Corresponding author: Department of Civil Engineering, University of Toronto, 35 St. George St., Toronto, Ontario M5S 1A4, Canada. (firstname.lastname@example.org)
 Experiments were conducted with a laboratory-scale variable-aperture dolomite rock fracture to compare the transport of virus-sized microspheres and viruses. Transport tests were conducted using bromide, two sizes (20 and 200 nm diameter) of carboxylate-modified latex (CML) microspheres, and two bacteriophages (MS2 and PR772) that are often used as pathogenic virus surrogates. Retention of negatively charged MS2 was two to three times lower than retention of similarly sized negatively charged 20 nm microspheres, in contrast to expectations from Derjaguin-Landau-Verwey-Overbeek theory. Retention and transport of MS2 and PR772 were much closer to that of the 200 nm microspheres, with approximately 20% greater retention of MS2 compared to PR772 for all conditions tested. Microsphere transport was more significantly affected by ionic strength than the bacteriophage transport, particularly the 20 nm microspheres. Impacts of calcium chloride were significant and different for microspheres compared to bacteriophages. Application of a one-dimensional advection-dispersion transport model with two types of kinetic attachment and detachment terms gave good fits to microsphere and bacteriophage transport data. However, blocking was required to accurately simulate transport of the 20 and 200 nm microspheres. Blocking was not a significant process for MS2 or PR772 under most conditions tested. Overall, results indicate that 20 nm CML microspheres are not suitable surrogates for transport of MS2 and PR772 in fractured dolomite, and therefore, likely not suitable as surrogates for other viral pathogens. The 200 nm microspheres would be more suitable as surrogates but show different responses to changes in solution chemistry compared to bacteriophages.
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 Many small rural and suburban communities in Canada and United States rely on the subsurface for both on-site septic wastewater disposal and drinking water supply. The septic system effluent often contains infective biological contaminants including protozoa, bacteria, and enteric viruses. In similar areas, other point and nonpoint sources of infective microorganisms to the groundwater include land surface irrigation with treated wastewater, wastewater discharges, unintentional release of sewage, agricultural runoff, etc. Viruses are of special interest as they are small in size (20–200 nm) and generally are not well removed from the effluents by physical filtration or sedimentation, and consequently, may be the most mobile microbial contaminants. Many studies have been conducted to determine distribution of viruses in groundwater [Abbaszadegan et al., 2003; Borchardt et al., 2007; Hunt et al., 2010; Johnson et al., 2010; Trimper, 2010]. An American Water Works Association Research Foundation survey, conducted in the United States, reported the presence of infective viruses and viral nucleic acids in ground waters of approximately 5% and 31% of wells, respectively [Abbaszadegan et al., 2003].
 In areas where septic systems and other virus sources immediately overlie fractured bedrock aquifers and the soil layers are shallow and provide little retention of viruses, viral contaminants may reach the underlying fractured aquifer and pose a risk of contamination to drinking water sources. Borchardt et al.  reported the presence of human enteric viruses in seven water samples out of 30 samples from wells in confined fractured bedrock aquifers. These aquifers were confined by a 3–9 m thick shale unit. Trimper  conducted a survey to identify human enteric viruses in three fractured bedrock aquifers in Canada and reported that 37.7% of the samples (total number of samples 61) and 58.1% of the wells (total number of studied wells 28) were at some time positive for viruses.
 Field-based studies indicated rapid transport of silica microspheres in granite rock [Vilks et al., 1997], latex microspheres in granite rock [Becker et al., 1999], bacteriophages in fractured clay rich till [McKay et al., 1993], and microspheres in karst limestone [Renken et al.,2005]. These field findings are consistent with lab-based studies of transport of bacteriophages in fractured tuff [Bales et al., 1989], bacteria-sized latex microspheres in fractured tuffs [Reimus et al., 1994], and bacteriophages in fractured shale saprolite [McKay et al., 2002]. In most of these studies, colloids and bacteriophages travelled at rates that were similar or faster than rates for conservative-dissolved tracers. Faster colloid transport was attributed to colloids following preferential flow paths and diffusion of dissolved tracers into matrix porosity. Thus, the time required for the microbial pathogens from a known source to reach the drinking water wells located in fractured rock can be much less than would be predicted based on first detection of conservative tracers.
 Carbonate-rock (limestone and dolomite) aquifers typically have fractures and karst fractures providing high yields, which are used for both community and noncommunity water supplies. In carbonate aquifers, water is naturally buffered, maintaining the water pH above 7. The typical minerals present in limestone and dolomite rocks, and in the stylolites in these rocks, are generally negatively charged at or above neutral pH. Most of the enteric viruses have low isoelectric points (IEP, pH at which surface charge is zero in a solution) and exhibit negative surface charge at or above a pH of 7. The nature of these minerals and enteric viruses provide unfavorable conditions for the virus attachment to the mineral surfaces. The groundwater velocity in rock fractures may also be much higher than that of porous media. Therefore, viruses are expected to travel long distances in rock fractures. In porous media, groundwater velocity, colloid size, water pH, and ionic strength (IS) influence colloid transport [Schijven and Hassanizadeh, 2000]. In fractured rock, these factors, as well as rock surface characteristics and fracture aperture distribution [Mondal and Sleep, 2012], would be expected to influence colloid transport.
 Only a few studies have examined the effect of colloid size on colloid transport in fractured systems. Reimus et al.  found no significant difference between 1 µm and 300 nm carboxylate-modified latex (CML) microsphere transport in fractured tuffs. In contrast, Cumbie and McKay  found that the diameter of CML microspheres (50 nm to 1 µm) had a significant influence on transport and retention of the microspheres through fractured shale saprolite, with the least retention occurring for 500 nm microspheres. Increased retention of small (50–100 nm) microspheres was attributed to diffusion of the microspheres to fracture surfaces and into the saprolite matrix regions, while increased retention of 1 µm microspheres was attributed to gravitational settling and physical straining. Becker et al.  conducted lab studies with a variety of sizes of CML microspheres. They found faster arrival times for 190 nm microspheres compared to 360 nm microspheres in fractured tuff, but found the opposite trend with 360 and 830 nm microspheres in a fractured granite block. These results are consistent with the findings of Cumbie and McKay  with respect to a minimum colloid retention at 500 nm. Mondal and Sleep  found significantly greater retention of CML microspheres in a dolomite rock fracture as the microsphere size was decreased from 500 to 20 nm, again consistent with the results of Cumbie and McKay . However, in contrast to the conclusions of Cumbie and McKay , Mondal and Sleep  concluded that matrix diffusion did not have a significant effect on transport of any of the microsphere sizes (from 20 to 500 nm) through two distinct dolomite rock fractures.
 In a study of the effect of IS on colloid transport in fractured systems, McCarthy et al.  found that increasing solution IS increased retention of latex microspheres in fractured shale saprolite columns, with greater impact from divalent cations (Ca2+) compared to monovalent cations (Na+) for the same IS. In the study of Mondal and Sleep , increasing IS (3–12 mM with NaCl) resulted in significant increases in retention of 20 nm CML microspheres in a dolomite rock fracture, but IS had little effect on 200 and 500 nm microspheres (effects of calcium chloride were not examined).
