion coefficient and v the flow velocity. The motion is coupled to adsorbed species described by the adsorbed amount qi(x, t) and ρ is the solid mass per unit pore volume. The time evolution of the adsorbed amount is in turn described by the mass balance equation Aqi ðdesÞ ðadsÞ ¼ −ji þ ji At

ð3Þ

where ji(des)and ji(ads) are the kinetic fluxes due to desorption and adsorption reactions. The species considered and the corresponding fluxes are summarized in Table 3. Complexation reactions in solution are also modeled by the appropriate choices of kinetic rate equations. Dissolution of calcite, CaCO3, was also included in the description by additionally considering the mass fraction of the solid as a time dependent variable. Reaction equilibria were modeled to be close to local equilibrium by choosing sufficiently fast reaction kinetics. The transport of colloidal particles was also described by convection–dispersion equations. The particles were divided into a discrete set of n populations (Table 4). For each population j

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Table 3 Chemical model used for the Riedhof Soil Phase

Reactions

Solution

H + OH ⇔H2O H + + HCO2− 3 ⇔H2CO3 − H + + CO2− 3 ⇔HCO3 X − Na + H +⇔X − H + Na+ 2X − Na + Ca2+⇔X2 − Ca + 2Na+ [X]tot = 28 μmol/g Y − Na + H+⇔Y − H + Na+ 2Y − Na + Ca2+⇔Y2 − Ca + 2Na+ [Y]tot=27 μmol/g Z − Na + H+⇔Z − H + Na+ 2Z − Na + Ca2+⇔Z2 − Ca + 2Na+ [Z]tot = 20 μmol/g

Interfaceb,c

a b c

−

+

Equilibrium constant log K

Rate forward 14 − 1

Rate backward

− 14 − 6.3a − 10.03a 3.00 1.65

1.7 × 10 s M 3.3 × 107 s− 1 M −1 3.3 × 108 s− 1 M −1 1.7 × 101 s− 1 3.1 × 101 s− 1

1.7 × 100 s− 1 1.7 × 101 s− 1 1.7 × 10− 2 s− 1 1.7 × 10− 2 s− 1 6.7 × 10− 1 s− 1 M− 1

3.00 1.63

1.7 × 101 s− 1 1.4 × 100 s− 1

1.7 × 10− 2 s− 1 3.3 × 10− 2 s− 1 M− 1

3.00 2.20

1.7 × 101 s− 1 5.3 × 101 s− 1

1.7 × 10− 2 s− 1 3.3 × 10− 1 s− 1 M− 1

a

−1

Stumm and Morgan (1996). Compare e.g. Sardin et al. (1986), Cernik et al. (1994), Grolimund et al. (1996) and Vulava et al. (2000). X, Y and Z represent different types of monovalent surface sites.

( j = 1, …, n), we consider the evolution of the solution concentration ĉj(x, t) and of the adsorbed amount qˆ j(x, t) by means of the transport equations Aqˆ j ˆ A2cˆ j Aˆc j Aˆc j þq ¼ D 2 − vˆ At At Ax Ax

ð4Þ

X Aqˆ j ðjÞ ¼ kdep ĉk −krel qˆ j At k

ð5Þ

ˆ is the particle dispersion coefficient and vˆ the particle velocity. For the Riedhof Soil, these where D two parameters differ little from the corresponding quantities for a conservative tracer (Grolimund et al., 1998). The deposition rate coefficient kdep is the same for all populations, while for each ( j) is different. The most important ingredient is an particle population the release rate coefficient krel appropriate model for the particle release. Based on the presented experimental data, we propose the following empirical relationship for the first-order release rate coefficient ð jÞ

krel ¼ kˆ rel ð1−yÞa f ðI=I0 Þ ð jÞ

ð6Þ

( j) are assumed to be equally spaced on a logarithmic grid. The ranges used are given in Table where kˆ rel 4. The release rate constants further depend on the fraction of exchange sites occupied by divalent cations y, and the ionic strength I of the solution phase. The dependence on the ionic strength is described by the function

f ðzÞ ¼ z−g e−z

ð7Þ

While it was possible to choose I0 = 0.05 M for all the experiments, the parameters a and γ were fitted to the data and are material specific (see Table 5).

