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Environ. Sci. Technol. 43, 8874–8880

Idling Time of Swimming Bacteria near Particulate Surfaces Contributes to Apparent Adsorption Coefficients at the Macroscopic Scale under Static Conditions JUN LIU AND ROSEANNE M. FORD* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904

Received June 24, 2009. Revised manuscript received October 12, 2009. Accepted October 16, 2009.

Static capillary assays were performed to observe the distribution of Escherichia coli and several mutant strains at the interface between an aqueous solution and a Gelrite particulate suspension, used as a model porous medium. Motile smoothswimming mutant bacteria (E. coli HCB437) accumulated at the interface, but did not penetrate very far into the Gelrite suspension. Motile wild-type bacteria (E. coli HCB1) penetrated much further than the smooth-swimming mutant, but did not accumulate to the same extent at the interface. Nonmotile tumbly mutant bacteria (E. coli HCB359) did not accumulate or penetrate to a significant degree. Computer simulations using a Monte Carlo algorithm, with input parameters based on bacterial swimming properties in static bulk aqueous systems, appeared to underestimate the bacterial idling time associated with solid surfaces. To account for physicochemical, biological and geometrical influences, an additional component of the bacterial idling time was included. The third component of the idling time was further analyzed semiquantitatively with a 1-D population-scale transport model with first-order association (kon) and dissociation (koff) adsorption-like kinetics. Computer simulation results suggested that this additional bacterial idling time not only increased the magnitudes of kon and koff, but also enhanced the ratio of kon to koff. This further implies that motile bacteria may tend to accumulate at the boundaries of lowpermeable regions in groundwater systems, which is beneficial for bioremediation of residual contamination that may not be accessible by conventional remediation approaches.

Introduction Groundwater contamination poses a severe problem to our environment and drinking water supplies. In-situ bioremediation, in which bacterial transport in porous media plays an important role, has been proven to be an effective way to reduce chemical pollutants in groundwater (1). One limiting factor of this technology is the inefficiency with which bacteria may be delivered to the pollutant source; often, the bacteria are retarded by adsorption to the soil matrix. To improve this efficiency, a significant research effect is focused on relating single bacterial swimming properties to macroscopic bacterial migration. * Corresponding author phone: (434) 924-6283; fax: (434) 9822865; e-mail: [email protected]. 8874

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In the bulk aqueous solution, individual bacterial swimming behavior can be described as a three-dimensional random walk, consisting of a series of alternating runs and tumbles, which has been well characterized using a threedimensional tracking microscope. The random walk is quantified in terms of the bacterial swimming speed (v), run time distribution (λ), and turn angle distribution (θ) (2). The bacterial random motility coefficient (µ0) is defined in terms of these bacterial swimming properties (3). A number of experimental techniques, including capillary assay (4), stopped flow diffusion chamber (SFDC) (5), and 3-D defocused particle tracking (DPT) microscopy (6) have been used to quantify this macroscopic parameter. However, unlike the bulk aqueous solution, the presence of granular media can significantly alter bacterial migration. Not only was the bacterial motility substantially reduced (7-9), but also the interaction between bacteria and solid surfaces complicated the prediction of bacterial transport by theoretical approaches (10). According to the observed individual bacterial swimming patterns in agar suspension (11, 12) and the results of Monte Carlo simulation algorithms (13, 14), Kusy and Ford (12) proposed the following hypothesis: Motile bacteria will reside on the encountered solid surfaces for an extended period of time exhibiting no translational motion until they reorient in a direction that allows them to swim away from the surfaces, and this extended period of time is defined as the bacterial idling time. Unlike Knudsen diffusion, this hypothesis incorporates the concept of sticky Brownian motion (15) by assuming an inelastic interaction between bacteria and solid surfaces. In addition, Narayanaswamy et al. (16) further mathematically correlated the average bacterial idling time over all the possible contact angles when a single bacterium approached the spherical collectors and concluded that the bacterial idling time was predetermined by bacterial run time distribution (λ) and turn angle distribution (θ) under idealized conditions. Although this bacterial surface association hypothesis offered an alternative mechanism for describing bacterial migration in porous media, it neglected environmental influences. Thus, our objective is to further explore this hypothesis and highlight the importance of environmental factors through both microscopic and macroscopic experimental observations and mathematical simulations (17).