 A variety of approaches have been applied to modeling colloid transport in fractured rock. Abdel-Salam and Chrysikopoulos  developed a one-dimensional advective-dispersive transport model for colloid transport in fractures, with colloid deposition on fracture walls assumed to be an irreversible first-order process. They also included colloid penetration into the rock matrix. The model of Abdel-Salam and Chrysikopoulos  also simulated colloid attachment as a first-order irreversible process, with a maximum number of sites available for colloid attachment. There have been a number of two-dimensional models developed for colloid transport in fractures. These models [James and Chrysikopoulos, 1999, 2000, 2003] are based on the two-dimensional Reynolds equation for fracture flow and simulate colloid transport at the micrometer to millimeter scale using particle tracking. In these models a variety of formulations are used to simulate attachment of particles to fracture walls, ranging from irreversible first-order attachment [James and Chrysikopoulos, 2003] to a probabilistic attachment function incorporating interaction energy and blocking [James and Chrysikopoulos, 2000]. Although these various models for colloid transport in fractures qualitatively reproduced many of the characteristics observed in colloid transport experiments, the model predictions were not compared to experimental data.
 A common feature among the models for colloid transport in fractured rock is the treatment of colloidal attachment as an irreversible process with a single attachment rate coefficient. In contrast, Schijven et al.  found that transport of viruses in columns of saturated dune sand could only be satisfactorily modeled by using a two-site kinetic model that incorporated both attachment and detachment for each of the two types of sites. Mondal and Sleep  used HYDRUS-1D (from PC-Progress) to model transport of CML microspheres in dolomite rock fractures and concluded that a two-site kinetic model was required to model the microsphere transport. However, the rising limbs of the microsphere breakthrough curves (BTCs) for the 20 and 200 nm microspheres was not well captured by this model, indicating that blocking might have been important.
 This study extends the work of Mondal and Sleep , which focused on the effect of dolomite rock fracture characteristics on CML microsphere transport. In the current study, the objective is to compare the transport of both CML microspheres (20 and 200 nm) and two different sized bacteriophages (PR772 and MS2) in a dolomite rock fracture. Of particular interest is the potential for using CML microspheres as surrogates for virus transport in fractured dolomite. Both microspheres and bacteriophages have been used as surrogates for pathogenic virus transport, but there are no studies that compare the transport of microspheres to bacteriophages MS2 and PR772 under the same conditions, particularly in fractured rock. If the microspheres are not suitable surrogates for transport of bacteriophages, then they will also not be suitable as surrogates for transport of pathogenic viruses. The current study includes an investigation of the influence of IS and cation type (Na+ and Ca2+) on CML microsphere in comparison to the influence on bacteriophage transport. One-dimensional models are applied to reproduce the experimental results and provide insights into the processes governing CML microsphere and bacteriophage transport in a lab-scale dolomite rock fracture. In particular, the importance of attachment, detachment, blocking, and bacteriophage inactivation are explored for both microspheres and bacteriophages.
2. Materials and Methods
2.1. Rock Fracture Characteristics
 A fracture was created in a dolomite rock block (quarried from Wiarton, Ontario) along a stylolite by using a loading machine. A stylolite represents plane of weakness in dolomite and a potential natural fracture plane. The fractured rock block was cut into sizes of 280 mm × 210 mm × 70 mm and five stainless steel needles (1.45 mm outer diameter) were installed on the top rock plate near the outlet side of the fractured block for hydraulic head measurement and effluent water collection. The outlet needles were connected together with small tubes to create a common outlet for water sample collection. The bulk rock material mineral composition was determined with X-ray diffraction, and the element composition was examined with X-ray fluorescence spectroscopy. Dolomite was the major mineral phase (∼96.5%) in the bulk rock material. The minor phases were silica and orthoclase (<4%). Scanning electron microscope-energy dispersive spectroscopy (SEM-EDS) analysis with remnant rock samples indicated that silica and orthoclase were present in significant amounts along the stylolite compared to the bulk rock matrix. Image analysis done on SEM-backscatter electron images of epoxy-impregnated polished rock samples indicated that the stylolite areas and rock matrix near stylolite areas had porosities of 15–20%, whereas, the bulk matrix areas had a porosity of 6%–12%. The fractured rock block was soaked in 1 mM sodium chloride (NaCl) and 1 mM sodium bicarbonate (NaHCO3) in distilled Milli-Q® water solution under vacuum (120–150 mm of mercury vacuum) for approximately 10 weeks to achieve matrix saturation. Afterward the fracture was assembled in the fracture containment cell for the bromide tracer, microsphere, and bacteriophage transport tests. A detailed description of the fracture characteristics and rock porosity measurement can be found in the study of Mondal and Sleep .
 Two bacteriophages MS2 (HER 462) and PR772 (HER 221) were used in the transport tests as pathogenic virus surrogates. Both of these bacteriophages have been widely used in virus transport studies in porous media [Dowd et al., 1998; Ryan and Elimelech, 1996; Schijven and Hassanizadeh, 2000]. These bacteriophages and their host bacteria E. coli C3000 (HER 1462) and E. coli K12-J53 (HER 1221) were collected from the Felix d'Herelle Reference Centre for Collection of Bacterial Viruses, Université Laval, Québec. MS2 is a male-specific icosahedral single-stranded RNA bacteriophage of the Leviviridae family and has been used as a surrogate for enteric viruses (e.g., echovirus). The size of this phage is 24–27 nm [Mayer et al., 2008] and the IEP is 3.4–4.1 [Langlet et al., 2008; Chrysikopoulos and Syngouna,2012]. At most natural groundwater pH values, the MS2 surface is negatively charged and is reported to have little adsorption in saturated sandy soil. MS2 was propagated using E. coli C3000 (HER 1462) as host. MS2 was propagated in tryptic soy broth solution as described in EPA Method 1602 [U. S. Environmental Protection Agency (EPA), 2001] and enumerated by double agar overlay plaque-forming method [Adams, 1959; Mesquita et al., 2010]. Using this propagation method, the stock titer of ∼1012 plaque forming unit mL−1 (PFU mL−1) was achieved, and stock was stored at 4°C before using in experiments within 6 weeks of preparation.
 PR772 is a double-stranded lipid containing DNA bacteriophage of the Tectiviridae family and a member of the PRD1 phage group [Bamford et al., 1981]. This phage is used as a surrogate for mammalian viruses (e.g., adenovirus). It is hexagonal-shaped with size of 53 nm measured by transmission electron microscopy (TEM) [Coetzee and Bekker, 1979] or hydrodynamic diameter (HD) of 82 nm measured by dynamic light scattering technique, and an IEP of 3.8–4.2 [Lute et al., 2004]. It has a thick inner membrane containing lipid and no tail. It has a buoyant density of 1.26 g cm−3 [Coetzee et al., 1979]. High titer PR772 stock suspension has been reported as homogeneous, intact, and monodispersed [Coetzee et al., 1979]. PR772 was propagated using E. coli K12-J53 (HER 1221) as host with the soft agar plating method and was enumerated by double agar overlay plaque forming method [Mesquita et al., 2010]. The stock titer of ∼ 1010 PFU mL−1 was achieved and stock was stored at 4°C before using in experiments within 6 weeks of preparation. For the bacteriophage enumeration, sample dilutions were prepared to achieve 20–200 plaque count in a 100 mm petri dish. The standard deviation for bacteriophage enumeration was within 20%.