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Table 4 Distribution of colloid populations for different subsurface materials Population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a b c d

Riedhof Soila

Norfolk Soilb

Eng Ground Soilc

Aquifer Materiald

Log release rate [s− 1]

Mass fraction [g/kg]

Log release rate [s− 1]

Mass fraction [g/kg]

Log release rate [s− 1]

Mass fraction [g/kg]

Log release rate [s− 1]

Mass fraction [g/kg]

− 4.5 − 5.0 − 5.5 − 6.0 − 6.5 − 7.0 − 7.5 − 8.0 − 8.5 − 9.0 − 9.5 − 10.0 − 10.5 − 11.0 − 11.5

0.2 0.3 0.4 0.7 1 2 3 4 6 8 10 15 20 30 40

−7.5 −8.0 −8.5 −9.0 −9.5 −10.0 −10.5 − 11.0 − 11.5

0.04 0.19 1.3 5.8 7.7 11.2 12.3 11.5 23.1

− 4.7 − 5.2 − 5.7 − 6.2 − 6.7 − 7.2 − 7.7 − 8.2

0.01 0.07 0.15 0.35 0.38 0.40 0.43 0.45

− 4.7 − 5.2 − 5.7 − 6.2 − 6.7 − 7.2 − 7.7 − 8.2 − 8.7 − 9.2 − 9.7

0.10 0.21 0.23 0.30 1.3 2.5 1.4 0.21 0.15 0.10 0.05

Grolimund et al. (1996). Kretzschmar et al. (1993). Boekhold et al. (1993). Kretzschmar et al. (1997).

Particle deposition was modeled by first-order deposition kinetics. For the Riedhof Soil, the deposition rate constants were previously determined to follow the relation (Grolimund et al., 1998) kdep ¼

kˆ dep

ð8Þ

1 þ ðc0 =cÞb

where c is the total concentration of all cations in solution, b = 1.5, kˆ dep = 3 × 10− 4 s− 1 and the critical deposition concentration c0 is obtained from the expression −1 −1 c−1 0 ¼ c1 ð1−xÞ þ c2 x

ð9Þ

where x is the molar fraction of the divalent cations in solution, and c1 = 0.155 M and c1 = 0.0032 M are the critical deposition concentrations for monovalent and divalent cations, respectively. Table 5 Release parameters for different subsurface materials Riedhof Soila Norfolk Soilb Eng Ground Soilc Aquifer Materiald Total mass fraction of mobile colloidal particles 141 g/kg Ionic strength exponent γ (cf. Eq. (7)) 2.5 Exchange exponent a (cf. Eq. (6)) 7.6 a b c d

Grolimund et al. (1996). Kretzschmar et al. (1993). Boekhold et al. (1993). Kretzschmar et al. (1997).

145 g/kg 2.5 n.d.

2.7 g/kg 0.4 n.d.