Materials and Methods Bacteria and Media. Experiments were performed with Escherichia coli K12 derivatives, provided by H. C. Berg at Harvard University (18), including a motile wild-type strain E. coli HCB1, possessing both run and tumble abilities, a motile smooth-swimming mutant E. coli HCB437, deficient of a tumbling mechanism and a nonmotile tumbly mutant E. coli HCB359, without running ability. All of these bacteria were grown and harvested according to a previously described protocol (12). Prior to performing an experiment, harvested bacteria were resuspended in random motility buffer (11.4 g K2H(PO)4, 4.8 g KH2(19)4, and 0.029 g ethylenediaminetetraacetic acid (EDTA) per 1 L DI water) with 2.5 g/L hydroxypropyl methylcellulose, which was used to reduce fluid convection in subsequent capillary assays (2) and maintain the maximum bacterial swimming velocity (20, 21). A Gelrite particulate suspension, used as a model porous medium, was prepared according to the protocol described in (12); it contained irregularly shaped impermeable particles, ranging from 50 to 500 µm in diameter with an averaged 10.1021/es901865p CCC: $40.75

 2009 American Chemical Society

Published on Web 11/30/2009

TABLE 1. Individual Bacterial Swimming Properties Adopted in the Monte Carlo Computer Simulation bacteria motile wild-type strain E. coli HCB1(22) hypothetical motile smooth-swimming mutant (e.g., E. coli HCB437) hypothetical nonmotile tumbly mutant (e.g., E. coli HCB359)

value around 200 µm and a porosity (ε) of 50% as estimated by visual inspection. Capillary Assay Setup. A square capillary 2 in. long with 1 mm2 inside cross-section and 0.2 mm thick walls (Vitrocom Inc., Mountain Lakes, NJ) was fixed in the capillary holder and oriented vertically. Half of it was filled with the bacterial suspension, and the remainder with either buffer solution for observing bacterial migrations in bulk aqueous solutions or Gelrite particulate suspension for observing bacterial migration at the porous media interface. A cold light source (Schott KL 1500) illuminated the fixed capillary from behind. The light scattering intensity was proportional to the bacterial concentration. A color video camera (Nikon) connected to a stereomicroscope (Zeiss STEMI SV8) was placed in front of the capillary. Images were collected by a Dell personal computer running the program NIS-elements F 2.30 and saved as 8-bit pixel tif files (17). Experimental Procedures and Data Analysis. After sealing one end of the square capillary using a Bunsen burner, a 4 in. long piece of microtubing with 0.51 mm i.d. and 0.94 mm o.d. (Dow Corning Corporation, Midland, MI) attached to a 1 mL Becton-Dickinson syringe was inserted into the open end of the capillary. When the mouth of the tubing reached the sealed end, the syringe was compressed to load the entire capillary with the first solution (buffer solution or the Gelrite particulate suspension). To add the second solution (bacterial suspension), a blunted 23-gauge stainless steel needle was attached to a 1 mL Becton-Dickinson syringe. When the needle was inserted about halfway into the capillary, the capillary was rotated slowly to make a sharp interface between the two solutions. The syringe was compressed at a steady rate during the whole insertion and removal process. The increased viscosity of both solutions helped to reduce mixing during the injection process and produce a well-defined interface. After that, the capillary was fixed in the capillary holder and the top of the capillary was sealed with parafilm. The capillary system was observed under static conditions (i.e., there was no bulk fluid motion). For each recorded image, after subtracting the background, grayscales were analyzed as a function of pixel number using the program ImageJ 1.38 (NIH). Data from replicate experiments were combined and analyzed using MATLAB algorithms to present averaged population distributions with standard deviations (17). Monte Carlo Computer Simulations. A 3-D Monte Carlobased computer algorithm, which extended the 2D code of Kusy and Ford (12), was developed to generate bacterial distributions by tracking 40 000 bacterial trajectories according to their swimming properties in a 0.4 × 0.1 × 0.1 cm simulation box. To approximate the capillary assay experimental setup, the box was half-packed with 200 µm diameter spheres by cubic packing method with fixed positions, yielding a 47% porosity (ε). In addition, to create a perfect interface between the free solution and model porous media, all the spheres near the free solution were aligned and tangent to the interface. To simulate bacterial swimming in 3-D, the selection of a new direction following a tumble incorporated a uniform distribution of azimuthal angles according to the algorithm of Duffy et al. (13). Similarly to Kusy and Ford’s algorithm (12), bacteria were assumed to tumble immediately