 In the transport tests CML fluorescent microspheres of 20 and 200 nm (FluoSpheres® microspheres from Molecular Probes, Invitrogen Canada Inc.) were used as virus-sized particles. These microspheres are anionic with a highly charged, relatively hydrophilic, and slightly porous surface layer. Working stock solutions of the microspheres were prepared by diluting the stock microsphere solutions 100 times in distilled Milli-Q® water. The tracer solutions were prepared with buffered and IS adjusted distilled Milli-Q® water to provide final microsphere concentrations of 4.55 × 1011 and 6.37 × 108 particles mL−1 (Pt mL−1) for 20 nm (M-1) and 200 nm (M-2) microspheres, respectively. Microspheres in the tracer solution and outlet fractions were analyzed by using a fluorescence spectrophotometer (Perkin-Elmer LS-50B) with 10 mm × 10 mm quartz cuvette and excitation and emission wave lengths of 365/415 nm and 540/560 nm for M-1 and M-2, respectively. The samples were diluted five times with Milli-Q® water in the cuvette. The excitation and emission slits of the instrument were set at 10 and 5 nm, respectively. The detection limits were 5 × 106 and 4 × 105 particles mL−1 (Pt mL−1) for M-1 and M-2, respectively, and the variation in measurement was within 10%.
2.4. Solution Preparation
2.4.1. Tracer and Particle Solutions
 The solutions (containing bromide and bacteriophages or bromide and microspheres) used in transport tests were prepared with distilled, degassed Milli-Q® water. Milli-Q® water (18.2 MΩ electrical resistance) was autoclaved at 121°C for 20 min and cooled to room temperature overnight to remove dissolved air/gas. Sodium bicarbonate (NaHCO3) solution (0.5 M) was added providing a concentration of 1 mM to buffer the water pH around ∼8.2. Sodium chloride (NaCl) solution (1 M) was added to the buffered water at the concentrations of 1 and 10 mM to provide two solutions containing NaCl salt. Calcium chloride (CaCl2) solution (1 M) was added to the buffered water at a concentration of 1 mM to provide solution containing CaCl2. Sodium bromide (NaBr) solution (1 M) was added to the solutions at a concentration of 1 mM. Bromide was added as a dissolved conservative tracer in tracer transport tests. All the stock solutions were sterilized by filtering through 0.45 µm pore-size filters. All the salts used in solution preparation were reagent grade and obtained from Sigma-Aldrich®. Working stock solutions of the microspheres (20 and 200 nm CML particles) or bacteriophages (MS2 and PR772) were added to provide the final concentrations as shown in Table 1. The zeta potentials (ZPs) and HDs of microspheres were determined for the various different solution conditions used in fracture transport experiments. Bacteriophage batch inactivation tests were also performed at different solution ISs and compositions used in fracture transport experiments.
Table 1. Bromide, Microsphere, or Bacteriophage Concentrations in Transport Tests
 Before and after adding tracer and particle solution to the fracture, the fracture was flushed with background solution that had the same composition as the tracer and particle solution, except that no microspheres or bacteriophages were added, and the 1 mM sodium bromide was replaced with 1 mM NaCl to maintain the same IS throughout each entire transport test. These background solutions were used to equilibrate the fracture for corresponding IS and composition test cases for more than 48 h before any transport test.
 The average temperature of the solutions was 21.0°C±0.3°C and average pH of all these solutions was 8.2±0.3. Three solution chemistries used in the transport tests were (a) 3 mM containing 2 mM NaCl salt, (b) 12 mM containing 11 mM NaCl salt, and (c) 5 mM containing 2 mM NaCl and 1 mM CaCl2 salts. These test cases will be referred as (a) 3 mM (Na+), (b) 12 mM (Na+), and (c) 5 mM (Ca2++Na+), respectively, to identify the IS and ionic composition of the solutions. Measured conductivities of these solutions were 328±7, 1378±38, and 455±10 μS cm−1, respectively.
2.5. Zeta Potential and Hydrodynamic Diameter of Microspheres
 The laser Doppler electrophoresis technique was applied to measure ZP and dynamic light scattering technique was applied to measure HD of the microspheres for different solution conditions using a Zetasizer Nano ZS (Malverns Instruments). The ZP was calculated from the measured electrophoretic mobility using Smoluchowski equation [Hunter,2001]. The refractive index value of CML particles (1.59) was used to change the distribution from intensity-based to a volume or number-based distribution. Microsphere solutions in a 15 mL polypropylene vial were sonicated for 1 min in a water bath sonicator (FS20, Fisher Scientific) before transferring into the measurement cuvettes.
 The ZP measurements were performed in clear disposable zeta cells (DTS1060C, Malvern Instruments) and HD measurements were performed in disposable cuvettes (ZEN0112, Malvern Instruments). All the analyses were performed at room temperature of 21°C. Each sample was analyzed three times. For each analysis, the prepared sample in the measurement vial was measured three times. For each measurement 10 runs were conducted. The ZP values were reported as the mean ZP (mV) of multiple measurements with measured average zeta deviation (mV) and standard deviation of the mean ZP in multiple measurements. The zeta deviation in each measurement indicates the extent of variability of ZP values among particles in the sample. The HDs were reported as the mean Z-average size (nm) and standard deviation of multiple measurements with average polydispersivity index (PDI) of multiple measurements. The PDI value indicates the extent of agglomeration of particles or the presence of different sizes of particles in a solution [Nobbmann et al., 2007]. The microsphere and bacteriophage solutions used in the transport tests in fractured rock were prepared in the same manner as those used to determine microsphere and bacteriophage HD and ZP.
2.6. Surface Charge of Rock Materials
 The ZP of the rock materials in the tested solutions was measured by SurPASS Electrokinetic Analyzer (Anton Paar® GmbH). Surface charge is related to ZP and can be determined using the Grahame equation derived from Gouy-Chapman theory for a double-layer model [Hans-Jurgen et al.,2006]. Materials from the fracture surface and from the matrix near the fracture surface were collected by carefully removing the bulk rock matrix (mostly dolomite) materials from small fractured rock pieces using a diamond handsaw. The collected materials were crushed with a rock crusher to sizes less than 1.7 mm. The crushed materials were sieved and materials within 0.6–0.1 mm were separated. These sieved materials were washed with distilled water and dried at 110°C overnight, and the ZPs were determined at the solution conditions used in the transport tests. For each measurement approximately 1.5 g of crushed materials were packed in the cylindrical measurement cell. Measurements were taken twice for each direction of electrolyte solution flow in the measurement cell. Duplicate packing and analyses were conducted for each case.
2.7. Experimental Setup
 Figure 1 shows the schematic diagram of the bench-scale experimental system. The experimental system includes: (a) the fractured dolomite rock block (∼280 mm × 210 mm × 70 mm), (b) acrylic inlet chamber, (c) a stainless steel frame for holding the fractured block and inlet chamber, (d) a dual-head peristaltic pump (MasterFlex® L/S with Easy-Load® II pump heads, 77201-60) to feed the system, (e) a syringe pump (74900 Series Syringe Pump, Cole-Parmer®) to inject tracer and particle pulse and background solutions, (f) a gear pump (Micropump, 120-000-110) to replace solutions in the inlet chamber, (g) a fraction collector (Pharmacia LKB Redifrac) to collect samples from the outlet manifold, and (h) glass tube piezometers (3 mm ID) at the inlet chamber and outlet manifold for water head measurement.
 The fractured rock block was placed in the middle of the stainless steel frame. Two opposing long sides of the fractured rock block were sealed with rubber gaskets (2 mm thick) and steel plates in the holding frame to provide no-flow boundaries. The short side at the downstream end was sealed with a rubber gasket and an acrylic block, which also provided a no-flow boundary. The other short side at the upstream end was connected to a channel (volume=20 mL) milled in an acrylic inlet chamber block. A rubber gasket with an opening in the middle was placed between the fractured block side and the inlet chamber block for sealing. Four screws on two cross steel plates on top of the frame were uniformly hand tightened to keep the fracture block under uniform pressure throughout the hydraulic and transport tests. The fracture was oriented horizontally during all hydraulic and tracer tests. Five stainless steel needles on the fracture block near the outlet (15 mm from the edge and 45 mm apart) were connected together to create a combined outlet manifold. The inlet chamber and the combined outlet were operated as constant-pressure boundaries.