6.5 g/kg 4.1 4.6

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Concerning the computational implementation, the resulting set of coupled partial differential equations is solved with existing numerical algorithms (Numerical Algorithms Group, 1996). The constructed reactive transport code was extensively tested against analytical solutions available for several special cases (e.g., Jury and Roth, 1990; Grolimund and Borkovec, 2001; Grolimund et al., 2001a). Further, the complex solution and interfacial chemistry part of the code, without consideration of mobile colloidal particles, was tested against an established numerical code (Jauzein et al., 1989) assuming near local equilibrium conditions. 4. Results and discussion The Riedhof Soil, which will be used to illustrate most of the processes, is a non-calcareous loamy soil (see Table 1). We shall first discuss the particle release in the presence of a single cation. From such experiments, we shall learn about the basic patterns of the release of colloidal particles. From the environmental point of view, however, systems dominated by a single cation are atypical and it is thus essential to investigate situations where several cations are present. In such systems, chromatographic transport fronts, which form due to ion-exchange reactions, determine the release of colloids. Such phenomena will be discussed later. Finally, we shall demonstrate by discussing three other subsurface materials that the proposed colloid release mechanisms are widely applicable and probably generally valid. 4.1. Monovalent ions Fig. 1 shows the result of an experiment investigating the release of colloidal particles in a Na+ saturated system in the Riedhof Soil. The column was equilibrated with 0.1 M NaCl solution and then the input solutions were changed step-wise according to the sequence shown in Fig. 1a. The sodium concentration in the outflow is shown in Fig. 1b. One observes that the change in the input solution is immediately followed by the corresponding change in the outflow solution. This change occurs exactly after one pore volume. For the present case where we consider sodium-saturated porous media, the total sodium concentration can be considered as a conservative tracer. Fig. 1c shows the pH of the outflow. One observes stepwise pH variations of one or two pH units, which accompany the changes of the sodium concentration. The pH changes are due to the breakthrough of a normality front, where the concentrations of all the ions decrease, protons included (Helfferich and Klein, 1970; Scheidegger et al., 1994). The intermediate plateau is determined by the exchange between sodium and protons on the porous material. One expects a second retarded front, where the pH should return to its initial value again (Scheidegger et al., 1994). However, this front is strongly retarded, and therefore is not observed in the present experiment. Note that, due to the large retardation of the second front, the adsorbed amount of protons remains approximately constant during the entire experiment. Experiments with pH buffered feed solutions have not evidenced any noticeable effects in the pH range of 5 to 6.5 Fig. 1. Column experiment demonstrating the release of colloidal particles from a Na+-saturated natural porous medium (Riedhof Soil). The mobilization is induced by step-wise changes in ionic strength. The concentrations of various species in the column effluent and characteristic properties of the eluted colloidal particles are shown. (a) Succession of infiltrating solutions. (b) Concentration of total sodium in the column effluent. (c) Effluent pH. (d) Concentration of colloidal particles suspended in the column effluent in a semi-logarithmic representation. (e) Elemental ratios for Si, Fe, Al, Mg, Mn and Ti of the particles suspended in the effluent. These quantities represent a measure for changes in the mineral composition. (f ) Mean radius of the colloidal particles in the column outflow determined by dynamic light scattering at a scattering angle of 90° is plotted. The dotted line in (d) represents the detection limit. Dashed lines represent model calculations neglecting deposition phenomena. Solid lines in (e) and (f ) serve to guide the eye.

