Environ. Sci. Technol. 2007, 41, 6976-6982
Kinetics of Coupled Primary- and Secondary-Minimum Deposition of Colloids under Unfavorable Chemical Conditions CHONGYANG SHEN,† BAOGUO LI,† Y U A N F A N G H U A N G , * ,† A N D Y A N J I N * ,‡ Key Laboratory of Plant-soil Interactions, MOE; Key Laboratory of Soil and Water, MOA; Department of Soil and Water Sciences, China Agricultural University, Beijing 100094, China and Department of Plant and Soil Sciences, University of Delaware, Newark, Delaware 19716
This study examines the deposition/release mechanisms involved in colloid retention under unfavorable conditions through theoretical analysis and laboratory column experiments. A Maxwell approach was utilized to estimate the coupled effects of primary- and secondary-minimum deposition. Theoretical analysis indicates that the secondary energy minimum plays a dominant role in colloid deposition even for nanosized particles (e.g., 20 nm) and primaryminimum deposition rarely happens for large colloids (e.g., 1000 nm) when diffusion is the dominant process. Polystyrene latex particles (30 and 1156 nm) and clean sand were used to conduct three-step column experiments at different solution ionic strengths, a constant pH of 10, and a flow rate of 0.0012 cm/s. Experimental results confirm that small colloids can also be deposited in secondary minima. Additional column experiments involving flow interruption further indicates that the colloids deposited in the secondary energy well can be spontaneously released to bulk solution when the secondary energy minimum is comparable to the average Brownian kinetic energy. Experimental collision efficiencies are in good agreement with Maxwell model predictions but different from the theoretical values calculated by the interfacial force boundary layer approximation. We propose a priori analytical approach to estimate collision efficiencies accounting for both primary- and secondary-minimum deposition and suggest that the reversibility of colloid (e.g., viruses and bacteria) deposition must be considered in transport models for accurate predictions of their travel time in the subsurface environments.
Introduction Deposition of colloids onto surfaces from flowing suspensions in porous media is extremely important in many natural and industrial processes. It involves two sequential steps: transport and deposition. The transport process is dominated by convection and diffusion, and the deposition process is * Address correspondence to either author. Phone: +86 1062732963 (Y. H.); (302)-831-6962 (Y. J.). Fax: +86 1062733596 (Y. H.); (302)831-0605 (Y. J.). E-mail:
[email protected] (Y. H.);
[email protected] (Y. J.). † China Agricultural University. ‡ University of Delaware. 6976
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 20, 2007
dominated by interaction forces between colloids and collectors. The interaction forces commonly used to characterize deposition include van der Waals attraction and double layer forces, described by the classic DerjaguinLandau-Verwey-Overbeek (DLVO) theory. A DLVO interaction energy profile is constructed by the total interaction energy (sum of the two interaction forces, ΦT) as a function of separation distance between a colloid and a collector surface. When the interactive surfaces are like-charged, the double layer force is repulsive and a typical DLVO energy profile is characterized by a deep attractive well (the primary minimum, Φpri) at a small separation distance, a maximum energy barrier (Φmax), and a shallow attractive well (the secondary minimum, Φsec) at a larger distance. Colloid deposition in the presence of repulsive interactions is regarded as unfavorable. According to the classic filtration theory, to achieve successful colloid deposition under such unfavorable conditions, colloidal particles must overcome the energy barrier to attach in the primary minimum. However, predictions of colloid deposition by the filtration theory have been found to deviate significantly from experimental observations (13). One common explanation for the discrepancies is colloid deposition in the secondary minimum, which is not taken into account in the filtration theory (1-6). This occurs when the secondary minimum is deep enough to prevent colloids from being released into the bulk aqueous phase by other forces (e.g., hydrodynamic forces, Brownian diffusion). Colloid-collector interaction energies depend on particle size; large colloids have deeper secondary-minimum depths than small ones under the same conditions. For this reason, previous studies on colloid deposition in secondary minima have mainly focused on relatively large particles (6-9). As a result, contribution of the secondary minimum to deposition of small colloids (e.g., virus-sized particles) is unclear at present. Because interaction energies are also determined by ionic strength, the combined influence of ionic strength makes the particle size effects on secondary-minimum deposition even more complex. According to DLVO energy calculations, increasing ionic strength decreases the height of the energy barrier and increases the depth of the secondary minimum, and ultimately, the energy barrier disappears, leaving only the primary minimum well in the energy profile. Accordingly, deposition of colloids may transition from secondary minima to primary minima when ionic strength is changed from low to high (8). At some intermediate ionic strength, primaryand secondary-minimum deposition may occur simultaneously when the energy barrier is relatively small and the secondary minimum is deep enough. Franchi and O’Melia (10) suggested that primary- and secondary-minimum