2.8. Hydraulic Tests
 Hydraulic tests were performed with the fractured rock block to determine the equivalent hydraulic aperture, as defined by Tsang  and the specific discharge. Water was injected through the fracture using the dual-head peristaltic pump. Head loss across the fracture length was determined using piezometers connected to the upstream inlet chamber and downstream outlet manifold. Water exited the system through a constant-head port at the downstream end of the fracture. The water used in the hydraulic tests was prepared by degassing the distilled-Milli-Q® water, equilibrating the water to room temperature (21°C±0.3°C), and adding 1 mM NaHCO3 as buffer to bring the pH to 8.2±0.3. After installation of each fractured rock block in the experimental system, the fracture void space, inlet chamber, tubes, and manifold were saturated with water. Hydraulic tests were conducted by injecting the prepared water into the fracture at a constant flow rate (7.67 × 10−9 m3 s−1) and by measuring the water head difference across the fracture. Equivalent hydraulic aperture (bh) and specific discharge (vh) were determined using the following equations:
where η is the dynamic viscosity of water (kg m−1 s−1), Q the volumetric flow rate of water (m3 s−1), L the length of the fracture (m), γ the specific weight of water (kg m−2 s−2), W the width of fracture (m), Δh the piezometric head difference between upstream and downstream of fracture (m).
2.9. Transport Tests
 In a transport test, following 48 h of flushing with background solution, the tracer and particle solution (containing bromide and microspheres, or bromide and bacteriophages) was injected into the fracture as a pulse of 11 pore volumes (PV ∼ 6.1 mL, calculated based on equivalent hydraulic aperture). This was followed by injection of 18 PV of buffered solution with no bromide, bacteriophages, or microspheres. For the duration of each test, a flow rate of 7.67 × 10−9 m3 s−1 was used. Water exiting the fracture system was collected by the fraction collector with each aliquot collected equivalent to 0.25 PV of the fracture. The total time for each transport test (including pulse and flush) was approximately 7 h. The samples collected by the fraction collector were analyzed for bromide, chloride, microspheres (M-1 and M-2), and bacteriophages (MS2 and PR772). Bromide concentrations were measured by ion chromatography (Dionex 500 Ion Chromatograph), and microsphere concentrations were analyzed by fluorescent spectrophotometer (Perkin-Elmer LS-50B). The phages in the samples were enumerated by double agar layer plaque-forming method [Adams, 1959; Mesquita et al.,2010]. Concentrations of tracer and particles in the effluent fractions were normalized by the injection concentrations (Co) to determine the normalized BTCs. For most of the transport test cases, duplicate experiments were conducted.
2.10. Phage Inactivation Tests
 To determine the inactivation rate of the bacteriophages (MS2 and PR772) at room temperature (21°C±0.3°C) for the solution chemistries used in the fracture transport tests, batch inactivation tests were performed in 500 mL Pyrex bottles for 8 h (similar duration as the bacteriophage transport tests in the fractured rock). Solutions were prepared following the same procedure as in fractured rock transport tests. At the beginning of the tests, 0.1 mL of stock bacteriopahge solution was added to each bottle to obtain MS2 concentration of 6.7 × 105 to 9.4 × 105 PFU mL−1 and PR772 concentration of 7.1 × 106 to 8.3 × 106 PFU mL−1. Samples were collected from each bottle and diluted and plated immediately to determine the initial phage concentration. For each sample, three dilutions were prepared in buffered water and each dilution was plated in triplicates. The bottles were then kept on an orbital shaker and shaken at 120 rpm speed. Samples were collected from the bottles at 2, 4, and 8 h. These samples were diluted and plated immediately after collection.
2.11. Temporal Moment Analysis
 Temporal moment analysis of the tracer and particle input and output breakthrough data were performed to determine the mean residence time of tracer and particle in the fracture and mass recovery in the effluent. Mean residence time (tm) was determined from the difference between the centroids of the output BTC and input pulse. The mass recovery (Mr) was determined from the ratio of mass recovered in the effluent and mass injected in input pulse. The following equations were used:
where C(t) is the tracer and particle concentration in effluent at time t (mg mL−1 or PFU mL−1 or Pt mL−1), t the time (min), Tp the duration of input pulse (min), Q the volumetric flow rate of water (mL min−1), Co the tracer and particle concentration in input pulse (mg mL−1 or PFU mL−1 or Pt mL−1).
2.12. Modeling of Solute and Colloid Transport
 A one-dimensional advection-dispersion model, HYDRUS-1D [Šimunek et al., 2008], accounting for chemical nonequilibrium was used to simulate the BTCs of microspheres M-1 (20 nm) and M-2 (200 nm), and bacteriophages MS2 and PR772. In this study bromide was assumed to be nonreactive with the rock minerals. Bromide has been widely used in various transport studies in porous media as a conservative tracer to determine the pore water velocity as well as dispersivity. A physical equilibrium model was not adequate to fit the observed bromide breakthrough data. A two-region model with dual-porosity type transport model (a physical nonequilibrium model) fitted the observed bromide breakthrough data well. The two-region concept assumes that the liquid phase can be partitioned into mobile (flowing), θmo (m3 m−3), and immobile (stagnant), θim (m3 m−3), porosity regions such that for saturated flow the porosity, θ=θmo+θim. The immobile porosity represents the nonflowing water in very low aperture regions in the fracture and the porous rock matrix near the fracture. In this case the solute exchange between the two liquid regions is modeled as a first-order process. Bromide transport parameters, saturated hydraulic conductivity, and fraction of immobile zones (f) were obtained by calibrating the HYDRUS-1D model solutions against the observed BTCs. Saturated hydraulic conductivity (Ks), dispersivity (αL), and fraction of immobile region (f) were estimated by fitting bromide breakthrough data following the procedures described by Schijven and Šimunek .
 The physical nonequilibrium model alone may not be adequate to fit the microsphere and bacteriophage BTCs. Vilker  proposed that virus transport in porous media could be appropriately described by models with nonequilibrium adsorption processes. Bales et al. [1993, 1997] and Kinoshita et al.  showed that bacteriophage MS2 adsorption in soil was kinetically limited, which was evident from the slow rising limbs and long tails of the BTCs. Schijven et al.  demonstrated that two-site kinetic model was necessary to satisfactorily fit BTCs of bacteriophages MS2 and PRD1 transport tests in columns containing dune sand. Their model fit well the skewness of the rising limbs and smooth transition of the declining limb to the tail of the BTCs. Therefore, the colloid (microspheres and bacteriophages) transport in this study was modeled using the chemical nonequilibrium (two-site kinetic) model. By fitting the observed BTCs, attachment and detachment coefficients for the two types of sites were estimated. A Langmuirian type blocking function ( ; where S is the sorbed concentration of the colloid and Smax is the maximum sorbed concentration of the colloid) was utilized to simulate the reduction in attachment coefficients due to filling of sorption sites with microspheres and bacteriophages [Šimunek et al., 2008]. In addition to blocking, inactivation was incorporated into modeling of bacteriophage transport. Batch bacteriophage inactivation test data were used to determine first-order inactivation rate coefficients and were used in the modeling.
