Geoderma 322 (2018) 89–100

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Transport of silver nanoparticles in intact columns of calcareous soils:
The role of ﬂow conditions and soil texture

T⁎

Samaneh Rahmatpoura, Mohammad Reza Mosaddeghia, , Mehran Shirvania, Jiří Šimůnekb
ab

Department of Soil Science, College of Agriculture, Isfahan University of Technology, Isfahan 84156-83111, Iran
Department of Environmental Science, University of California Riverside, Riverside, CA, USA

A R T I C L E I N F O

A B S T R A C T

Handling Editor: A.B. McBratney

Growing production of manufactured nanomaterials has increased the possibility of contamination of groundwater resources and soils by nanoparticles (NPs). It is crucial to study the fate of NPs in subsurface porous media
in order to evaluate and control their risks to ecosystems and human health. Hence, this study was conducted toinvestigate the transport and retention of polyvinylpyrrolidone (PVP) stabilized silver nanoparticles (AgNPs, adiameter of 40 nm) under saturated and unsaturated conditions in intact columns of two calcareous sandy loam(TR) and loam (ZR) soils. Furthermore, similar experiments were conducted using sand quartz as a reference
medium. A pulse of the AgNP suspension with an input concentration (C0) of 50 mg L−1 was injected into thecolumns for 3 pore volumes. The transport of bromide (Br), as a non-reactive inert tracer, was also examined.
High mobility of AgNPs was observed through the sand columns due to unfavorable conditions for AgNP deposition on the quartz sand surfaces. Nearly all AgNPs introduced into the columns of both soils were retained in
the soil. Percentages of AgNPs leached out of the columns were < 1% of the total injected mass in both soils.
Hyperexponential retention proﬁles (RPs) were observed in both soils and maximum concentrations of
100–130 mg kg−1 were determined near the columns' inlet. However, slightly stronger retention of AgNPs andgreater maximum retained concentrations on the solid phase (Smax) in the ZR soil compared with the TR soil may
be attributed to smaller grain sizes of the ZR soil. Hydrodynamic forces adjacent to the solid surfaces near thecolumn inlet can provide a viable explanation for the hyperexponential shape of RPs. The one-site kinetic attachment model in HYDRUS-1D, which accounted for time- and depth-dependent retention, was successfully
used to analyze the retention of AgNPs. The results showed that the degree of saturation had little eﬀect on themobility of AgNPs through undisturbed soil columns. Our results suggested the limited transport of AgNPs in
neutral/alkaline calcareous soils under both saturated and unsaturated conditions.

Keywords:
Ag nanoparticles
Breakthrough curve
Retention proﬁleHYDRUS-1D
One-site kinetic attachment model
Flow condition

1. Introduction
Silver nanoparticles (AgNPs) are most commonly used for theirstrong antimicrobial and antiviral properties in medicine, dentistry,cosmetics, jewelry, photography, textile, and food packaging (Cornelis
et al., 2013). Discharged nanoparticles (NPs) ﬁnd their way into thesoils during their manufacturing, transportation, application, and disposal (Pachapur et al., 2016), and soils and aquifers act as primary ﬁlter
systems to remove particulate materials from percolating water andprotect water resources (Kasel et al., 2013a; Liang et al., 2013a). Many
previous studies have shown the negative eﬀects of AgNPs on humanhealth and the environment (e.g., He et al., 2011; Carbone et al., 2014).
Hence, a detailed understanding of the processes governing the transport and retention of AgNPs in soil is required to accurately assess thefate and distribution of AgNPs and to design eﬀective strategies for⁎

Corresponding author.
E-mail address: mosaddeghi@cc.iut.ac.ir (M.R. Mosaddeghi).

https://doi.org/10.1016/j.geoderma.2018.02.016
Received 2 June 2017; Received in revised form 3 February 2018; Accepted 8 February 2018
0016-7061/ © 2018 Elsevier B.V. All rights reserved.

reducing their toxicity in the environment.
According to the particle ﬁltration theory, retention and mobility of
NPs in porous media are controlled by physicochemical properties ofboth NPs and collector surfaces, such as the grain size (texture), input
concentration, mineralogical composition, the presence of humic acid,the type of coatings or stabilizing agents, the solution chemistry, as well
as by hydrodynamic forces (Lin et al., 2011; Liang et al., 2013a,b; Braunet al., 2015). The ﬁltration theory has commonly been employed todescribe the deposition of NPs on porous media surfaces. However,studies with NPs and natural colloids often showed deviations in predictions from ﬁltration theory. For example, the retention of NPs may
occur even under unfavorable conditions for attachment due to local
surface charge heterogeneities (Lin et al., 2011), aggregation (Bradford
et al., 2006), and straining in small pores and at locations of highsurface roughness (Kasel et al., 2013a). Additionally, an increase in theGeoderma 322 (2018) 89–100