swimming speed v (µm/s)

run time λ (s)

turn angle θ (degrees)

22.8

1.24 ( 1.16

70 ( 39

22.8

1.24 ( 1.16

27

22.8

0.02

70 ( 39

after reaching the end of the simulation box in order to match the no-flux boundary conditions along the length of the capillary. In addition, once a bacterium encountered a spherical particle, the subsequent bacterial idling time was collected according to the bacterial surface association hypothesis. Bacterial swimming properties, speed (v), run time distribution (λ), and turn angle distribution (θ), which were used to represent various types of bacteria, are listed in Table 1. Due to the instrumental limitation of the 3-D tracking microscope, only the motile wild-type bacterial swimming properties have been well characterized (22). For the motile smooth-swimming mutant E. coli HCB437, its observed average turn angle value, 27 degrees, was used to account for the bacterial rotational diffusion (23). For the nonmotile tumbly mutant E. coli HCB359, its relatively small random motility coefficient was mechanistically based by using the same speed (22.8 µm/s) with less average run time (0.02 s). These approximations as listed in Table 1 are reasonable as the simulated bacterial random motility coefficients (µ0): 2.4 × 10-6cm2/s (E. coli HCB1), 1.7 × 10-5cm2/s (E. coli HCB437), and 3.2 × 10-8cm2/s (E. coli HCB359), are in good agreement with values reported in the literature (6, 17, 22). Population-Scale Mathematical Model. A one-dimensional two-phase bacterial transport model represented by µo,eff ∂2C ˆ ˆ ∂C ˆ + koffaSˆ - konaC ) ∂t ε ∂x2

(1a)

∂Sˆ ˆ - koffaSˆ ) konaC ∂t

(1b)

was used to characterize bacterial diffusive migration at the porous media interface (12) where x is distance (cm), t is time (s), a is the surface area of the porous media per total ˆ is bacterial concentration within the volume (cm2/cm3), C bulk liquid phase per total volume, which can be correlated with bacterial concentration in bulk free aqueous solution ˆ ) εC, Sˆ is the bacterial concentration associated with C by C the porous medium, kon and koff are the first-order bacterial association and dissociation rate constants (cm/s) describing bacterial association with surfaces, ε is porosity, µ0,eff is the bacterial effective motility coefficient (cm2/s), and it is further correlated with bulk liquid phase random motility coefficient (µ0) by µ0,eff/ε ) µ0/τ (7), in which, tortuosity (τ) represents the increased length of the bacterial path due to the presence of the solids in the porous matrix. A no-flux boundary condition was applied to the two ends ((L) of the Monte Carlo simulation box ˆ ∂C ) 0 at x ) (L ∂x

(2)

and the internal boundary condition assumed that the bacterial flux across the interface was equal -

µo,eff2 ∂C µo,eff1 ∂C ˆ ˆ )at x ) 0 ε1 ∂x ε2 ∂x

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(3)