3.1. Colloid and Rock Properties
 Figure 2 shows ZPs and HDs of the microspheres for different solution conditions. The ZP values of both microspheres were similar for the 3 mM (Na+) and 12 mM (Na+) solutions, and were significantly lower for the 5 mM (Ca2++Na+) solution. In all solutions M-2 microspheres had higher ZP values than the M-1 microspheres. For bacteriophages, ZP of PR772 was measured to be −27.0±1 mV at 3 mM (Na+) solution. ZP measurements were not performed for PR772 for other solution chemistries or for MS2 in any solution chemistry.
 The average HDs of both microspheres were larger than the supplier-specified sizes. Particularly for M-1 the HD was more than twice the supplier specified diameter. The PDI values for M-1 were between 0.3 and 0.33, which indicated the possibility of agglomeration of the particles or presence of particles with a wide size range. In contrast, the PDI for microsphere M-2 was less than 0.03 in all solutions, indicating monodispersive particle diameter distribution [Nobbmann et al., 2007].
 The SEM-EDS analysis of the fracture surface indicated presence of silica, orthoclase, and dolomite in the stylolite materials. At the water pH of 8.2±0.3 the major mineral (dolomite) and minor minerals (silica and orthoclase) of the rock materials were expected to have negative ZP values as their IEP values are lower than pH value of 8.2. The IEP of dolomite was reported to be 6.3 for measurements done on samples equilibrated with atmospheric carbon dioxide [Gence and Ozbay,2006]. The IEP was reported to be less than 3 for silica and 2 to 2.4 for orthoclase [Parks,1965]. The ZPs of the crushed stylolite rock materials were −30.9±0.6, −26.6±0.7, and −9.0±0.3 mV at solution conditions of 3 mM (Na+), 12 mM (Na+), and 5 mM (Ca2++Na+), respectively.
3.2. DLVO Interactions of Particles With Rock Minerals
 Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energy profiles (sum of electrostatic double-layer repulsion and London-van der Waals attraction) for the colloids (both microspheres and bacteriophage PR772) and rock materials (dolomite, silica, and orthoclase) were calculated following the procedure described by Bergendahl and Grasso  using sphere-plate type interaction. For the London-van der Waals interaction energy calculation, the combined Hamaker constant of 6.4 × 10−21 J and 6.0 × 10−21 J were used for the rock materials-water-CML microsphere and rock materials-water-PR772 systems, respectively. The measured ZP values of the microspheres, PR772, and crushed rock materials for different solution conditions were used in the energy profile calculation. Figure 3 shows the interacting energy profiles between colloids (microspheres M-1 and M-2, and PR772) and rock materials. Energy profiles are shown for 3 (Na+) and 12 mM (Na+) solution conditions (solution with 1:1 electrolyte salt) for the microspheres. For PR772, only the 3 mM solution case profile is shown. The interaction energies were normalized by kT, where, k is the Boltzmann constant (1.3806503 × 10−23 m2 kg s−2 K−1) and T is the absolute temperature (K). The negative values of the energy profile represent attractive interaction between the colloid and the surface. The energy profile data show that secondary energy minima, although small (from −0.01 to −0.46 kT), were present in all cases. For the microsphere M-2, the respective minimum energies were more negative than for M-1, and the energy barriers were higher.
3.3. Hydraulic Test Results
 From all the hydraulic tests performed at the flow rate of 7.67 × 10−9 m3 s−1, the equivalent hydraulic aperture of the fracture was calculated to be 109±3 μm (n=35) and specific discharge rate was calculated to be 3.3 × 10−4 ± 0.1 × 10−4 m s−1. The hydraulic conductivity of the fracture was calculated to be 1.01 × 10−2 ± 6.0 × 10−4 m s−1. Hydraulic tests were conducted periodically to ensure that the equivalent hydraulic aperture of the fracture remained unchanged. The equivalent hydraulic aperture value varied between 101 and 117 μm over the period of all the hydraulic and tracer and particle transport tests, indicating stable aperture of the system.
 The Reynolds number (Re) for the experiment flow (7.67 × 10−9 m3 s−1) in the fracture was 0.04 as defined by the relationship: , where, ρ is the water density (kg m−3), v the water velocity (specific discharge, m s−1), b the equivalent hydraulic aperture (m), and μ the dynamic viscosity of water (kg m−1 s−1). It was demonstrated by Sharp and Maini  and Schrauf and Evans , using natural fracture samples, that inertial forces may be nondominant but significant at Re values above 1–10. It can be expected that in this study the flow in the fracture was laminar, the influence of inertial forces on the bulk flow rate across the fracture was small, and use of the cubic law for determining the equivalent hydraulic aperture was valid [Brush and Thomson, 2003]. The Peclet number ( ; Dm is the diffusion coefficient of the tracer) for the bromide transport was 17.
3.4. Bacteriophage Batch Inactivation Test Results
 Figures 4a and 4b present the results of inactivation tests for PR772 and MS2, respectively, for different solution conditions for the total test duration of ∼8 h. Inactivation is expressed by normalizing the bacteriophage concentration (C) at different times with the initial concentration (Co). The extent of inactivation (up to ∼30% for PR772 and up to ∼40% for MS2) measured in the batch inactivation tests could be a combination of phage inactivation due to the test temperature (21°C) and sorption of phages on the batch test bottle walls. Yates  found that temperature is the most important factor that influences virus inactivation and that inactivation rate increases with temperature. Using the inactivation data in Figures 4a and 4b and additional inactivation tests (data not shown), the first-order inactivation rate coefficients were calculated to be 5 × 10−4, 8 × 10−4, and 1.2 × 10−3 min−1 for PR772 in 3 mM (Na+), 12 mM (Na+), and 5 mM (Ca2++Na+) solutions, respectively. The corresponding coefficients for MS2 were 8 × 10−4, 3 × 10−4, and 3.1 × 10−3 (min−1).
3.5. Bromide and Microsphere Transport
 Figure 5 presents a typical experimental BTC for bromide and the HYDRUS-1D model (dual-porosity) fitted BTC. The bromide peak normalized effluent concentration (C/Co) was close to unity (0.99±0.04) in all the test cases. Bromide mass recovery (from moment analysis) was 96.8±2.8% (n=10) and the mean residence time was 29.3±1.4 min in all the tests. Figure 6 illustrates the experimental and model (two-site kinetic) fitted BTCs for the microspheres for the transport tests at different water ISs and compositions. For microsphere M-1 (20 nm) the peak C/Co decreased from 0.48 to 0.16 with increased IS from 3 to 12 mM (Na+). For the 12 mM (Na+) and 5 mM (Ca2++Na+) solutions, the peak C/Co values were similar (0.16 and 0.17, respectively). For microsphere M-2 (200 nm) the peak C/Co value also decreased from 0.93 to 0.55 with increased IS from 3 to 12 mM (Na+). However, for the 5 mM (Ca2++Na+) case, the peak C/Co was higher (0.78) than for 12 mM (Na+) case. The tailing in concentrations for M-1 in 3 and 12 mM solutions was significant; whereas, less tailing occurred for the 5 mM (Ca2++Na+) solution case. Figures 7a and 7b show the average residence time and average mass recovery of microspheres M-1 and M-2 for different test conditions. The mean residence time of microsphere M-1 was 57.4±8.8 min for 3 mM (Na+) solution case and increased to 80.5 min for 12 mM (Na+) solution case. However, the residence time was lower for the 5 mM (Ca2++Na+) solution case with a value of 34.3 min. For the microsphere M-2, the mean residence time was very similar in all the cases (22.3 to 24.0 min).