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(Grolimund and Borkovec, 1999). The transport model easily captures the breakthrough of sodium and pH very well (solid line), and further confirms that the surface proton concentration remains basically constant. The particle concentration at column outlet is shown in Fig. 1d and it varies inversely to the changes of the electrolyte concentration. However, after the first decrease in the salt concentration, a peak in the particle concentration is observed. While not obvious on the scale of Fig. 1d, the maximum in the particle concentration of about 20 mg/L is reached after two pore volumes. This maximum is followed by a gradual decrease in the particle concentration. This decrease is rather slow, and it takes about 65 pore volumes until the particle concentration drops to 30% of the peak concentration. In case of an exponential release process, the particle concentration in the outflow would drop linearly in the present semi-logarithmic representation. While such a linear decrease is observed initially (first 15 pore volumes), the decrease slows down signaling a non-exponential process. After 65 pore volumes, the feed solution was changed to higher sodium concentration leading to a sudden reduction of the particle concentration simultaneously with the normality front. All changes in the electrolyte concentration lead to analogous effects; increase in salt concentration lead to a decrease in the particle concentration and vice versa. These trends can be interpreted in terms of a release rate coefficient, which increases with decreasing salt concentration. Note that the salt concentrations of the feed solutions starting at 105 and 150 pore volumes, respectively, are exactly the same as the initial ones. However, the resulting particle concentrations in the outflow are much smaller. While the initial decrease leads to the pronounced peak in the particle concentration, the decrease at 105 and at 150 pore volumes, respectively, lead to an apparently constant particle concentration in the outflow. Only, a slight overall downward trend in the particle concentration can de deduced. These effects are caused by a finite supply of colloidal particles, which can be potentially mobilized. This supply is depleted in the course of the experiment. Nevertheless, the nature of the released colloidal particles remains surprisingly constant in the course of the experiment. Fig. 1e shows the ratios of Fe, Si, Al, Mg, Mn and Ti. These elements were used as indicator elements for colloidal particles, and their ratios represent a measure for the variation in the mineral composition of the released colloidal particles. All elemental ratios remain constant within experimental errors during the whole experiment. Fig. 1f shows the hydrodynamic radii of the particles, and one observes that the particle radius remains constant around 250 ± 50 nm. We thus conclude that properties of the released particles are hardly varying in spite of the fact that their supply is being depleted. The mathematical transport model captures the particle release pattern very well. Two aspects are important. First, it is essential to assume a distribution of release rate constants, as otherwise the particle concentration would decrease in an exponential fashion in the outflow. We shall not dwell on this point here, as it was discussed in earlier publications (Grolimund and Borkovec, 1999, 2001; Grolimund et al., 2001a). Second, it is important to properly capture the dependence of the release rate constant on the salt concentration. We have found that a power-law type relationship as given in Eq. (7) describes the data very well with an exponent γ = 2.5. This observation is consistent with results elaborated during previous investigations focusing on the non-exponential nature of the release process (Grolimund et al., 2001a). During long-term mobilization experiments with a single-step input change, the average release rate coefficient was observed to depend on the sodium concentration in a similar power-law type manner. The exponential cut-off function has to be introduced to inhibit particle release at high salt levels. The importance of deposition phenomena was investigated by comparing model calculations with and without the consideration of deposition (Fig. 1d, dashed line represents model calculations

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neglecting deposition phenomena). Clearly, deposition processes have only small effects on the concentrations of mobilized particles. The explanation of this phenomenon is simple. During conditions favorable for release, deposition rates of colloidal particles are very slow and particle reattachment is unlikely (Grolimund et al., 2001b). 4.2. Divalent ions The behavior of the Riedhof Soil, when fully saturated with calcium, is shown in Fig. 2. The feed sequence reported in Fig. 2a consists of a simple change in input solutions. The column, which was previously saturated with 500 mM CaCl2 solution, was infiltrated with pure water exposed to air. The resulting calcium concentration at the outlet is shown in Fig. 2b and one observes a drop by about 4 orders of magnitude within the first 10 pore volumes. At the same time, the pH increases from 4.9 to about 6.6, as shown in Fig. 2c. As in the previous experiment, this breakthrough pattern is dominated by a normality front, where calcium and proton concentrations decrease, which is followed by an intermediate plateau before the retarded exchange front between calcium and protons arrive. This

Fig. 2. Release behavior of a Ca2+-saturated porous media (Riedhof Soil). (a) Feed sequence. (b) Calcium concentration at the column outlet. (c) Effluent pH. (d) Concentration of colloidal particles suspended in the column effluent in a semi-logarithmic representation. No release of colloidal particles can be observed. The dotted line in (d) represents the detection limit.