S. Rahmatpour et al.

occurred at the SWI, while an equilibrium sorption to the AWI led toretardation of AgNPs. They concluded that reversibility of attachment
to the AWI was sensitive to the properties of the AWI and AgNPs, and to
the solution chemistry. Moreover, Chen and Flury (2005) concluded
that colloids were repelled from the AWI. Fang et al. (2013) showedthat decreasing water saturation had little eﬀect on the mobility of TiO2
NPs through packed sand columns owing to net repulsive interactions
between negatively charged AWI and TiO2 NPs.
To the best of our knowledge, no previous study has evaluated thetransport of AgNPs in calcareous soils, despite their widespread occurrence in the arid and semi-arid regions around the world. Calcareous
soils contain a high amount of calcium carbonate, and Ca2+ bridging
due to the high activity of Ca2+ cations may play an important role in
NPs retention. Divalent cations such as Ca2+ and Mg2+ have beenshown to be more eﬀective in NPs retention than monovalent cations
like Na+ (El Badawy et al., 2010; Liang et al., 2013a). In general, it canbe expected that alkaline soils have a high potential to retain NPs
compared to acidic soils because the pH value of these soils (7.0 to 8.5)
is closer to the pH value at the point of zero charge (pHPZC) of NPs. Also,
the high Ca2+ concentration in calcareous soils could lead to aggregation of NPs (Hotze et al., 2010). Moreover, only a few studies haveevaluated the transport and retention of AgNPs in undisturbed and/or
unsaturated soil systems.
The primary objective of this research is thus to evaluate the eﬀects
of the degree of soil saturation and soil texture on the transport andretention of AgNPs in intact columns of calcareous soils. To allow for
direct comparisons with previous studies, similar AgNP transport experiments were also conducted in sand columns. In addition, AgNP
transport and retention data were modeled using HYDRUS-1D to better
understand their transport and retention mechanisms. This informationis needed to properly assess the risk of exposure of ecosystems to AgNPs
and to develop strategies for waste management and remediation.

NPs transport due to stabilizing agents causing short-range repulsive
forces (El Badawy et al., 2013), retarded and asymmetric BTCs, anduniform, non-monotonic, and hyperexponential retention proﬁles (RPs)(Liang et al., 2013a) are examples of violations of the ﬁltration theory.
Most researchers have studied the transport of AgNPs in highly
idealized systems consisting of repacked, homogeneous, coarse-textured porous media (e.g., glass beads, quartz sands) under water-saturated or unsaturated conditions (e.g., El Badawy et al., 2013; Fanget al., 2013; Liang et al., 2013b). While these studies have provided
valuable insights into the mechanisms controlling the transport of
AgNPs, they do not exactly resemble natural soil conditions. Soilcomponents such as clay minerals, organic matter, and carbonates
would interact with the NPs and subsequently have a dominant eﬀect
on their fate, mobility, and potential risks to reach groundwater resources. For example, recent batch studies have shown that the retention of NPs in natural soils is correlated with the clay content (Cornelis
et al., 2012). Simple porous media are not able to account for thecomplexity and heterogeneity (such as a wide particle size distribution,
irregular grain shapes, variations in surface chemical heterogeneity,and a complex pore structure) of natural soils (Sagee et al., 2012; Lianget al., 2013a).
Unfortunately, to date, only a few column studies have focused on
studying the transport of AgNPs in natural systems, leading to a serious
lack of information about their fate and distribution in the environment. In natural soils, clay content and type, soil pH, the presence oforganic material, and the ionic strength of the soil solution can aﬀect
mobility and bioavailability of AgNPs (Liang et al., 2013a). The information on the fate and behavior of AgNPs in soils will ultimately
determine the environmental risk of AgNPs applications. Only recently,
have some studies involving the transport of AgNPs in intact soil columns been conducted (Nowack and Bucheli, 2007; Sagee et al., 2012;
Cornelis et al., 2013; Liang et al., 2013a; Braun et al., 2015). Neukum
et al. (2014) suggested that the transport of AgNPs in sandstones isaﬀected by the pore size distribution, mineralogy, and solution chemistry. Liang et al. (2013a) observed a signiﬁcant retardation in breakthrough curves (BTCs) and hyperexponential RPs of AgNPs in natural(undisturbed) soils. Sagee et al. (2012) reported high mobility and early
breakthrough of AgNPs in a disturbed sandy clay soil. They found thatmechanical straining and chemical interactions between AgNPs and thesoil surfaces played key roles in retention of AgNPs. Cornelis et al.
(2013) suggested that straining was enhanced following fast heteroaggregation between negatively charged AgNPs and positively charged
soil colloid sites and that the mobility of polyvinylpyrrolidone (PVP)
coated AgNPs was signiﬁcantly reduced in the natural soils. Despite thefrequent existence of unsaturated water ﬂow conditions in natural soils,
information is scarcely available on the transport of NPs through unsaturated soils. Colloid retention under unsaturated ﬂow conditions ismore complicated due to the presence of air in the soil system and due
to water ﬂow being constrained to smaller pores. Colloid retention in
unsaturated porous media under electrostatically unfavorable deposition conditions has been attributed to attachment to the solid–waterinterface (SWI), attachment to the air–water interface (AWI), deposition on solid surfaces, retention at the solid–air–water triple point and,straining in thin water ﬁlms (Chen and Flury, 2005; Bradford and
Torkzaban, 2008; Torkzaban et al., 2008; Fang et al., 2013; Kumahor
et al., 2015). Under unsaturated conditions, colloid transport may increase due to moving AWI (McCarthy and McKay, 2004) or decrease
due to greater colloid attachment to stationary AWI (Chen et al., 2008).
However, most previous studies on colloid transport reported thatcolloid retention increased in unsaturated porous media. Bradford et al.
(2002) reported that the retention of colloids under unsaturated ﬂow
conditions was controlled by the spatial distribution of water saturationand may increase due to limited preferential ﬂow and a greater contact
time between the media matrix and the colloids. Kumahor et al. (2015)
also investigated the transport of citrate-coated AgNPs in unsaturated
sand columns. They suggested that a non-equilibrium interaction