deposition could coexist because a fraction of the colloids deposited in the secondary minimum, due to fluctuations in their internal energy, might be able to jump over the energy barrier and be deposited in the primary well. Hahn and O’Melia (4), using a Brownian Dynamics/Monte Carlo model, qualitatively demonstrated the possibility of colloid deposition in both primary and secondary minima. Using a Maxwell approach, they also quantitatively estimated collision efficiencies by assuming deposition occurs in secondary minima, but ignored primary-minimum deposition. Tufenkji and Elimelech (3) presented a dual deposition model that considers the combined effects of fast (due to secondary minimum deposition and surface charge heterogeneity) and slow (due to transport over the energy barrier and deposition in the primary minimum) particle deposition. However, their 10.1021/es070210c CCC: $37.00
2007 American Chemical Society Published on Web 09/08/2007
model is not a priori, i.e., the fast and slow deposition rate coefficients must be inversely obtained from experimentally measured particle spatial distributions in packed beds. Johnson et al. (11) developed a three-dimensional particle tracking model which includes the effects of fluid drag, gravity, diffusion, and colloid-surface interaction, to predict colloid retention in porous media. Their model requires large computer capability and time, and it does not have an analytical solution, which may limit its application. Whereas some studies have proposed analytical kinetic approaches to combining primary- and secondary-minimum coagulations in the analysis of colloidal dispersion (12-14), an analytical model that can provide a priori and quantitative descriptions of colloid retention in porous media by coupling primary- and secondary-minimum deposition has not been developed to date. The objectives of this study were to (i) analyze colloid deposition as functions of particle size and ionic strength using a Maxwell approach that combines primary- and secondary-minimum deposition; (ii) examine the role the secondary minimum plays in deposition and release of small colloids; (iii) compare deposition and release behavior of virus-sized (30 nm) and bacteria-sized (1156 nm) colloids; (iv) test the Maxwell model experimentally and discuss its validity.
Theoretical Considerations DLVO Colloidal Interaction Energies. The classic DLVO theory of colloidal stability considers two interaction forces: (i) van der Waals attraction and (ii) electrical double layer forces. The total interaction energy (ΦT) is the sum of energies of the two interactions. The expression for a constant surface potential interaction derived by Hogg et al. (15) and the Hamaker approximate expression for a sphere-plane case (16) were used in this study for calculating the double layer and the retarded van der Waals attractive interactions, respectively. Experimental Collision Efficiency. The experimental collision efficiency Rexp is obtained from the following expression derived for the case where particles move across a packed bed of identical collectors with length L:
R exp ) -
ac 4 ln(C/C0) 3 (1 - f)Lη0
(1)
where C and C0 are effluent and influent particle concentrations, respectively; ac is radius of the collector; f is porosity of the packed bed; η0 is the single collector removal efficiency without inclusion of electrical double layer interaction, as developed by Tufenkji and Elimelech (17): 0.052 η0 ) 2.4As1/3N-0.081 N-0.715 NvdW + 0.55AsN1.675RN0.125 + R Pe A
0.053 0.22N-0.24 N1.11 R G NvdW (2)
where As is the porosity-dependent parameter of the Happel’s model; NR is an aspect ratio; NPe is the Peclet number; NvdW is the van der Waals number; NA is the attraction number; NG is the gravity number. Theoretical Collision Efficiency. The theoretical collision efficiency R developed using the interaction force boundary layer (IFBL) approximation can be found in Elimelech and O’Melia (2):
R)
(1 +β β)S(β)
(3)
where S(β) is a function of β with tabulated values given by Spielman and Friedlander (18) and β is defined as
β ) (1/3)21/3Γ(1/3)As-1/3
( )( ) D∞ Uac
1/3
KFac D∞
(4)
where Γ is the Gamma function; D∞ is a diffusion coefficient in an infinite medium; U is superficial velocity; KF is a pseudo first-order rate constant given by
KF ) D∞(
∫
∞
[f(h,ap)exp(ΦT/kT) - 1]dh)-1
0
(5)
where k is the Boltzmann Constant; T is absolute temperature; ap is radius of colloid; h is separation distance (surface to surface) between colloid and collector; f (h, ap) is a hydrodynamic function accounting for the reduced mobility of the colloids at close separation due to hydrodynamic interactions. The approximate expression for the hydrodynamic function is given by Dahneke (19):
f(h,ap) ) 1 + ap/h
(6)
Maxwell Model. In the study of Hahn and O’Melia (4), a Maxwell approach was used to estimate particle collision efficiencies by assuming deposition in secondary minima and calculating the probability of release. In this study, both primary- and secondary-minimum deposition are considered in the Maxwell model to calculate colloid collision efficiencies, as outlined in the following. Similar to Hahn and O’Melia (4) and Marmur (13), transport of colloids in a flowing suspension toward secondary minima is assumed to be at a mass transfer controlled rate. After colloids reach the separation distance corresponding to the secondary minimum, they may (i) be deposited and remain at the secondary minimum, (ii) overcome the energy barrier and be deposited in the primary minimum, or (iii) escape back to bulk suspension. Which of the above three processes will take place depends on the energy