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FIGURE 1. Bacterial initial 2 min and final 20 min light scattering images observed in static capillary assays and comparison of the normalized bacterial concentration profiles at the porous medium interface with experimental observations (exp data) and the Monte Carlo computer simulations (MC data). In addition, because bacterial motility in porous media occurs within a transition regime between bulk diffusion and Knudsen diffusion (13) and tortuosity (τ) is usually a fitting parameter (24), the adjusted tortuosity (τ*) was used to account explicitly for the impact of Knudsen diffusion (9) according to

(

τ ) τ∗ 1 +

µ0 µK

)

(4)

where µK is the Knudsen diffusion coefficient, defined as µK ) dpv/3 (25), in which v is the average bacterial swimming speed and the pore diameter (dp) is empirically correlated with porous media porosity (ε) and the average particle diameter (ds) by (26) dp )

2 ε d 31 - ε s

(5)

Bacterial population distributions predicted by the Monte Carlo computer simulations were compared with the mathematical equations solved with a Crank-Nicolson finite difference algorithm using MATLAB to generate the bestfitted transport parameters: adjusted tortuosity (τ*), first8876

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order association (kon), and dissociation rate constant (koff) via visual inspection and minimization of the sum of the squared errors of each data point.

Results and Discussions Population-Scale Bacterial Migration at Porous Media Interface. In static capillary assays, the bacterial population distributions of motile wild-type strain E. coli HCB1, motile smooth-swimming mutant E. coli HCB437 and nonmotile tumbly mutant E. coli HCB359 were observed at the interface created by the buffer solution with methylcellulose and the Gelrite particulate suspension. Figure 1 displays the initial 2 min and final 20 min bacterial light scattering images. The corresponding normalized bacterial concentration profiles are further compared with those predicted by the Monte Carlo computer simulations. In addition, Table 2 summarizes the bacterial idling time collected from the simulations and previous experimental measurements (27). Nonmotile tumbly mutant E. coli HCB359 lacks running ability, so it is unable to actively explore the surrounding spaces and has relatively small random motility. Therefore, as can be seen in Figure 1g-i, within a short time period, most of these mutants did not significantly deviate from their original positions, thus preserving the initial step-change

TABLE 2. Comparisons of Bacterial Idling Time between the Monte Carlo Computer Simulations and the Experimental Measurements simulated idling time (s) bacteria motile wild-type strain E. coli HCB1 motile smooth-swimming mutant E. coli HCB437

experimental bacterial idling time (s) (27)

flat surface

porous medium

I ) 0.202

2.88 12.38

2.82 12.60

5.75 15.63

concentration profiles that were created in the square capillary and the simulation box. However, for motile bacteria, their final population distributions were substantially different from the initial step-change profile and there were differences between the experimental observations and the simulation results. More specifically, as the experimental observations show in Figure 1a-b, the motile wild-type strain E. coli HCB1 not only penetrated into the porous media region but also accumulated at the porous media interface. By contrast, the Monte Carlo computer simulation in Figure 1c did not predict this accumulation. Moreover, as the capillary assay results exhibit in Figure 1d-f, the motile smoothswimming mutant E. coli HCB437 demonstrated a significant degree of accumulation at the porous medium interface with little penetration into the porous medium region, whereas less accumulation and a large penetration distance was predicted from the simulation. In addition, the Gelrite particulate itself does not appear to have any effects on bacterial interaction, because in a previous study, Kusy and Ford (17) observed similar characteristics of bacterial distributions in a glass-bead pack, which demonstrated that the bacterial interactions with the surface were independent of any specific characteristics of the Gelrite media. The bacterial idling times summarized in Table 2 reveal that, for each type of bacteria, the simulated bacterial idling time from their association with flat surface was the same as that associated with spherical surfaces and both of them were reasonably consistent with the experimental measurements. Note that the experimental values were obtained from bacterial association with a piece of flat glass coverslip (27), for which, the smooth surface was deemed as the idealized condition. Therefore, these consistencies suggest that, under idealized conditions, when the surface curvature is relatively large compared to the individual bacterial dimension, it does not affect bacterial surface association and the resulting bacterial idling time is consistent with the conceptual model, in which, the bacterial idling time is predetermined by bacterial run time distribution (λ) and turn angle distribution (θ) (16). However, if the surface curvature is comparable to the diameter of bacterial circling motion (27), its influence