2. Materials and methods
2.1. Synthesis of AgNPs
All chemicals reagents used in our experiments were of analyticalgrade and were used as received without further puriﬁcation. A sonochemical method was applied for preparing AgNPs in aqueous polyvinylpyrrolidone (PVP) solutions (Zhu et al., 2010). In a typical preparation, 0.05 g of PVP was added to 100 mL of aqueous solution
containing 0.1 g of AgNO3. The PVP acts as both reducing and capping
agent. The mixture was stirred for complete dissolution and agitatedunder sonication. Ultrasound irradiation was carried out with a multiwave ultrasonic generator (Sonicator 3000; Bandeline, MS 72, Germany), equipped with a converter/transducer and titanium oscillator(horn), 12.5 mm in diameter, operating at 20 kHz with a maximum
power output of 60 W. The operating condition was at 5 s pulse on and
5 s pulse oﬀ with amplitude of 72% at 25 °C for 20 min.
The suspension for each experiment was freshly prepared (in orderto minimize the dissolution of AgNPs) by dilution of the concentrated
stock suspension of stabilized AgNPs into selected electrolyte solutions
to achieve an approximate concentration of 50 mg L−1. The stock suspension was sonicated for 30 s with the probe before dilution. During
injection into the columns, the suspension was continuously sonicatedin a sonication bath.
2.2. Characterization of AgNPs
Transmission electron microscope (TEM) images of the synthesized
AgNPs were obtained on a Philips CM30 instrument at an accelerating
voltage of 150 kV. An average hydrodynamic diameter and surface
charge characteristics of the AgNPs were determined using the Malvern
ZEN 3600 Nano ZS Zetasizer (Malvern Instruments Ltd., Malvern, UK).
Zeta potential (ζ) was measured with the same equipment between
90