changes of the colloids due to their Brownian collisions with molecules in the aqueous phase. Because flow velocities are relatively low in natural systems and the densities of colloids that are of environmental concerns (e.g., viruses and bacteria) are close to that of water, the effects of fluid drag and sedimentation are always low and, therefore, are not included in our analysis. In this study, only the processes that occur shortly after the colloids arrive at the secondary minimum are considered in the Maxwell model. As will be discussed later, our experimental results show that release of colloids from secondary minima to bulk solution is a longterm and rate-limited process; therefore, the Maxwell model is only valid model for estimating the initial collision efficiency. Based on above analyses, we made the following assumptions when applying the Maxwell model: (i) distribution of colloid velocities at the separation corresponding to a secondary minimum follows the Maxwell distribution; (ii) the colloids in a secondary minimum will remain there if their kinetic energies are smaller than the interaction energy of the secondary minimum; (iii) the colloids in a secondary minimum will transport over the energy barrier and be deposited in the primary minimum if their kinetic energies are larger than ∆Φ (sum of Φmax and Φsec). The collision efficiency may be overestimated as a result of the third assumption because the colloids in a secondary minimum whose kinetic energy is larger than ∆Φ may also transport back to bulk suspension. In terms of assumption (i), the velocity distribution of the colloids in the secondary minimum follows the function:
( )
f(v) ) 4π
mp 2πkT
(3/2)
(
v2 exp -
)
mpv2 2kT
VOL. 41, NO. 20, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
(7) 9
6977
where
∫
∞
f(v)dv ) 1
0
(8)
and mp is mass of a colloid and v is its velocity. Here a dimensionless kinetic energy of the colloid is defined as
x2 )
mpv2 2kT
(9)
According to assumption (ii), the fraction of successful collisions (arrival at the separation distance corresponding to the secondary minimum) that result in deposition in the secondary minimum, Rsec, is given by
Rsec )
∫x
Φsec
0
4 2 x exp(-x2)dx π1/2
(10)
Similarly, the fraction of successful collisions resulting in colloid deposition in the primary minimum, Rpri, is
Rpri )
∫x ∞
∆Φ
4 2 x exp(-x2)dx π1/2
(11)
The total fraction of successful collisions R (sum of Rsec and Rpri) is written as
R ) Rpri + Rsec ) 1 -
∫xx
∆Φ Φsec
4 2 x exp(-x2)dx π1/2
(12)
The detailed derivation of eqs 10, 11, and 12 can be found in the Supporting Information.
Experimental Materials and Procedures Colloidal Particles and Porous Media. Two different sizes (30 and 1156 nm) of white carboxyl-modified polystyrene latex microspheres (Interfacial Dynamics Corporation, Portland, OR) were used as model colloids. Both are hydrophilic particles with a density of 1.055 g/cm3 (reported by the manufacturer). Particle concentrations were determined by UV-vis spectrophotometry (DU Series 640, Beckman Instruments, Inc., Fullerton, CA), at a wavelength of 440 nm for the 1156 and 218 nm for the 30 nm colloid, respectively. Quartz sand with sizes ranging from 300 to 355 µm was used as model collector grains. The sand was sieved from Accusand 40/60 (Unimin Corporation, Le Sueur, MN) with a stainless steel mesh. The procedure from Zhuang et al. (20) was used to remove metal oxides and other impurities from the sand. Electrophoretic mobilities of the colloids and sand were determined by a Zetasizer Nano ZS (Malvern Instruments, Southborough, MA) at 25 °C. The finest fraction of sand sieved from Accusand was used for the measurement. Colloid Deposition and Release Experiments. Colloid transport experiments were conducted in acrylic columns packed with the sand. The column was 3.8 cm in diameter and 10 cm long with a top and a bottom plate. A piece of nylon membrane with 20 µm size pores (Spectra/Mesh, Spectrum Laboratories, Inc.) was placed on the bottom plate. Sand was wet-packed in deionized (DI) water with vibration to minimize any layering and air entrapment in the column. The porosity of the packed sand for each experiment was determined to be 0.33 (based on a particle density of 2.65 g/cm3 for the sand). Analytical reagent-grade NaCl (Fisher Scientific) and DI water were used to prepare electrolyte solutions at desired ionic strengths. The pH for all the electrolyte solutions was adjusted to 10 by addition of NaOH. Column experiments were performed over a range of ionic strengths (0.001, 0.01, 6978
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 20, 2007
0.1, and 0.2 M) at an approach velocity of 1.2 × 10-5 m/s for both 1156 and 30 nm colloids. For each experiment, background electrolyte solution (degassed) was first delivered to the column upward for at least 20 pore volumes (PVs) to standardize the ionic strength and pH of the system. Then a three-step procedure, similar to that adopted in previous studies (4, 10), was used for colloid deposition and release. Briefly, 20 PVs of colloid suspension (10 mg/L, corresponding to 1.2 × 1010 and 6.7 × 1014 particles/mL for 1156 and 30 nm colloids, respectively) were first introduced to the packed column (phase 1), followed by elution with colloid-free electrolyte solution (phase 2), and finally elution with 10 PVs of DI water (phase 3). After colloid deposition and release with electrolyte and DI water, each column was dissected into 10 layers and sand in each fraction was extracted with DI water to determine the spatial distribution profile of the retained colloids. A more detailed procedure can be found in Bradford et al. (21).