I ) 0.06

I ) 0.02

I ) 0.006

8.13 N/A

6.79 N/A

N/A 13.88

may not be negligible. In conclusion, the bacterial surface association hypothesis was shown to be effective in describing bacterial surface interaction under idealized conditions, but it was unable to accurately predict motile bacterial migration in the experimental system with Gelrite particulates. Bacterial Surface Association Mechanism. As discussed before, one limitation of the current bacterial surface association hypothesis is that only the bacterial swimming properties are correlated with the bacterial idling time, which results in an underestimate of the value. As a matter of fact, a number of factors, such as porous media surface geometry, physical straining, and ionic strength, coupled with the bacterial swimming mechanism, have a tendency to retain bacteria near the solid surfaces for a longer period of time. Figure 2 shows a schematic comparison of the bacterial swimming trajectories in bulk aqueous solution, under idealized porous media circumstances and the approximated actual Gelrite particulate suspension surroundings. As illustrated in Figure 2a, in bulk aqueous solution, the bacterium is able to fully exhibit its basic run-and-tumble mechanism. By comparison, in the presence of solid particles, the pore space available for bacterial swimming is reduced and the actual pathway is extended because of its prolonged hypothetical traveling distance AB (See Figure 2b) to achieve the same net displacement. According to the bacterial surface association hypothesis, when a bacterium encounters a solid surface, it will first finish its previous run time, which is designated as t1, and reside near the surface. The second part of the idling time, t2, accounts for the time that elapses over several bacterial runs and tumbles to search for a new swimming direction that orients itself to run away from the surface and back into the bulk aqueous solution (16). However, as shown in Figure 2c, the actual Gelrite particulates have a highly amorphous structure. As a result, once a single bacterium has been trapped into the groove area of a solid surface, it will spend more time, relative to scenario in Figure 2b, searching for a direction that will return it to the bulk. Also consider that the ratio of average bacterial size (2 µm in diameter) to the Gelrite particulates (50-500 µm in diameter) ranged from 0.004 to 0.04. Above a critical value

FIGURE 2. Schematic illustrations of bacterial swimming trajectories (a) in bulk aqueous solution, (b) under idealized porous media circumstances, and (c) in the approximated actual Gelrite particulate suspension. AB represents the same bacterial displacement accomplished by different actual traveling distance in (a) and (b). The * indicates the potential physical straining scenario. VOL. 43, NO. 23, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Normalized bacterial initial 0 -min and final 20 min population distributions across the porous medium interface predicted by the Monte Carlo simulations (MC data) under the bacterial surface association mechanism: t3 ) 0 s (a), 5 s (b), 15 s (c) for motile wild-type strain E. coli HCB1, t3 ) 0 s (d), 60 s (e), 100 s (f) for motile smooth-swimming mutant E. coli HCB437, and t3 ) 0 s (g), 15 s (h), 30 s (i) for nonmotile tumbly mutant E. coli HCB359. In addition, the best-fitted 1-D transport model prediction curves (fitting data) are also superimposed for motile wild-type strain E. coli HCB1. of 0.005 for the ratio, the physical straining scenario might occur (28). In that case, as the * indicates in Figure 2c, a single bacterium would typically leave from this restricted region in a direction that was nearly opposite to its incoming one after a long period associated with the searching process. In contrast, because the current Monte Carlo simulation algorithm assumed each single bacterium as infinitesimally small, the simulated bacterium was likely to pass through the pore throat if it happened to find an appropriate swimming direction as shown by the * in Figure 2b. Several studies have reported that spatial restrictions could limit the ability of bacteria to tumble (19, 29), which means that bacterial reorientation would become more time-consuming. In addition, so far, the actual relationship between the environmental ionic strength and the overall bacterial tendency to stay near the solid surfaces is still unclear (27). The impacts of molecular-scale interaction between bacteria and solid surfaces are also uncertain (10). One approach is to lump all of the influences into a new empirical variable, an additional bacterial idling time, t3. Therefore, in addition to t1 and t2, the more general empirical correlation includes the third part bacterial idling time (t3). Figure 3 displays the simulated bacterial population distribution of motile wild-type E. coli HCB1, motile smoothswimming mutant E. coli HCB437 and nonmotile tumbly 8878