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

−200 and +200 mV. The X-ray powder diﬀraction (XRD) pattern wasrecorded by a Philips X'Pert Pro diﬀractometer using CuKα radiation todetermine the crystallite size of the AgNPs. The crystallite size (D) of
AgNPs was calculated using the Scherrer equation (Moore andReynolds, 1997):D=kλβ cos θ2.4. Column experiments
The transport of AgNPs and bromide (Br), as an inert tracer, in thesand and undisturbed soil columns was studied. A hydrophilic nylon
membrane (opening size 210 μm), as a ﬁlter, was placed at the bottomof the columns. A peristaltic pump (Longer BT100-1F, Hebei, China)
with a sprinkler head was used to inject Br solutions and AgNPs suspensions at a steady ﬂow rate (i.e., q in the range 0.03–0.70 cm min−1,
depending on the soil type and ﬂow conditions) into the columns.
Leaching experiments were conducted under both saturated and unsaturated ﬂow conditions for both AgNPs and Br. The columns wereﬁrst conditioned with several pore volumes of an electrolyte solution of
6 mM Ca(NO3)2 to achieve steady-state ﬂow. Gravitational saturated
ﬂow was established by imposing a negligible pressure head on the inletof the columns, establishing a unit hydraulic gradient and the Darcian
ﬂow rate equal to Ks. Unsaturated ﬂow was established by controllingthe inlet ﬂow rate so that the approximate degree of saturation of 0.90
was obtained in the soil columns. Column and ﬂow parameters for thecolumn experiments are shown in Table 3.
Br tracer (KBr with a concentration of 10 mg Br L−1, C0) was applied
to each column prior to the AgNPs transport experiments, in order toobtain ﬂow and transport parameters. The ionic strength (IS) of the
background solution was adjusted to 6 mM Ca(NO3)2 to be similar to
the natural soil solution. The electrolyte solution was not buﬀered andpH values of the inﬂuent and eﬄuent were in the range of 6–7. Column
eﬄuent samples were collected continuously in plastic centrifuge tubes
with diﬀerent increments. Br concentrations in the leachate samples
were measured using an ion-selective electrode (Zhejiang Nade
Scientiﬁc Instrument Co., MP523-06, Hangzhou, China) connected to a
pH meter (CyberScan, model 2100, Eutech Instruments, Nijkerk, The
Netherlands). Similar electrolyte solutions and ﬂow rates were used inboth Br and AgNPs transport experiments.
Suspensions of AgNPs (C0 of 50 mg Ag L−1) were injected into thecolumns, followed by ﬂushing with several pore volumes of a particlefree electrolyte [Ca(NO3)2] solution. A high concentration of AgNPs
was selected based on the results of batch and preliminary transport
experiments, which conﬁrmed high retention of AgNPs in these soils.
Column eﬄuent samples were collected continuously in plastic centrifuge tubes with diﬀerent increments. The eﬄuent samples weretreated with concentrated HNO3 at 175 °C for 10 min before the Ag
measurement to dissolve the particles and diminish sorption onto thesampling tubes (Cornelis et al., 2010). Solutions were diluted asneeded, and an Ag concentration (C) was measured by a PerkinElmer
AAnalyst200 AAS (USA). Each sample was measured three times andthe average value was used for further analyses. Relative concentrations(C/C0) were plotted vs. the number of pore volumes (PV) as a breakthrough curve (BTC). The pore volume was calculated by multiplying
the soil volume and the volumetric water content.
After completion of the transport experiments, the soil columns
were carefully excavated in 1 cm increments (i.e., 15 layers). The total
residence Ag concentration (S) in the soil columns was determined by
the AAS after open vessel aqua regia digestion (1:3 HNO3:HCl) at 140 °C(Cornelis et al., 2010). The retention proﬁle (RP) of AgNPs was subsequently determined from this information and the measured dry mass(1)

where k is the so-called shape factor that usually has a value of about
0.9, λ depicts the wavelength of CuKα radiation, and β is the breadth ofthe observed diﬀraction line at half of the maximum intensity (FWHM).

2.3. Sand, soil sampling and characterization
Quartz sand with an average grain size of 264 μm and dry bulk
density of 1.53 g cm−3 was used as an inert reference medium. To remove metal and organic impurities, the sand was washed sequentiallywith tap water, nitric acid (10%) and distilled water. The sand was
packed into stainless steel cylinders (an inner diameter of 7 cm, a heightof 15 cm, and a thickness of 2 mm).
Soil was sampled from the top 30 cm of two locations in the Isfahan
Province, central Iran. The sandy loam soil (Typic Torriorthents) was
sampled from the Tiran region (TR), located at 32° 40′ 20″ N 51° 13′ 46″E, and the loam soil (Typic Haplocalcids) was sampled from the Ziar
region (ZR) at 32° 30′ 57″ N and 51° 55′ 49″ E. After careful removal of
possible vegetation, undisturbed soil columns were collected by using
stainless steel cylinders (an inner diameter of 7 cm, a height of 15 cm,
and a thickness of 2 mm) with sharpened edges. Both ends of soilcontaining cylinders were then sealed with pieces of cloth.
Selected physical and chemical properties of the studied soils are
given in Tables 1 and 2, respectively. Soil pH and EC values were determined in 1:2 soil:water extracts with a pH meter (CyberScan, model
2100, Eutech Instruments, Nijkerk, The Netherlands) and an EC meter(Elmetron, model CC-501, analysio GmbH, Greifswald, Germany), respectively. Soil calcium carbonate equivalent (CCE) was determinedusing the back-titration method (Loeppert and Suarez, 1996). Organiccarbon (OC) was measured using the wet digestion method (Nelson andSommers, 1996). Cation exchange capacity (CEC) was determined using
the ammonium acetate method at pH 8.2 (Sumner and Miller, 1996).
Particle size distribution was determined by the pipette method as described in Gee and Bauder (1986). Total silver concentration in the soils
was determined by a PerkinElmer AAnalyst200 atomic absorption
spectrometer (AAS) after open vessel aqua regia digestion (1:3
HNO3:HCl) at 140 °C (Cornelis et al., 2010).
Soil bulk density (ρ) was calculated for the intact columns according
to Blake and Hartge (1986). The columns were ﬁrst saturated and thesaturated hydraulic conductivity (Ks) of all columns was determinedusing the constant-head method (Klute and Dirksen, 1986). The soil
aggregate stability was characterized by the mean weight diameter(MWD) of water-stable aggregates (< 4 mm) as determined by the wet
sieving method (Yoder, 1936).