Results and Discussion Electrokinetic Potentials and DLVO Interaction Energy Profiles. Electrophoretic mobilities of the colloids and sand were measured as a function of ionic strength at pH 10, and they were converted to zeta potentials using the Smoluchowski equation. The zeta potentials of both colloids and sand are negative over the range of ionic strengths used in this study, indicating that the experimental conditions were unfavorable for colloid deposition. The DLVO interaction energy profiles for the two colloids were calculated using the measured zeta potentials at different ionic strengths. A value of 1 × 10-20 J was chosen as the Hamaker constant for the polystyrene-water-SiO2 system (1, 2). The zeta potentials, calculated DLVO interaction energy (including maximum energy barriers and secondary-minimum depths and distances), and energy profiles are given in the Supporting Information (Figure S1 and Table S1). Theoretical Predictions of Collision Efficiency by Maxwell Model. Through numerical integrations of eqs 10 and 11, Rsec as a function of Φsec and Rpri as a function of ∆Φ were obtained (Figure 1(a)). Also plotted in Figure 1(a), as comparison, are collision efficiencies calculated by the Boltzmann factor model (BFM), which has previously been used as an approximate expression for Rpri (22), given as
R ) exp(-Φmax)
(13)
Similar to the Maxwell model, collision efficiency in BFM is only related to Φmax, i.e., independent of the specific experimental parameters and the specific model used for energy calculation. As shown in Figure 1(a), the Maxwell model predicts a greater Rpri than BFM for the same energy barrier. The Maxwell model predicts that Rpri decreases quickly with increase of ∆Φ and reaches a very small value when ∆Φ is ∼10 kT, revealing that few colloids can transport over this energy barrier and be deposited in the primary minimum. In contrast, predicted Rsec increases rapidly with the increase of Φsec and approaches a high value of 0.4 when the secondary minimum is only 1 kT. This suggests that the Maxwell model predicts a high efficiency of secondary minima for attracting colloids. Figure 1(b) shows R as a function of ∆Φ for different Φsec values to further demonstrate the effect of secondary minima on collision efficiency. For a given value of Φsec, with increase of ∆Φ, primary-minimum deposition becomes gradually negligible and secondaryminimum deposition becomes more dominating. For a given value of ∆Φ, R increases with increasing Φsec. The effect of Φsec on R is already significant when Φsec is only 0.5 kT, illustrating the dominant role the secondary minimum plays in colloid deposition under unfavorable conditions.
FIGURE 1. (a) Collision efficiency as a function of interaction energy: (a) rsec vs Φsec; (b) rpri vs ∆Φ; (c) exp(-Φmax) vs Φmax (BFM). (b) Total collision efficiency r as a function of ∆Φ for various constant values of Φsec: (a) 0; (b) 0.0125; (c) 0.125; (d) 0.5; (e) 1.0; (f) 2.0.