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behavior is described reasonably well by the transport model. However, the situation is further complicated by slow dissolution of calcium containing minerals (e.g., clays, feldspars). In spite of a substantial reduction in ionic strength, Fig. 2d illustrates that there is no measurable release of colloidal particles. The particle concentration remains always below the detection limit of 0.07 mg/L. The lowest calcium concentration reached is already almost 5 orders of magnitude lower than the corresponding sodium concentration, when particle release could be observed in the sodium system. If a similar experiment had been carried out in a sodium-saturated medium, one would observe very pronounced particle release, which may leads to clogging of the system. Similar differences between systems dominated with monovalent or divalent cations were observed for other natural porous media (Khilar and Fogler, 1987) as well as in model systems involving latex particles deposited onto glass beads (Hahn, 1995). This trend has been explained by “bridging” by calcium ions in the soil science literature (Sposito, 1984). The proper interpretation of the phenomenon is probably related to attractive electrostatic forces, which occur in the presence of divalent cations. Such ion–ion correlation forces, however, cannot be explained on the basis of the Poisson–Boltzmann model (Kjellander et al., 1988; Quirk, 1994). 4.3. Mixtures of monovalent and divalent ions Fig. 3 shows particle release during a classical cation exchange experiment for the Riedhof Soil. The input sequence is given in Fig. 3a. The column, which was previously equilibrated with 100 mM NaCl, was infiltrated with a 12.5 mM CaCl2 solution and after 10 pore volumes the feed was changed to 30 mM NaCl. The resulting outflow pattern of sodium and calcium are shown in Fig. 3b and c. First, one observes a normality front, whereby the sodium concentration levels off at 25 mM. This value corresponds to the normality of the new feed solution. After 4 pore volumes, a second sharp front arrives, after which the final composition of the feed is attained. After 10 pore volumes, the feed was changed back to a pure sodium solution. This change results mainly in the development of a diffuse front leading to a slow variation in the sodium and calcium concentrations. The model describes the solution concentrations well. However, one should note that it is necessary to assume slow exchange kinetics in order to describe the decrease of the sodium concentration after 4 pore volumes. The concentration of colloidal particles in the outflow is illustrated in Fig. 3d. In the first part of the experiment, an immediate release of colloidal particles is observed. This release begins with the breakthrough of the normality front, but ends abruptly after 4 pore volumes with the arrival of the retarded front. After the complete breakthrough of calcium, no colloidal particles can be detected in the column outlet. After the change to the sodium containing feed, the colloidal particles reappear in the outflow along with the development of the diffuse front. Initially, the particle release strongly resembles the situation in the sodium-dominated system (see Fig. 1). In the present situation, however, the concentration of colloidal particles drops very quickly with the arrival of the retarded front, after which the medium is saturated with calcium. However, in the second part of the experiment, a new type of release phenomenon is observed. In spite of the presence of the calcium in the outflow, the release sets in smoothly, but not immediately after the change in input solution. Furthermore, a continuous increase in the particle concentration can be observed, which goes along with the decrease of the calcium concentration. In this mixed sodium– calcium system, we observe significant concentrations of released colloidal particles in the outflow, in spite of substantial concentrations of calcium (N 1 mM). Recall that, in the pure calcium system, no particle release was observable at concentrations of 0.01 mM. Our interpretation of this behavior is as follows. The release rate coefficient is not only a function of the ionic strength, but also depends on the relative saturation of different counterions on the exchanger. In the second part of the experiment

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Fig. 3. Release of colloidal particles during a classical cation exchange experiment. The column was packed with Riedhof Soil. (a) Input sequence of feed solutions. Resulting outflow pattern of (b) sodium and (c) calcium in a semi-logarithmic scale. (d) Concentration of colloidal particles suspended in the outflow plotted in semi-logarithmic scale. In the second part of the experiment, despite the presence of divalent cations in the outflow and slightly increased ionic strength, the mobilization of particles is enhancing. The dotted line in (d) represents the detection limit. Dashed lines represent model calculations neglecting deposition phenomena.

shown in Fig. 3, the exchanger is occupied roughly with 70% sodium and we suspect that the release behavior will be similar to the sodium-dominated system. On the other hand, the detailed behavior will be different, since the relative proportions of both cations are changing in the course of the experiment, whereby the release process will be influenced as well. We model this effect by the power-law dependence of the release rate on the exchanger saturation (cf. Eq. (6)). The exponent a = 7.6 is determined by fitting the particle release curves. Note that the experiment shown in Fig. 3 is carried out at relatively high ionic strengths. For this reason, the particle deposition is relatively rapid, and therefore particle re-deposition phenomena play a more important role when compared to the previous (or subsequent) experiments.