Table 1
Physical properties of the studied sand and soils.
SampleTexture

Clay

Silt

Sand

kg 100 kg−1
Sand
Tiran (TR)
Ziar (ZR)

–
SL
L

–
17.8
15.7

–
19.9
41.5

–
62.3
42.8

ρ

MWD

dc

Ks

φ

g cm−3mm

μm

cm min−1

cm3 cm−3

1.53
1.52
1.20

–
0.41
1.29

264
49.0
20.4

1.700
0.032
0.080

0.420
0.425
0.544

SL - sandy loam, L - loam; dc - median particle diameter determined using the wet sieving method, ρ - bulk density, MWD - mean weight diameter of water-stable aggregates, φ - porosity,
Ks - saturated hydraulic conductivity.

91Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

Table 2
Chemical properties of the studied sand and soils.
SampleEC

pH

dS m−1

CEC

OC

CaCO3

KF

NF

Location
latitude/longitude

cmol kg−1

kg 100 kg−1

kg 100 kg−1

L g−1

–

N

E

0.9
11.8
13.0

0.11
0.63

–
47.5
32.2

–
80.02
721.70

–
0.60
0.42

–
32.40.20
32.30.57–
051.13.46/3
51.55.49

(1:2)
Sand
Tiran (TR)
Ziar (ZR)

0.08
0.21
1.43

7.80
8.00
7.98

EC - electrical conductivity at 25 °C, CEC - cation exchange capacity, OC - organic carbon, KF - Freundlich coeﬃcient, NF - Freundlich constant.
Table 3
Experimental parameters and HYDRUS-1D optimized transport parameters from Br breakthrough curves.
SampleDegree of saturation

qm
cm min−1

θmqp
cm min−1

θpv
cm min−1

λ
cm

R2

SE

Sand
TR soil
ZR soilSand
TR soil
ZR soil

1
1
1
0.887
0.831
0.921

1.7
0.07
0.09
0.85
0.03
0.04

0.375
0.407
0.453
0.339
0.306
0.419

1.900
0.059
0.081
0.827
0.053
0.035

0.430
0.542
0.450
0.356
0.290
0.350

4.42
0.109
0.181
2.32
0.093
0.100

0.09
6.79
8.46
0.68
1.70
6.16

0.998
0.987
0.982
0.983
0.973
0.959

0.00190.01570.02470.04720.01760.0500Column experiments were conducted at pH 7.0 and ionic strength (IS) = 6 mM Ca(NO3)2, q - Darcy velocity, θ - volumetric water content, v = qp/θp - mean pore water velocity, λ dispersivity. Subscripts m and p stand for measured and predicted values, respectively. R2 - coeﬃcient of determination, SE - standard error.

hyperexponential with depth (Kasel et al., 2013a).
The ﬁrst term on the right side of Eq. (4) accounts for time-dependent blocking/ﬁlling of attachment sites based on Langmuirian dynamics (Liang et al., 2013a). This model indicates that retention decreases with time as the attachment sites are gradually being ﬁlled with
NPs and the retention proﬁle becomes uniform with depth as S approaches Smax. When Smax is large, the blocking term approaches unity
and the decrease in retention with time is not considered (Kasel et al.,2013a). The second term on the right side of Eq. (4) accounts for depthdependent retention.
Similarly to Kasel et al. (2013a), four diﬀerent model formulations
for blocking were considered in our study: Model 1 (M1) is the conventional attachment and detachment model (ψ = 1); Model 2 (M2)when β = 0 includes attachment, detachment, and Langmuirian
blocking; Models 3 (M3) and 4 (M4) when β > 0 additionally also
consider depth-dependent retention, producing retention proﬁles of
AgNPs, which exhibit a hyperexponential shape (e.g., a higher deposition rate close to the column inlet). Liang et al. (2013a,b) used optimalvalues of β = 0.432 and β = 1.532 for simulations of the AgNPs
transport in sand and soil, respectively. However, these β values did notadequately describe the shape of the observed depth-dependent retention proﬁles in our study. Therefore, we used β = 0.765 based on information presented in the literature (Kasel et al., 2013a). In M3, Smax
was set to a large value so that the ﬁrst term on the right side of Eq. (4)is approximately equal to 1. In M4, Smax was set equal to a value that
resulted in the ﬁrst term on the right side of Eq. (4) smaller than 1.
The AgNPs retention model parameters (katt and Smax) were optimized by simultaneously ﬁtting the experimental BTCs and RP datausing HYDRUS-1D. The pore water velocity (v) and dispersivity (λ)
were ﬁxed at values optimized using the Br BTCs. The coeﬃcient oflinear regression (R2), Akaike Information Criterion (AIC), root meansquare error (RMSE), and standard error (SE) were used to evaluate themodeling eﬃciency. The AIC was calculated using the following
equation (Akaike, 1998):