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mutant E. coli HCB359 across the porous media interface under the bacterial surface association mechanism, for several t3 values. As shown in Figure 3a-c, for motile wild-type strain E. coli HCB1, with the increase of t3, an accumulation peak was created. Notice that when t3 ) 15 s, the normalized peak value reached around 1.3 and its penetration distance was nearly 0.1 cm, which compares favorably with the experimental results displayed in Figure 1b. For motile smoothswimming mutant E. coli HCB437, the increasing t3 value greatly reduced its simulated penetration distance from more than 0.2 cm (t3 ) 0 s) to 0.07 cm (t3 ) 100s) and the corresponding normalized bacterial accumulation peak further increased from 1.1 (t3 ) 0 s) to 4 (t3 ) 100 s), which were reasonably close to the experimental trends in Figure 1e. Moreover, because of its inability to tumble, the motile smooth-swimming mutant E. coli HCB437 was unable to reorient efficiently and the t3 value needed to match the experimental observations was expected to be larger than the wild-type. For nonmotile tumbly mutant E. coli HCB359, the addition of t3 did not have an impact on its migration, because its final simulated population distribution still maintained the initial step-change style even when t3 reached 30 s, which lends further support to the idea that bacterial motility plays an important role in bacterial transport in

TABLE 3. Summary of the Motile Wild-Type Strain E. coli HCB1 Best-Fitted Transport Parameters t3(s)

ε τ* a (cm2/cm3)