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Fig. 4 shows the outflow pattern for another experiment in a mixed sodium–calcium system for the Riedhof Soil, but now with substantial variations in the ionic strength. The column is fed with chloride solutions with a constant sodium-to-calcium molar ratio of 200, but the total electrolyte concentration is decreased stepwise. The sequence of feed solutions is summarized in Fig. 4a. The corresponding breakthrough patterns of sodium and calcium are shown in Fig. 4b and c. Prior to the experiment, the column was equilibrated with a solution containing 99 mM NaCl and 0.5 mM CaCl2 (total chloride concentration 100 mM). The experiment starts with an infiltration of a solution of containing 19.8 mM NaCl and 0.1 mM CaCl2 (total chloride concentration 20 mM). At

Fig. 4. Release of colloidal particles in the simultaneous presence of sodium and calcium. The feed solutions (a) contain a constant sodium/calcium molar ratio of 200:1. The mobilization is induced by step-wise changes in normality. Resulting outflow pattern of (b) sodium and (c) calcium in a semi-logarithmic scale. (d) Concentration of colloidal particles suspended in the outflow in a semi-logarithmic representation. In spite of the presence of divalent cations in the outflow mobilization of particles can be observed. The dotted line in (c) represents the detection limit.

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one pore volume, the normality decreases to the value of the new feed solution. This decrease corresponds to the breakthrough of the normality front and, consequently, the concentration of all the cations decreases. At about 150 pore volumes, a sharp front arrives and the sodium and calcium concentrations adjust to the composition of the feed. In between these two fronts, the concentration of calcium is far below the feed concentration, while the sodium concentration is slightly above. (This small difference is not visible on the scale of the graph.) Analogous sequences of fronts can be observed for the following reductions in ionic strength. After the second reduction, the normality front appears at 350 and the retarded front at 1450. After the third reduction, the normality front appears at 2200, while the breakthrough of the retarded front lies outside of the experimental time window. The breakthrough of major cations governs the particle release pattern shown in Fig. 4d. One observes the typical colloidal release peak after each normality front. The tail of the peak ends abruptly with the arrival of the retarded exchange front. The sequence of the heights of the particle peaks is determined by three competing effects: First, the release rate coefficient increases with decreasing ionic strength, second, the release rate coefficient decreases with increasing calcium saturation of the exchanger, and thirdly the supply of colloidal particles is finite and becomes partly exhausted during the experiment. The model includes all these effects and therefore captures the particle release reasonably well. Note that no parameter adjustment was made and the results shown are pure model predictions. The good agreement between experiment and model is

Fig. 5. Column experiment demonstrating the release of colloidal particles from a Na+-saturated natural porous medium (Norfolk Soil). The mobilization is induced by step-wise changes in ionic strength. (a) Succession of infiltrating solutions. (b) Concentration of total sodium in the column effluent. (c) Concentration of colloidal particles suspended in the column effluent in a semi-logarithmic representation. The dotted line in (c) represents the detection limit.

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a strong indication of appropriateness of the present modeling framework, and illustrates its predictive capabilities. In the present case, particle re-deposition is again irrelevant. 4.4. Other subsurface materials In order to address the generality of the proposed model, we have conducted release experiments for three additional subsurface materials with sodium. The experiments are similar in spirit to the one shown in Fig. 1 for the Riedhof Soil. The subsurface materials were saturated with 100 mM NaCl solution and, in the subsequent feed solutions, its concentration was varied. The release of colloidal particles was monitored as discussed above. The model parameters are summarized in Table 5. Fig. 5 shows the particle release for the Norfolk Soil, which is a loamy top-soil material (see Table 1). Very similar release characteristics to the previously discussed Riedhof Soil can be established. The particle release is again triggered by the breakthrough of the normality front and is obviously dictated by the solution concentration. In addition, one observes that the characteristic non-exponential release and exhaustion of the particle supply. The release pattern described quantitatively with the same model developed before, but only the distribution of particle population had to be modified. Since particle deposition had only marginal influence for the Riedhof Soil, it was not considered further.

Fig. 6. Column experiment demonstrating the release of colloidal particles from a Na+-saturated natural porous medium (Eng Ground Soil). The mobilization is induced by step-wise changes in ionic strength. (a) Succession of infiltrating solutions. (b) Concentration of total sodium in the column effluent. (c) Concentration of colloidal particles suspended in the column effluent in a semi-logarithmic representation.