of soil in each increment.
2.5. Theory and modeling
The version 4.14 of the HYDRUS-1D software package (Šimůnek
et al., 2008, 2016) was used to simulate the transport and retention of
Br and AgNPs. The BTCs of a conservative tracer (Br) for each column
were simulated using the equilibrium advective-dispersive equation(ADE) to inversely estimate the pore water velocity (v) and dispersivity(λ) of the undisturbed soil columns (Table 3).
Transport and retention of AgNPs in the soils were simulated using
the ADE with terms representing a one-site kinetic attachment-detachment model. The aqueous and solid phase mass balance equations
for AgNPs are given in this model as:

θ

∂C
∂S
∂ ⎛ ∂C ∂C ⎞
+ρ
=
θD –q
∂t
∂t
∂z ⎝ ∂Z ∂z ⎠

(2)

ρ

∂S
= θkatt ψC –k det ρS∂t(3)

where θ [−] is the volumetric water content, t [T, T denotes time units]
is time, C [NcL−3, Nc and L denote the number of NPs and units oflength, respectively] is the aqueous phase AgNPs concentration, ρ[ML−3, M denotes mass units] is the soil bulk density, S [NcM−1] is thesolid phase AgNPs concentration, z [L] is the distance from the column
inlet, D [L2T−1] is the hydrodynamic dispersion coeﬃcient, q [LT−1] isthe Darcian water ﬂux, katt [T−1] is the ﬁrst-order attachment coeﬃcient, kdet is the ﬁrst-order detachment coeﬃcient, and ψ [−] is a dimensionless function to account for time- and depth-dependent
blocking given as (Bradford et al., 2006):

S ⎞ ⎛ dc + z ⎞ψ = ⎛1–⎝ Smax ⎠ ⎝ d c ⎠
⎜

⎟⎜

–β

⎟

(4)

where dc [L] is the median diameter of soil grains, β [−] is an empiricalparameter, which controls the shape of the retention proﬁle of NPs (i.e.,the depth dependence of the retention coeﬃcient), and Smax [NcM−1] isthe maximum solid phase concentration of deposited AgNPs. Eq. (4) can
account for time- and depth-dependent retention and can produce retention proﬁles which can be exponential, uniform, or

RSS ⎞AIC = 2K + N ln ⎛
⎝ N ⎠

(5)

where K is the number of adjustable parameters in the model, N is thenumber of data points to be ﬁtted, and RSS is the residual sum of92

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

and 0.98, respectively). Therefore, Br transport parameters accurately
characterize the physical conditions of leaching experiments. The
modeled and measured hydraulic parameters and dispersivity values of
the repacked quartz beads and undisturbed soil columns are given in
Table 3.
The transport of Br, as an inert tracer, is not aﬀected chemically andits BTCs should depend only on physical processes in the porous media.
The Br BTCs have steep increases and decreases of concentrations andare approximately symmetric in shape (Fig. 2a), indicating that physicalnon-equilibrium is not signiﬁcant for the Br transport in the sandcolumn experiments due to a narrow pore size distribution of the sand.
Although the physical non-equilibrium model can provide a better description to the Br BTCs than the simple ADE model in unsaturated sandand intact soils columns, we decided to use the ADE model due to its
simplicity. Fig. 2b and c show that in the intact soils, the Br BTCs deviated from the symmetrical shape and shifted to the left relative to theequilibrium transport curve. In contrast to the sand columns, Br was
detected in the ﬁrst collected volume of the eﬄuent from the intact soil,
which suggests the existence of preferential ﬂow (Dousset et al., 2007).
The BTC for the TR soil shows a less diﬀuse front compared to that for
the ZR soil, which is characterized by a more gradual increase of Br
concentrations to C/C0 = 1 before 3PV. The breakthrough of Br in the
ZR soil columns shows a sharp front between 3PV and 4PV (Fig. 2c).
The BTCs were more symmetrical in saturated than in unsaturated
sand columns (Fig. 2a). Similar to the literature (e.g., Torkzaban et al.,2008), the dispersivity values were greater for unsaturated conditions
than for saturated conditions in the sand columns. Although considerable diﬀerences between saturated and unsaturated conditions were notobserved in soil columns, the dispersivity values were greater for saturated conditions (Table 3). The BTC under saturated conditions in the
TR soil exhibits more asymmetry and early appearance of Br in theeﬄuent (Fig. 2b). This behavior indicates that Br was transported relatively rapidly by a small fraction of the total soil water (bypassing thesoil matrix). Similar results were reported by Seyfried and Rao (1987)
in undisturbed soil columns, who suggested that under unsaturated
conditions, conducting pore sequences do not contribute to the transport processes, which results in the reduction of the asymmetry in BTCs
and in compressing the solute front in undisturbed soil columns.
Moreover, Bradford et al. (2004) suggested that the asymmetric shape(early appearance, tailing, and approach to the peak eﬄuent concentration) of the Br BTCs is controlled by the degree of bypassing
water. However, in the ZR soil, saturation conditions had a negligible
eﬀect on the Br BTCs. These diﬀerences could be explained by the
structural heterogeneity in this soil. The pore network in the ZR soil islikely suﬃciently interconnected so that drainage of large pores cannot
disconnect the conducting pore sequences.