FIGURE 2. Collision efficiencies (r, rpri, and rsec) calculated by Maxwell model (solid line) and Boltzmann factor model (dotted line) as a function of ionic strengths (I) for colloids of various sizes: (1) 1000 nm; (2) 500 nm; (3) 100 nm; (4) 50 nm; (5) 20 nm. Maxwell model: (a) r vs -Log(I); (b) rpri vs -Log(I); (c) rsec vs -Log(I). Boltzmann factor model: r and rpri are the same. The surface potentials of colloids and collectors are chosen as -40 mV at all ionic strengths. The effects of particle size on collision efficiency as a function of ionic strength are evaluated with the Maxwell model as shown in Figure 2. Results of BFM predictions are again presented for comparison. Figure 2(a) indicates that predicted R by the Maxwell model increases with increasing particle size for a given ionic strength, contrary to that predicted by BFM. The Maxwell model also predicts much larger values of R than those calculated by BFM at all ionic strengths for different particle sizes. Additionally, the Maxwell model predicts a less significant size dependence of R than BFM. Figure 2(b) presents the Rpri values (Rpri ) R for BFM) calculated by the two models as a function of ionic strength for different particle sizes. Both models predict greater Rpri for smaller colloids. The extremely steep curves of the 500 and 1000 nm colloids reveal that primary-minimum deposition rarely happens under unfavorable conditions for those colloids when diffusion is a dominant process. The turning point in each Maxwell model curve is where the maximum energy barrier reaches 0. When the energy barrier decreases further to negative values, colloid deposition becomes favorable and Rpri is assumed to be 1. Figure 2(c) shows that the calculated Rsec by the Maxwell model decreases with decreasing ionic strength at a given particle size but increases with increasing particle size at a given ionic strength. The similarity of Figure 2(c) with 2(a) strongly suggests that
secondary-minimum deposition is the dominant process in colloid deposition under unfavorable conditions, even for particles as small as 20 nm. Colloid Breakthrough Curves and Mass Recovery. Breakthrough curves are plotted in Figure 3 over a range of ionic strengths for both colloids. Each breakthrough curve contains three phases: (1) colloid deposition in an electrolyte solution, (2) elution with colloid-free electrolyte solution, and (3) elution with DI water. Phase 2 displaces the colloids retained in pore water. The introduction of DI water in phase 3 eliminates the secondary energy well that is present in an electrolyte solution (see Figure S1, Supporting Information) and thus releases the colloids deposited in secondary minima (4, 8, 23). The release of both colloids in phase 3 is significant, as indicated by the large colloid peaks measured. This is a clear indication that deposition in secondary minima played an important role even for the small 30 nm colloid. This result agrees with the predictions of the Maxwell model (Figure 2). For both colloids, deposition in phase 1 and release in phase 3 increases with increase of ionic strength. This is not surprising because with the increase of ionic strength, depth of the secondary-minimum well increases, which allows more colloids to be deposited there and, subsequently, more are released. VOL. 41, NO. 20, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
6979
FIGURE 3. Effect of ionic strength on colloid deposition and release in packed bed at a flow rate of 0.0012 cm/s. Phase 1, deposition of colloids in electrolyte solution at pH 10; Phase 2, elution with colloid-free electrolyte solution; Phase 3, elution with DI water.
TABLE 1. Fraction of Colloids Recovered from Phase 1 and Phase 2 (M12), Phase 3 (M3), and Dissection Experiments (MS), and Total Recovered Colloids (MT) for Column Experiments colloid (nm)
ionic strength (M)
M12
M3
M3/η0
MS
MT
1156 1156 1156 1156 30 30 30 30
0.001 0.01 0.1 0.2 0.001 0.01 0.1 0.2
0.99 1.00 0.93 0.77 0.99 0.97 0.90 0.57
0.01 0.02 0.03 0.05 0.004 0.01 0.05 0.08
0.34 0.68 1.02 1.70 0.01 0.03 0.13 0.19
0 0.01 0.01 0.07 0 0 0.01 0.01
1.00 1.03 0.97 0.89 0.99 0.98 0.96 0.66
The fractions of colloids recovered from phase 1 and 2 (M12), phase 3 (M3), column dissection (Ms), and total mass recovery (MT) from the column experiments are given in Table 1 for both colloids. Each fraction was calculated by dividing the mass recovered from that phase by the total input mass. The total mass recovery is the sum of M12, M3, and Ms. Here M3/η0 is approximately taken as the fraction of colloids arriving at the secondary minimum that remained attached (i.e., similar to Rsec). The M3/η0 value for the 1156 nm colloid is larger than that of the 30 nm colloid at the same ionic strength, in agreement with the Maxwell model prediction. The M3/η0 is greater than 1 for the large colloid at 0.2 M, which suggests that other mechanisms that are not included in the filtration theory may have caused additional deposition. Note that Ms for the 1156 nm colloid at 0.2 M is much greater than the values from all other experiments. This additional retention was likely caused by straining. Furthermore, because straining was not observed at lower ionic strengths, we believe the straining at 0.2 M was attachment-induced, namely, high ionic strength (and thus great attractive force coupled with short secondary-minimum distance) facilitated colloid retention at grain-to-grain contacts. This experimentally verifies a conclusion from the theoretical analysis in Johnson et al. (11) stating that increased secondary minimum depth increases deposition via wedging (i.e., straining). The small values of Ms for the 30 nm colloid indicate that this colloid is too small to be strained. Total mass recovery MT values for both colloids and at all ionic strengths except the highest one (0.2 M) are close to 1. The low mass recovery of the 30 nm colloid at 0.2 M is expected because the energy barrier of the small colloid (3.02 kT) is comparable to the average Brownian kinetic energy (on the order of 1 kT), hence, the particles can easily transport over the energy barrier and be deposited in the primary minimum. On the other hand, the energy barrier of 101.2 kT for the 1156 nm colloid at 0.2 M is much greater than the 6980