 The mass recovery of microsphere M-1 was 41.9±2.1% for the 3 mM solution case and decreased to 15.4% for the 12 mM solution case. The recovery was lowest (12.8%) for 5 mM (Ca2++Na+) solution case (Figure 7). The mass recovery of microsphere M-2 decreased from 92.5% to 45.4% when solution IS increased from 3 to 12 mM. However, the mass recovery was 73.5% for 5 mM (Ca2++Na+) solution case. For each test condition, the mass recovery was higher for the larger microsphere, M-2.
3.6. Bacteriophage Transport
 Figure 8 shows experimental and model (two-site kinetic) fitted BTCs for MS2 and PR772 for the transport tests at different water ISs and compositions. The normalized concentrations (C/Co) in the plots are shown in log scale as bacteriophages in the outlet samples were enumerated over several orders of magnitude. The log-scale plots in these cases clearly show the tailing behavior in bacteriophage concentration. The peak C/Co for MS2 and PR772 decreased with increased IS (IS increased from 3 to 12 mM) and peak C/Co decreased significantly in the presence of Ca2+ ions (IS case of 5 mM).
 Figures 7c and 7d present the residence time and average mass recovery of bacteriophages MS2 and PR772 for different test conditions. Lower residence times of PR772 (20.4 to 27.2 min) compared to bromide (29.3±1.4 min) for all test conditions indicate earlier arrivals compared to the conservative solute tracer. MS2 arrived earlier than bromide in 3 and 12 mM (Na+) solution cases and arrived later than bromide in 5 mM (Ca2++Na+) solution case. The mass recovery results indicate that the recovery of bacteriophages decreased with higher IS. For each test case the recovery was also lower for the smaller bacteriophage MS2 (diameter of 24–27 nm) as compared to PR772 (diameter of 82 nm). Lowest recovery was observed with the presence of Ca2+ ion for both phages.
3.7. Estimated Transport Parameters
 The temporal moment analysis of all the bromide transport BTC data yielded an average bromide velocity of 1.52 × 10−4 m s−1, which was approximately half of the specific discharge (3.50 × 10−4 m s−1) calculated from the hydraulic tests. The dispersivity was calculated to be 0.03 m. Data from 10 transport test BTCs for bromide at 3.5 × 10−4 m s−1 specific discharge were also fitted with HYDRUS-1D using the dual-porosity model (a two-region model). The fracture dispersivity (αL), fraction of immobile water content (f), and water mass transfer coefficient (ω) between mobile and immobile zones were found to be 1.7 × 10−2 ± 6.0 × 10−3 m, 2.1 × 10−1 ± 2.6 × 10−2, and 6.0 × 10−5 ± 1.3 × 10−5 s−1, respectively. R2 values (indicates goodness of the fit) for the fittings were higher than 99% in all the cases. The immobile water content fraction determined from modeling the bromide transport experiments most likely represents stagnant zones associated with small aperture regions and pores and microfissures in the rock matrix near the fracture surface (matrix porosity of the rock was 15–20%). However, with this dual-porosity model, one cannot separate the contributions of the low aperture regions from those of the porous rock matrix.
 The dual-porosity model was not suitable for modeling microsphere and bacteriophage transport. Instead, the two-site kinetic model was used to fit the microsphere and bacteriophage BTCs. This involved fitting microsphere and bacteriophage attachment and detachment coefficients and blocking parameter (Smax) for the two types of kinetic sites and corresponding dispersivity (Table 2). The dispersivity values obtained from fitting the microsphere M-1, bacteriophages MS2 and PR772 BTCs (1.2 × 10−2 to 2.7 × 10−2 m), were similar to the dispersivity value obtained from the bromide BTC fitting (1.7 × 10−2 m). However, the dispersivities obtained from microsphere M-2 BTCs fitting (1.8 × 10−4 to 1.0 × 10−2 m) were lower. The earlier arrival and these lower dispersivities for microsphere M-2 indicated that M-2 microsphere was likely less affected by diffusion into small aperture regions and porosity in the near fracture surface zones.
Table 2. Modela-Fitting Parameters for Transport of Microspheres and Bacteriophages
3 mM (Na+)
12 mM (Na+)
5 mM (Ca2++Na+)
M-1 (20 nm)
M-2 (200 nm)
M-1 (20 nm)
M-2 (200 nm)
M-1 (20 nm)
M-2 (200 nm)
Two-site kinetic attachment-detachment model.
Smax, the Langmuirian blocking function parameter (unit: number of particle per unit mass of media). Suffix 1 is for first kinetic site type and suffix 2 is for second kinetic site type.
 The rising limbs and declining portions of the BTCs and the tailing could only be replicated by a model incorporating two types of sites, each with distinct attachment and detachment rate coefficients. For all conditions for both microspheres and bacteriophages, the first type of sites had attachment coefficients (katt1) that were much greater than the corresponding detachment coefficients (kdet1), indicating a nearly irreversible attachment. For the second type of sites, the attachment and detachment coefficients (katt2 and kdet2) were similar in magnitude, indicating a highly reversible attachment. As indicated by Schijven et al. , microsphere removal in the simulations is largely governed by attachment to type 1 sites, the skewness of the increasing and decreasing portions of the BTCs are influenced by the value of kdet2, and the long tails are governed by the value of kdet1.
 The continual increase in concentrations evident for the microspheres could only be reproduced by including blocking for the sites. The value of the blocking function parameter Smax was higher for the first type of site in all cases, and was generally smaller for the microspheres compared to the bacteriophages. In several of the conditions tested, there was no blocking required for the bacteriophages (fit values of Smax by HYDRUS-1D parameter estimation routine were very large). The two-site kinetic model fit the BTCs of microsphere M-2 very well. Inclusion of the Langmuirian type blocking function improved the M-2 fits slightly. However, inclusion of the blocking function improved the microsphere M-1 BTC fittings significantly, indicating that blocking was a significant process for M-1. The influent concentrations of M-1 were approximately 3 orders of magnitude greater than the influent concentrations of M-2, while the surface areas of the particles only varied by a factor of 7. This may explain the more significant impact of blocking for M-1, in combination with the greater retention of M-1 compared to M-2.
 The two-site kinetic model with blocking and inactivation fit most of the bacteriophage BTCs well, except for the late time tails of the MS2 BTC in the 3 mM (Na+) case and the PR772 BTC in 12 mM (Na+). In this case the model overestimated the concentrations at later time. Inactivation of viruses is usually insignificant for the time scale of laboratory experiments in saturated soil column, and therefore, is often neglected in the modeling virus transport [Bales et al., 1991, 1993; Dowd et al., 1998; Redman et al., 1997]. The total time for the experiments in this study was short; however, the bacteriophage batch inactivation results indicated some inactivation and inactivation was incorporated. However, it should be noted that model fitting with and without inactivation did not change the goodness of fit (expressed with R2 value) significantly since the inactivation was low for both bacteriophage in 3 and 12 mM solutions.
4.1. Effects of Ionic Strength
 Transport of bacteriophages and microspheres was significantly affected by solution IS. The mass recovery and peak concentrations of both microsphere sizes decreased when the IS was increased from 3 to 12 mM (Figure 7). Consistent with this pattern, the values of katt1 increased for both microspheres, while changes in Smax with increasing IS were small. The same trend was evident for the bacteriophages, but the relative reductions in mass recovery and peak concentration and increases in katt1 were smaller than for the microspheres. In particular, the effect of increasing IS on the transport of the 20 nm microspheres was much greater than the effect on the similarly sized MS2. This indicates that IS had a greater impact on attachment of these microspheres to the dolomite fracture surface compared to the impact on attachment of the bacteriophages. Consequently, bacteriophages might be expected to exhibit greater mobility in dolomite fractures under conditions of increasing IS than would be expected from the behavior of CML microspheres of similar sizes.