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Fig. 6 compares similar results for the Eng Ground Soil, which is a sandy dune material (see Table 1). Again, very similar particle release characteristics can be established, including the control of the release by the solution concentration, non-exponential release kinetics and finite supply of particles. However, distinct differences are readily apparent. The most pronounced is the nearly complete release of the mobile particles in the course of the experiment and the weak

Fig. 7. Particle release behavior of a system with a dissolving mineral phase (calcite). The column was packed with a calcareous aquifer material. (a) Sequence of feed solutions applied to the system. Corresponding outflow pattern for (b) sodium and (c) calcium in a semi-logarithmic representation. (d) Effluent pH. (e) Concentration of colloidal particles suspended in the outflow in a semi-logarithmic representation. The dotted line in (e) represents the detection limit. The dissolution of the mineral phase contributes to the observed release pattern only secondarily.

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dependence of the release rates on the solution concentration (Table 5). This system features a higher organic matter content and probably also a different proton buffering capacity. These factors might be responsible for the reduced susceptibility of particle release against ionic strength reductions. Fig. 7 illustrates the release behavior of a calcareous sandy aquifer material (see Table 1). Even though there is no calcium in the column feed for this system, calcium is generated by dissolution of calcite, CaCO3, as shown in Fig. 7c. The final plateau values of the calcium concentrations after each change in input concentration result from a constant dissolution rate of calcite. These processes are accompanied by characteristic changes in pH, as illustrated in Fig. 7d. The calcium and proton concentrations decrease after the breakthrough of the normality front, since the overall normality of the solution is decreased, and consequently concentrations of all cations decrease. Due to calcium dissolution, the calcium and protons concentrations increase and lead to a plateau in the breakthrough curves. For this reason, the calcium concentrations and the pH remains approximately constant before the breakthrough of each normality fronts within the whole experiment. This behavior is well captured by the transport model, when provided the proper cation exchange capacity and the precipitation–dissolution reactions of calcite are taken into account. The outflow pattern of colloidal particles is shown in Fig. 7e. Again, after a reduction in ionic strength, the typical release peak is observed which levels out at a constant concentration of approximately 1 mg/L. For the first three reductions in ionic strength, the observed peak increases with decreasing ionic strength. However, after the pronounced release event at pore volume 250, the supply of colloidal particles appears to be exhausted. The mobilized particles already represent a considerable fraction of the clay particles available in this coarse sandy aquifer material. 5. Conclusions In the presence of monovalent and divalent cations, the release of colloidal particles from natural subsurface materials such as soils and groundwater aquifers is typically coupled to the non-linear chromatographic transport of these ions. The particle release can be described quantitatively by combining a classical transport model with particle release kinetics, whereby the following phenomena must be considered. Firstly, the release kinetics is a non-exponential process and cannot be modeled with a single exponential. This non-exponential behavior can be rationalized in terms of a distribution of populations of colloidal particles (Grolimund and Borkovec, 1999; Grolimund et al., 2001a), and interpreted based on the existing chemical and physical heterogeneities of the system. Secondly, the supply of colloidal particles, which can be potentially mobilized, is finite and can be partly exhausted in the course of a mobilization event. Thirdly, the particle release rate coefficient increases with decreasing ionic strength of the solution, but it also strongly depends on the relative saturation of the porous medium by divalent cations. Particle release is fastest when the porous medium is fully saturated with monovalent cations, but negligible when the medium fully saturated with divalent cations. Particle release depends sensitively on the relative saturation of the medium with divalent cations. A saturation of about 10% by calcium is sufficient to slow down the release rate by a factor of two. We interpret the strong dependence of the release on the valency of the cation as originating from attractive electrostatic interactions. Such interactions may be important in systems containing multivalent ions, and they originate from to correlations between the ions (Kjellander et al., 1988; Quirk, 1994). In addition, however, we suspect that other types of repulsive interactions may trigger particle release, and corresponding forces might be generated in the presence of other chemical species such as surfactants, complexing agents or natural organic matter (Dunnivant et al., 1992; van de Weerd et al., 1998; Grolimund et al., 2001a).

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