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 20, 2007
average Brownian kinetic energy or kinetic energy (0.02 kT), and cannot be overcome by diffusion or fluid drag force. We suspect that the low mass recovery observed for the 1156 nm colloid may be caused by surface roughness of the sand. Because nanoscale asperities exist on the sand surface, some large colloids and asperities can reach through the energy barrier and result in attachment in the primary minimum at high ionic strength (24). Effects of surface heterogeneity, which would cause irreversible attachment, are likely negligible because the sand was acid-washed to remove metal oxides and the experiments were conducted at pH 10 at which any remaining metal oxides are negatively charged. Furthermore, because the rate of colloid deposition decreases with increasing ionic strength under favorable conditions (25), irreversible attachment due to heterogeneity is more pronounced at low ionic strength. This is contrary to what we observed in this study. Reversibility of Secondary Minimum Attachment. Because the depths of secondary minima are small for the 30 nm colloid at all ionic strengths, whether these small particles can remain at the secondary minimum after deposition is a question we addressed next. A set of two column experiments was conducted to examine the effect of elapsed time on the release of deposited colloids (1156 and 30 nm) at ionic strength 0.2 M with a flow rate of 0.012 cm/s (10 times higher than the previous experiment). Breakthrough curves from these experiments are shown in Figure 4. The experiments followed the same sequence of deposition and elution in phases 1 and 2 as those presented in Figure 3. However, phase 3 in Figure 4 represents two weeks of flow interruption, phase 4 is elution with the same electrolyte solution, and phase 5 is elution with DI water. While none of the large 1156 nm particles were released in phase 4, the small 30 nm particles were immediately detected in the effluent following introduction of the electrolyte solution. This clearly shows that the small colloids deposited in phase 1 were released into the bulk solution. Based on DLVO theory, colloid deposition in the primary minimum is irreversible due to the deep energy well and the steep increase of the interaction energy function (the derivative of the function is very large, indicating strong attractive force). Therefore, the colloids released in phase 3 are likely those deposited in the secondary minimum during phase 1 and liberated subsequently due to Brownian diffusion because the secondary minimum depth of the 30 nm colloid at 0.2 M (1.05 kT) is close to the average kinetic energy of Brownian particles in solution. It is obvious that this release process is rate-limited and thermodynamic equilibrium between deposited colloids and those in the bulk solution will establish given sufficient time. When the equilibrium is disturbed (e.g., the colloids in the bulk solution are flushed out), more colloids from the collector surface
FIGURE 4. Effect of flow interruption on colloid deposition and release in packed bed at 0.2 M with a flow rate of 0.012 cm/s. Phase 1, deposition of colloids at 0.2 M; Phase 2, elution with colloid-free electrolyte solution; Phase 3, flow interruption for two weeks; Phase 4, elution with colloid-free electrolyte solution; Phase 5, elution with DI water. will be released into the bulk solution with elapsed time and a new equilibrium will develop. The secondary minimum depth (41.3 kT) for the 1156 nm particles at 0.2 M is much larger than the average Brownian kinetic energy, therefore, these larger colloids cannot be released by Brownian motion. This is in agreement with the experimental result, i.e., none of the 1156 nm colloids were detected in phase 4. The release peak in phase 4 of the 30 nm colloids first gradually decreased and then followed with a sudden small increase at ∼0.8 PV after flow interruption. The gradual decrease of the peak corresponds to the gradual displacement of trapped colloids in pores by input solution. The sudden slight increase is likely due to the abrupt change of flow velocity between phase 3 and phase 4, which caused the release of a small fraction of the deposited colloids near the entrance of the column. In phase 5, the release was observed for both colloids. DI water effectively eliminated the secondary energy well so that the large colloids and the remaining small colloids (those not released in phase 4) deposited in secondary minima during phase 1 were released. Previous studies that conducted similar column experiments terminated their experiments when no colloids in the outflow samples could be detected in phase 2 (3, 5, 6, 20, 26), or elution with DI water was immediately followed after a short period of phase 2 (4, 8, 10). Our study is the first to examine the effect of flow interruption on the reversibility of colloids deposited in secondary minima. The results suggest that small colloids deposited in phase 1 can be released back into the bulk solution by Brownian diffusion without any chemical or hydrodynamic disturbance and the release is a continuous, dynamic, and rate-limited process. Comparison of Theoretical and Experimental Collision Efficiencies. The experimental and theoretical collision efficiencies calculated by the IFBL and Maxwell model as a function of ionic strength are presented in Figure 5. The IFBL model predicts strong dependence of R on both ionic strength and particle size, as indicated by the curves’ steep slopes. The features of the Maxwell curves are similar to those discussed previously (see Theoretical Predictions of Collision Efficiency by Maxwell Model). Comparing the two models, it is clear that the Maxwell model predicts much higher collision efficiencies than IFBL for both colloids under unfavorable conditions except in a small region at high ionic strength for the small colloid. This exception is because the collision efficiency in the Maxwell model is determined by ∆Φ at this region (where secondary-minimum deposition is minimal), whereas it is approximately determined by Φmax in the IFBL model. The values of Rexp are similar for the two colloids at all ionic strengths except 0.2 M. The insignificant effect of particle