 At the experimental water pH of 8.2 and ISs of 3 and 12 mM, the minerals on the fracture surface would have been negatively charged, as the measured ZP was negative and became less negative with increased solution IS (Figure 2). The DLVO interaction energy profiles of M-1 and M-2 with the rock materials at 3 and 12 mM solution conditions (Figure 3) indicate the presence of an energy barrier for microsphere attachment and the presence of a secondary energy minimum. Several studies have indicated that with unfavorable attachment conditions colloids could still be retained by the collector in the secondary energy minimum [Bradford et al., 2011; Kuznar and Elimelech, 2004; Pelley and Tufenkji, 2008] as well as on patches of oppositely charged sites due to the surface charge heterogeneity [Johnson and Tong, 2006; Litton and Olson, 1993; Tufenkji and Elimelech, 2005; Song et al., 1994]. The increased IS of the solution reduces the electrical double-layer thickness of the rock minerals and colloids causing increased depth of the secondary energy minimum (as shown in Figure 3), thereby increasing retention of microspheres in the fracture. Increased retention of latex particles (63–500 nm) with increasing IS were also observed in porous media under unfavorable attachment conditions in other studies [Bradford et al.,2011; Pelley and Tufenkji,2008; Tufenkji and Elimelech,2005]. Kuznar and Elimelech  demonstrated with a flowthrough cell that CML microspheres (4.1 μm) became trapped in the secondary minimum and accumulated near the downstream side of the spherical collectors (glass beads) under unfavorable attachment conditions. Tong and Johnson  showed higher retention of particles on porous media relative to flat surfaces under equivalent conditions. Inspection of SEM images (not shown here) of the fracture indicated significant roughness. The surface asperity of the fracture walls could act similarly to granular collectors in porous media and provide rear-flow stagnation zones where particles could be retained. The fracture aperture distribution could also produce zones with stagnant water or very low-flow velocity [Chrysikopoulos and Abdel-Salam, 1997]. The near-surface rock matrix porosity would also be a stagnant water zone [Cumbie and McKay, 1999]. Colloids could diffuse into these zones and be retained at the secondary energy minima under unfavorable attachment conditions.
 The IEP (pH at which the net surface charge is zero) values of MS2 and PR772 were reported to be less than 4.5 by Langlet et al.  and Lute et al. . The ZP of PR772 was measured to be −27.0±1 mV at 3 mM solution in this study. Chrysikopoulos and Syngouna  reported ZP value of MS2 of −40.4 mV at 2 mM IS (at pH 7). Therefore, the bacteriophages MS2 and PR772 in this study were expected to have net negative surface charges at the experimental solution pH of 8.2. The measured ZPs of the CML microspheres used in this study were also found to be similar or more negative compared to those of the bacteriophages MS2 and PR772. Yuan et al.  determined the DLVO interaction energy between bacteriophage MS2 and bare silica at pH 7.5 (with 1 mM NaHCO3 buffer) and showed that an energy barrier existed for solution IS up to 60 mM provided by monoelectrolyte salt, however, did not discuss the presence and effects of a secondary minimum.
 The M-1 and M-2 BTC curves for 3 and 12 mM (Na+) solution conditions (Figure 6) have long tails indicating slow release of the retained microspheres from the fracture following colloid injection for both IS levels. In few tests, a subsequent flush with low IS solution (buffered water with 1 mM NaHO3) as well as higher water flow rate generated a sharp peak of microspheres in the BTCs (data not shown). Several studies in porous media have suggested that particle retention in the secondary energy minimum is a reversible process and that particles can be released from the collector when the secondary energy minimum well is eliminated by decreasing the solution IS [Franchi and O'Melia, 2003; Hahn and O'Melia, 2004; Litton and Olson, 1996] and increasing the fluid drag force [Johnson and Tong, 2006]. Loveland et al.  suggested that under strong repulsive conditions with no secondary minimum effect, colloids may accumulate in the boundary layer in front of the energy barrier and with time diffusion and advection will carry them out of the boundary layer into the advective flow. In this case, one would perhaps expect the minimal effect of IS on colloid retention and the BTC.
 In contrast to the tailing observed for the microspheres, normalized concentrations of bacteriophages in the post-injection flushing period are much lower than the corresponding values for the microspheres. This may be attributed to the lower injected concentrations of bacteriophages compared to microspheres, to inactivation of phages at later times, or to a lack of reversibility in bacteriophage attachment compared to microsphere attachment.
4.2. Effects of Cation Valency
 The microsphere M-1 mass recovery in the 5 mM test with Ca2+ was similar to that of the 12 mM (Na+) test, showing that the effect of adding 1 mM Ca2+ was similar to adding 10 mM Na+. In contrast to the lower mass recovery of M-1 with Ca2+, the mean residence time for M-1 decreased with the addition of Ca2+. However, this is primarily due to the much lower tailing with Ca2+, compared to the tailing with 3 and 12 mM Na+. These results suggest that attachment of M-1 in the presence of Ca2+ was less reversible than with Na+. Blocking for type 1 sites was also reduced (higher Smax1 values, Table 2) in the presence of Ca2+compared to 12 mM Na+, suggesting that more attachment sites were available with Ca2+, compared to the cases with Na+ only.
 Recovery of microsphere M-2 was higher in the 5 mM IS (Na+ and Ca2+) solution than in the 12 mM IS (Na+) solution in contrast to the trend for M-1 and the bacteriophages. The reason for this difference is not apparent, but it suggests that the effect of Ca2+ on rock and M-2 surface charge had little effect on retention of M-2, and that formation of cation bridges was also not a significant factor in retention of M-2. It should also be noted that the HD of M-2 (Figure 2) was lower in the Ca2+ solution compared to either of the Na+ solutions, in contrast to the situation for M-1, where HD was similar for all solution chemistries. The ZP values for microspheres and rock minerals were significantly lower in 5 mM (Ca2+ and Na+) solution (Figure 2) compared to 3 and 12 mM (Na+) solutions.
 With the 5 mM (Ca2+ and Na+) IS solution, bacteriophage retention in the fracture was greater than either 3 mM IS (Na+) or 12 mM IS (Na+) as mass recoveries of both bacteriophages were the lowest for this case, and the mean residence times were higher. Although the total IS of this solution (5 mM) was close to the IS of the 3 mM (Na+) solution and lower than that of 12 mM (Na+) solution, the presence of 1 mM Ca2+ ions contributed to the higher retention of bacteriophages in the fracture, likely by reducing the surface potential of bacteriophages and rock minerals. Israelachvili  showed that relatively small amounts of divalent ions substantially lowered the magnitude of surface potential (100 times more effective than increasing the concentration of monovalent salt). Multivalent cations can form cation bridges between viruses and adsorbents linking like charges [Lipson and Stotzky, 1983] and can also contribute to the charge reversal of the viruses [Grant et al., 1993]. Janjaroen et al.  also showed that the presence of calcium ions increased retention of Cryptosporidium on natural organic matter due to calcium ion bonds with carboxylate groups. Dowd et al.  showed that presence of multivalent cations contributed to higher attachment of negatively charged viruses to sandy soils. Redman et al.  also demonstrated increased attachment of bacteriophage SJC3 due to the presence of 1 mM CaCl2 salt and easy detachment when the salt concentration was changed to 1 mM NaCl. Schijven and Hassanizadeh  summarized literature on the use of MS2 as a model virus and suggested that it meets the requirement for a worst-case model virus provided the temperature is low and the concentration of multivalent cations is low. In this study Ca2+ ions affected both MS2 and PR772 in a similar manner that was quite different from the effect on 20 and 200 nm microspheres.