30% 3.5 230.51

47% 2.7 157.08

60% 1.7 128.37

73% 1.4 80.42

0

kon (cm/s) koff (cm/s) kon/koff

2.0 × 10-8 2.0 × 10-8 1

1.0 × 10-8 1.0 × 10-8 1

1.0 × 10-8 1.0 × 10-8 1

1.0 × 10-8 1.0 × 10-8 1

5

kon (cm/s) koff (cm/s) kon/koff

3.5 × 10-6 3.5 × 10-6 1

1.8 × 10-6 1.8 × 10-6 1

1.6 × 10-6 1.6 × 10-6 1

1.1 × 10-6 1.1 × 10-6 1

15

kon (cm/s) koff (cm/s) kon/koff

6.3 × 10-5 4.0 × 10-5 1.6

7.9 × 10-5 5.0 × 10-5 1.6

5.0 × 10-5 4.5 × 10-5 1.1

8.9 × 10-6 8.9 × 10-6 1

30

kon (cm/s) koff (cm/s) kon/koff

3.5 × 10-5 1.1 × 10-5 3.2

3.2 × 10-5 1.3 × 10-5 2.5

2.5 × 10-5 1.1 × 10-5 2.2

8.9 × 10-5 4.5 × 10-5 2

porous media. The smaller the bacterial motility, the fewer opportunities that bacteria have to approach the porous media solid surfaces. Note that all the simulation data can only semiquantitatively match with the experimental results, because the porous medium interface created in the capillary assays was not as sharp as the one in the Monte Carlo computer simulations. This issue is described in the Supporting Information. In order to investigate the combined impacts of this bacterial surface association mechanism and granular media configuration on macroscopic coefficients similar to sorption rate coefficients, a series of Monte Carlo computer simulations were performed with motile wild-type bacterial strain E. coli HCB1. The simulation box was half-packed with three different sized spheres (50, 100, and 200 µm in diameter) by either simple cubic packing or body-centered packing method to generate different porosities (ε) (30, 47, 60, and 73%). Table 3 summarizes the best-fitted transport parameters: adjusted tortuosity (τ*), first-order association rate constant (kon), and dissociation rate constant (koff), all of which were obtained from the simulation box half-packed with 200 µm diameter spheres. Note that the fitting curves generated from 47% porosity conditions, which were closest to the experimental systems, are also superimposed in Figure 3a. As demonstrated in Table 3, the adjusted tortuosity values with Knudsen diffusion (τ*) fell within the range of observed values for packed beds, reported as 2-6 (25), with averaged value around 3. Additional simulation results indicate that, with specified porous medium porosity (ε), τ* does not correlate with sphere size (data not shown). In addition, because each fitted τ* tolerated less than (0.5 deviation, it is reasonable to conclude that τ* is also independent of t3. Therefore, as expected, the influences of t1 and t2 were revealed by τ*, while the impact of t3 was primarily reflected in kon and koff. As can be seen from Table 3, for the simulation box with 47% porosity (ε), when t3 increased from 0 s to 30 s, the threshold magnitudes of kon and koff were enhanced from 10-8 to 10-5 cm/s, and the ratio of kon to koff increased from 1 to 2.5, suggesting that more bacteria were associated with the porous medium surfaces for a longer time. Moreover, a larger porous media surface area (a) and smaller porosity (ε) seem to exaggerate the effect of bacterial surface association. For example, when t3 was fixed at 30 s, the ratio of kon to koff increased from 2 to 3.2 with the expanding surface area (a) from 80 to 231 cm2/cm3, while the porosity decreased from 73 to 30%, and this best-fitted kon/koff even reached as high as 22.7 in a simulation box, which was half-packed with 50 µm diameter spheres by body-centered simple packing

method and had 930 cm2/cm3 surface area (a) and 30% porosity (ε). Normal bacterial swimming behavior includes runs and tumbles. Both features are important for bacterial transport in porous media. Once a single bacterium encounters the solid surface, its running mechanism will first complete its predetermined run time (t1), and then, combined with its tumbling ability, bacterium will search for a new swimming direction in order to be unimpeded by the obstacles (t2). The impact of porous media morphology can significantly retard this reorientation process (t3). Theoretical investigations performed in this work indicate that the larger this extended bacterial additional idling time (t3), the more likely for bacteria to accumulate within the porous media. In reality, the lowpermeable clay region, with small pore space and large surface area, is inclined to exaggerate bacterial accumulation, which is beneficial for bioremediation, as this region usually contains highly concentrated contaminants (30). Thus, this bacterial surface association mechanism offers a more descriptive approach to predict bacterial transport in groundwater, as the transport coefficients may be adjusted to account for the impact of bacterial idling time. A future study will apply this mechanism to investigate the migration behaviorsofanaturalsoil-inhabitingbacterialstrainPseudomonas putida in porous media. Compared with wild-type E. coli, P. putida bacteria have a greater swimming speed and different turn angle distribution (31). The turn angle distribution suggests that P. putida reorient by backing up and moving forward rather than tumbling (32), which we expect will contribute to a smaller bacterial idling time.

Acknowledgments We gratefully acknowledge Dr. Tao Long, Dr. Kevin Kusy, and Dr. Meng Wang for their useful discussions, the anonymous reviewers for their valuable comments, and support provided by National Science Foundation in the Hydrologic Science Program (EAR-0408454) and the Donors of the American Chemical Society Petroleum Research Fund (ACS-PRF 38031-AC9).

Supporting Information Available Document S1 and Figures S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

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