squares.
The Peclet number (Pe), a measure that characterizes the ratio of
advective transport to diﬀusive transport, was calculated using thefollowing equation (Tufenkji and Elimelech, 2004):

Pe =

νL
D

(6)

where D (L2T−1) is the hydrodynamic dispersion coeﬃcient and L is thesoil column length.
The following equation was used to determine the ﬁltration coeﬃcient (λf, m−1) (Matthess et al., 1988):

C1
λ f = ln ⎛ influent ⎞ ×CLeffluent
⎝
⎠
⎜

⎟

(7)

where Cinfluent and Ceffluent represent the average inﬂuent and eﬄuent
concentrations over the leaching time (NcL−3) and L is the sampling
depth (L), which is equal to the soil column length. The Cinfluent andCeffluent concentrations were determined using the numerical integrationof inﬂuent (C0) and eﬄuent (BTC) concentration curves.
3. Results and discussion
3.1. Characterization of AgNPs
Fig. 1b illustrates the XRD pattern of the synthesized AgNPs. The
XRD pattern of the AgNPs showed diﬀraction peaks at 2θ = 38, 44, 64,
and 77 assigned to (111), (102), (110) and (120) planes, respectively, ofa faced centered cubic (FCC) lattice of silver (Majeed Khan et al., 2011).
The average size of the synthesized AgNPs, calculated from the XRD
pattern by the Scherrer equation (Eq. (1)), was around 29 nm. The TEM
images of AgNPs revealed that the average size was about 40 nm(Fig. 1a). The Z-average hydrodynamic diameter of the AgNPs was
157.59 nm, as measured by DLS, and the zeta potential (ζ) value wasclose to neutral (−2.7 mV). The size obtained by DLS is considerablylarger than that determined by XRD and TEM, which can be explainedby the predominant contribution of the large particles or aggregates on
the light scattering signal and by the fact that DLS measures not only
the size of the NPs, but also the additional layer corresponding to thesolvent moving together with the particles (Ito et al., 2004).
3.2. Transport of bromide through saturated and unsaturated columns
Fig. 2 presents the observed and simulated BTCs of Br under bothsaturated and unsaturated ﬂow conditions in the sand and soil columns.
The classical ADE, Eq. (2), well describes the BTCs of a conservative
tracer under both saturated and unsaturated ﬂow conditions (R2 = 0.99

Fig. 1. (a) Transmission electron microscopy (TEM) images and (b) X-ray diﬀraction (XRD) patterns of the synthesized silver nanoparticles (AgNPs).

93

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

asaturated
fitted-saturated
unsaturated
fitted-unsaturated

0.8

fitted-saturated

0.6
0.4
0.2
0.0
0

1

2

PV

3

4

5

1.0

unsaturated
fitted-unsaturated

0.8
0.6
0.4
0.2
0.0
0

1

2

6

b

b

saturated
fitted-saturated

1.0

unsaturated
fitted-unsaturated

0.8
0.6
0.4
0.2

4

5

saturatedunsaturated

0.015

0.010

0.005

0.000
0

2

4

6

8

10

12

PV

0

1

2

3
4
PV

5

6

7

8

c

c
Relative concentration of Br (C/C0)

3

PV

0.020

0.0
Relative concentration of Ag (C/C0)

Relative concentration of Br (C/C0)

saturated

Relative concentration of Ag (C/C0)

1.0

Relative concentration of Ag (C/C0)

Relative concentration of Br (C/C0)asaturated
fitted-saturated
unsaturaed
fitted-unsaturated

1.0
0.8
0.6
0.4
0.2
0.0
0

1

2

3

4
5
PV

6

7

8

0.020

saturatedunsaturated

0.015
0.010
0.005
0.000
0

2

4

6
PV

8

10

12

14

Fig. 3. Observed and simulated breakthrough curves for silver nanoparticles in (a) sandcolumns, and observed breakthrough curves for AgNPs in (b) TR soil, and (c) ZR soilcolumns (PV is the number of pore volumes). The background electrolyte was 6 mM Ca(NO3)2 and the AgNPs input concentration was 50 mg L−1. The arrows indicate the end of
the AgNPs pulse. Continuous curves represent the HYDRUS-1D simulations using the onesite kinetic attachment-detachment model (Model 1, M1). Note diﬀerent vertical scales in
the graphs.