FIGURE 5. Comparison of collision efficiencies calculated by Maxwell model and IFBL model with experimental collision efficiencies at different ionic strengths. Measured zeta potentials were used as the surface potentials of colloids and collectors, flow velocity ) 0.0012 cm/s, porosity ) 0.33, and collector diameter ) 0.328 mm. size on experimental collision efficiencies has also been observed in previous studies (2, 27). The experimental collision efficiencies measured for the 30 nm colloids are in good agreement with the Maxwell model predictions (within 1-1.5 orders of magnitude), but are significantly different from those predicted by the IFBL model. In the study of Hahn and O’Melia (4), they found that experimental collision efficiencies of a 46 nm colloid were underestimated by theoretical predictions using the Maxwell approach that only accounted for secondary-minimum deposition. By taking into account of both primary- and secondary-minimum deposition, the Maxwell model used in our study provides much more accurate estimations of collision efficiencies for the small colloid. For the large colloid, the experimental collision efficiencies are slightly smaller than Maxwell predictions (within 1.5 orders of magnitude) whereas they are much greater than the IFBL predictions. A possible reason that the Maxwell model predicts greater collision efficiencies may be because the model does not account for hydrodynamic effects on the deposited colloids. This deficiency would be more pronounced for large colloids as they suffer greater hydrodynamic shear (28). Nanoscale protuberances on collector surfaces make the small colloids deposited in the secondary minimum, whose size is similar to the protuberances, less likely to be swept away from the collector. Thus the Maxwell model provides a good prediction of collision efficiencies for small colloids. VOL. 41, NO. 20, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
6981
It is important to note that, as mentioned earlier, small colloids deposited in secondary minima will be released when given sufficient time, so the Maxwell model is only suitable for predicting collision efficiencies of those colloids at the initial stages of deposition. Similarly, it is expected that large colloids deposited at low ionic strengths (when the secondary minimum is comparable to the average Brownian kinetic energy) will also be released with lapsed time. The slow detachment process has been observed in the studies of viruses, bacteria, and Cryptosporidium parvum transport, characterized by long tails in breakthrough curves when plotted on a semilog scale (29, 30). Our study suggests that the reversibility of colloid (e.g., viruses and bacteria) deposition must be considered in transport models for accurate predictions of their travel time in the subsurface environments.
Acknowledgments We acknowledge the financial support provided by the National Natural Science Foundation of China (no. 50479009) and the Program for Changjiang Scholars and Innovative Research Team (IRT0412), and by the U.S. National Science Foundation’s Delaware EPSCoR grant EPS-0447610 through Delaware Biotechnology Institute.
Supporting Information Available The zeta potentials, calculated DLVO interaction energy (including maximum energy barriers and secondary-minimum depths and distances), energy profiles and detailed derivation of Maxwell model are provided. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Elimelech, M.; O’Melia, C. R. Kinetics of deposition of colloidal particles in porous media. Environ. Sci. Technol. 1990, 24 (10), 1528-1536. (2) Elimelech, M.; O’Melia, C. R. Effect of particle size on collision efficiency in the deposition of Brownian particles with electrostatic energy barriers. Langmuir 1990, 6 (6), 1153-1163. (3) Tufenkji, N.; Elimelech, M. Deviation from the classical colloid filtration theory in the presence of repulsive DLVO interactions. Langmuir 2004, 20 (25), 10818-10828. (4) Hahn, M. W.; O’Melia, C. R. Deposition and reentrainment of Brownian particles in porous media under unfavorable chemical conditions: some concepts and applications. Environ. Sci. Technol. 2004, 38, 210-220. (5) Tufenkji, N.; Elimelech, M. Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities. Langmuir 2005, 21 (3), 841-852. (6) Litton, G. M.; Olson, T. M. Particle size effects on colloid deposition kinetics: evidence of secondary minimum deposition. Colloids Surf., A 1996, 107, 273-283. (7) Redman, J. A.; Walker, S. L.; Elimelech, M. Bacterial adhesion and transport in porous media: role of the secondary energy minimum. Environ. Sci. Technol. 2004, 38, 1777-1785. (8) Hahn, M. W.; Abadzic, D.; O’Melia, C. R. Aquasols: on the role of secondary minima. Environ. Sci. Technol. 2004, 38 (22), 59155924. (9) Tong, M.; Johnson, W. P. Excess colloid retention in porous media as a function of colloid size, fluid velocity, and grain angularity. Environ. Sci. Technol. 2006, 40 (24), 7725-7731. (10) Franchi, A.; O’Melia, C. R. Effects of natural organic matter and solution chemistry on the deposition and reentrainment of colloids in porous media. Environ. Sci. Technol. 2003, 37, 11221129.