4.3. Effects of Microsphere and Virus Size and Surface Characteristics
 As expected from previous studies, the mass recovery of 200 nm microspheres was much higher than that of 20 nm microspheres, consistent with the results of Cumbie and McKay  and of the predictions of colloid filtration theory (CFT). From CFT calculations, using the equation proposed by Tufenkji and Elimelech , the single collector contact efficiency (the probability of colloid collision with the collector surfaces, η) can be calculated. To use the Tufenkji and Elimelech  equation, it was assumed that the effective collector diameter was equal to half of the fracture aperture, and the effective porosity (0.87) was equal to the volume calculated from the areal extent and hydraulic aperture of the fracture divided by the actual measured fracture volume. The actual fracture volume was calculated from the fracture aperture distribution data that was collected with 3-D optical scanning technique using Advanced Topometric Sensor [Mondal, 2012]. This calculation gives a value of η for the 20 nm microspheres that is three to seven times that of the 200 nm microspheres at different solution ISs. These higher η values for 20 nm microspheres were due to increased diffusion across flow streamlines to collector surfaces. Cumbie and McKay  also hypothesized that smaller particles could also experience greater retention in fractures because of diffusion into stagnant flow regions. The depth of secondary energy minimum for M-2 is higher than for M-1 and P2772 (Figure 3), and deposition in the secondary minimum should be more significant for M-2 compared to M-1, a phenomenon that could counter the effects of greater diffusion rates for smaller particles. However, Bradford et al.  suggested that DLVO theory is not adequate for characterizing interaction energy when the size of the colloid approaches that of the heterogeneity on the collector surface. Thus, if surface heterogeneity is a significant factor for microsphere transport in the dolomite fracture, the DLVO interaction energy trends with colloid size may not have significantly influenced microsphere transport.
 The mean residence time of microsphere M-2 was also smaller than that of bromide and M-1 in all tests conditions indicating the possibility of size exclusion effects for M-2, although bromide transport is also affected by matrix diffusion. The phenomenon of size exclusion, which is caused by preferential and increased transport of colloids through apertures (and pores in porous media) larger than their physical size [Chrysikopoulos and Abdel-Salam, 1997; Powelson et al., 1993], enhanced the microsphere M-2 migration in the fracture. Together with the size exclusion, aperture variability in fracture can also cause preferential water flow and increased colloid transport [James and Chrysikopoulos, 2000; Mondal and Sleep, 2012].
 The mass recovery of the smaller bacteriophage MS2 (24–27 nm) was about 20% less than that of PR772 (82 nm) for all conditions tested, a much smaller difference than that observed between the 20 and 200 nm microspheres. Studies in sandy aquifer materials [Kinoshita et al., 1993; Dowd et al., 1998] reported greater retention of PRD1 (similar to PR772) compared to MS2. Penrod et al.  invoked steric repulsion associated with hydrophilic polypeptide loops on the MS2 surface to explain lower MS2 attachment to quartz than expected from DLVO considerations [see also Mylon et al., 2010]. Harvey and Ryan  indicated that PRD1 has much shorter polypeptide loops and would be less influenced by steric repulsion effects than MS2. Therefore, in the current study, bacteriophage size may be more significant in determining bacteriophage retention than the surface characteristics, as the bacteriophages have similar IEPs. Dowd et al.  suggested that for diameters greater than 60 nm virus size may become the most important factor governing virus adsorption and transport.
 While steric repulsion effects may not explain the greater retention of MS2 compared to PR772, they may be a significant factor explaining the factor of two to three lower retention of MS2 compared to similarly sized 20 nm microspheres. As both microspheres and MS2 would have been negatively charged under all solution chemistries investigated, with similar size and charge, similar transport behavior would be expected based on DLVO considerations alone. In terms of mass recovery, and peak C/Co values, the behavior of MS2 was much closer to that of the 200 nm microspheres than it was to the 20 nm microspheres, despite the order of magnitude difference in particle diameters. Where there were differences in responses to changes in solution chemistry, as previously discussed, PR772 transport behavior was closer to that of the 200 nm microspheres than was MS2. However, blocking effects were less significant for PR772 compared to the 200 nm microspheres, perhaps due to the lower influent concentrations of PR772 compared to the microspheres.
4.4. Suitability of Microspheres as Surrogates for Bacteriophages
 Based on colloid size, the 20 nm microspheres (HD of approximately 60 nm) would be expected to be the most suitable surrogates for the 27 nm MS2 and similarly sized pathogenic viruses. However, results clearly show that either the small difference in size or differences in surface characteristics were sufficient to produce very significant differences in retention and transport, with the 20 nm microspheres experiencing two to three times greater retention, even in the presence of blocking. The 200 nm microspheres had similar behavior to MS2 and PR772 with respect to the effect of IS, but were more significantly retained in the dolomite rock fracture when IS was increased from 3 mM (Na+) to 12 mM (Na+). In addition, the effect of Ca2+ was more significant for the bacteriophages than for either the 20 nm or 200 nm microspheres, indicating a greater impact of Ca2+ on bacteriophage surface charge compared to CML microspheres, or a greater impact of cation bridge formation on bacteriophage retention.
 Transport behaviors of bacteriophages (MS2 and PR772) and similarly sized CML microspheres in fractured dolomite rock were quite different, with retention of 20 nm microspheres greatly exceeding retention of either MS2 or PR772 under a range of solution chemistries. In contrast to studies in porous media, retention of MS2 was greater than that of the PRD-like PR772 in the dolomite fracture. While retention and transport of 200 nm CML microspheres in fractured dolomite more closely resembled that of the smaller sized MS2 and PR772. Effects of IS and cation valency (Na+ versus Ca2+) were quite different, with addition of Ca2+, leading to greater increases in retention of the bacteriophages than in retention of either 20 or 200 nm microspheres. While slow release of both microspheres and bacteriophage occurred during post-injection flushing, the tailing was much more significant for the 20 nm microspheres compared to the bacteriophages. Both microsphere and bacteriophage transport and retention in the two-dimensional variable aperture fracture could be very closely simulated using a one-dimensional two-site kinetic model with attachment, detachment, and blocking, with inactivation added for bacteriophages. Trends in detachment parameters for both bacteriophages and microsphere transport in fractured dolomite were very similar to the findings of Schijven et al.  for virus transport in dune sands (high attachment, low detachment rates for type 1 sites, high attachment and detachment rates for type 2 sites). However, given the relatively high microsphere concentrations used in the experiments, it was necessary to add blocking for the microspheres, while blocking was not significant for MS2 or PR772 for some of the solution chemistries tested. Overall, 20 nm CML microspheres are poor surrogates for MS2 and PR772 and therefore likely for other pathogenic viruses. The behavior of 200 nm CML microspheres more closely resembled that of the bacteriophages but showed different responses to changes in solution chemistry.
 This research was supported by the Canadian Water Network (CWN) through the Pathogens-in-Groundwater Research Consortium and an NSERC Discovery Grant. The authors thank the anonymous reviewers for their suggestions in improving the manuscript.