6982
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 20, 2007
(11) Johnson, W. P.; Li, X.; Gozde, Y. Colloid retention in porous media: mechanistic confirmation of wedging and retention in zones of flow stagnation. Environ. Sci. Technol. 2007, 41, 12791287. (12) Wiese, G. R.; Healy, T. W. Effect of particle size on colloid stability. Trans. Faraday. Soc. 1970, 66, 490-499. (13) Marmur, A. A kinetic theory approach to primary and secondary minimum coagulations and their combination. J. Colloid Interface Sci. 1979, 72, 41-48. (14) Feke, D. L.; Prabhu, N. D. Kinetics of coupled primary- and secondary-minimum coagulation in colloidal dispersions. Langmuir 1985, 1 (6), 691-696. (15) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Mutual coagulation of colloidal dispersions. Trans. Faraday Soc. 1966, 62, 16381651. (16) Gregory, J. Approximate expressions for retarded van der Waals interaction. J. Colloid Interface Sci. 1981, 83, 138-145. (17) Tufenkji, N.; Elimelech, M. Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ. Sci. Technol. 2004, 38 (2), 529-536. (18) Spielman, L. A.; Friedlander, S. K. Role of the electrical double layer in particle deposition by convective diffusion. J. Colloid Interface Sci. 1974, 46 (1), 22-31. (19) Dahneke, B. Diffusional deposition of particles. J. Colloid Interface Sci. 1974, 48 (3), 520-522. (20) Zhuang, J.; Qi, J.; Jin, Y. Retention and transport of amphiphilic colloids under unsaturated flow conditions: effect of particle size and surface property. Environ. Sci. Technol. 2005, 39, 78537859. (21) Bradford, S. A.; Yates, S. R.; Bettahar, M.; Simunek, J. Physical factors affecting the transport and fate of colloids in saturated porous media. Water Resour. Res. 2002, 38 (12), 1327-1338. (22) Hahn, M. W. Deposition and reentrainment of Brownian particles under unfavorable chemical conditions. Ph.D. Dissertation. The Johns Hopkins University, Baltimore, 1995. (23) McDowell-Boyer, L. M. Chemical mobilization of micron-sized particles in saturated porous media under steady flow conditions. Environ. Sci. Technol. 1992, 26, 586-593. (24) Kuznar, Z. A.; Elimelech, M. Direct microscopic observation of particle deposition in porous media: role of the secondary energy minimum. Colloids Surf., A 2007, 294, 156-162. (25) Elimelech, M. Kinetics of capture of colloidal particles in packed beds under attractive double layer interactions. J. Colloid Interface Sci. 1991, 146 (2), 337-352. (26) Kretzschmar, R.; Barmettler, K.; Grolimund, D.; Yan, Y.; Borkovec, M.; Sticher, H. Experimental determination of colloid deposition rates and collision efficiencies in natural porous media. Water Resour. Res. 1997, 33 (5), 1129-1137. (27) Elimelech, M. The effect of particle size on the kinetics of deposition of Brownian particles in porous media. Ph.D. Dissertation, The Johns Hopkins University, Baltimore, 1989. (28) Bergendahl, J. A.; Grasso, D. Mechanistic basis for particle detachment from granular media. Environ. Sci. Technol. 2003, 37 (10), 2317-2322. (29) Schijven, J. F.; Hassanizadeh, S, M. Removal of viruses by soil passage: overview of modeling, processes, and parameters. Crit. Rev. Environ. Sci. Technol. 2000, 30 (1), 49-127. (30) Cortis, A.; Harter, T.; Hou, L.; Atwill, E. R.; Packman, A. I.; Green, P. G. Transport of Cryptosporidium parvum in porous media: long-term elution experiments and continuous time random walk filtration modeling. Water Resour. Res. 2006, 42, W12S13, doi:10.1029/2006WR004897.
Received for review January 26, 2007. Revised manuscript received July 16, 2007. Accepted July 25, 2007. ES070210C