9Fig. 2. Observed (dots) and ﬁtted (lines) BTCs of Br tracer in (a) sand, (b) TR soil, and (c)ZR soil columns under saturated and unsaturated ﬂow conditions (PV is the number ofpore volumes). The arrow indicates the end of the tracer pulse. Continuous curves represent the HYDRUS-1D simulations using the equilibrium advective-dispersive equation(ADE).

Because of considerable diﬀerences between model parameters for two
replications of natural soil columns, each soil column replicate has been
considered as a separate sample. Other studies, such as those by
Cornelis et al. (2013) and Sagee et al. (2012), also reported similarly
large variations between natural soil columns.
In both saturated and unsaturated sand columns, AgNPs are ﬁrst
detected in the eﬄuent when PV < 1. Afterward, the C/C0 values increased sharply and reached a plateau close to values of 0.9 and 0.8 at
PV = 1 in the saturated and unsaturated columns (Fig. 3a), respectively. This suggests that the deposition rate of AgNPs is not aﬀected by
the concentration of deposited AgNPs on the sand grain surfaces. The
eﬄuent (Meﬀ), sand or soil column (Msoil), and total(Mtotal = Meﬀ + Msoil) mass recoveries of AgNPs are shown in Table 4.
The mass recoveries of AgNPs in both saturated and unsaturated sandcolumns are > 84% (i.e., 88.9 and 84.9 for saturated and unsaturated

3.3. Transport and retention of AgNPs through saturated and unsaturated
columnsFig. 3 presents the observed and simulated BTCs of AgNPs underboth saturated and unsaturated conditions in the sand columns (Fig. 3a)and observed BTCs of AgNPs in soil columns (Fig. 3b,c). Furthermore,
retention proﬁles (RPs) of AgNPs for the undisturbed soil columns forboth ﬂow conditions are illustrated in Fig. 4. The BTCs are plotted using
normalized concentrations (C/C0) of AgNPs as a function of the numberof pore volumes (PV) and RPs are plotted using normalized solid phase
concentrations (S/C0) as a function of depth. In the sand columns,
around 85%–90% of AgNPs were transported through the columns andrecovered in the eﬄuent. We believe that 10%–15% of AgNPs wereretained in the sand columns, which cannot be measured accurately.
94

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

0.0

0.5

S/Co (cm3 g-1)
1.0
1.5
2.0

2.5

3.0

sand beads because of the small size of AgNPs and a low dp/dc value(i.e., 0.0009), where dp [L] is a diameter of the particles and dc [L] is themedian grain diameter of the collector. However, the low retention isprobably attributed to other retention mechanisms such as chemical
heterogeneity of colloids, surface charge heterogeneity on the sandgrains, surface roughness, colloid aggregation, and enhanced colloid
retention in low-velocity regions (Fang et al., 2013).
The results show that the BTCs obtained under unsaturated conditions exhibit the same behavior as those under saturated conditions inthe sand columns (Fig. 3a). The peak eﬄuent concentration of AgNPs
under unsaturated conditions is lower than under saturated conditions(Fig. 3a). Bradford et al. (2006) discussed that the colloid-accessible
fraction of the pore space decreases with decreasing water saturation.
Furthermore, the unsaturated hydraulic conductivity rapidly decreases
with decreasing water saturation. Hence, the retention forces acting on
the attached colloids in unsaturated systems are expected to be stronger
than in saturated systems (Bradford and Torkzaban, 2008; Torkzaban
et al., 2008).
Small ﬂuctuations in AgNP concentrations were observed at someparts of BTCs (Fig. 3) for both soil and sand columns. Although otherauthors such as Kasel et al. (2013a) and Kumahor et al. (2015) also
observed such ﬂuctuations, no acceptable explanation has been suggested so far.
Fig. 3b and c present the BTCs for AgNPs in the TR and ZR soils,
respectively. Nearly all AgNPs introduced into both soils were retainedin the soil columns. Percentages of AgNPs leached out of the ZR and TR
soil columns were < 1% of the injected total mass and the averages of
the total column mass recoveries of AgNPs in the soil columns were in
the range of 90–100% (except for the unsaturated ZR soil-2 column, see
Table 4). This ﬁnding indicates the accuracy and correctness of ourexperimental procedures and protocols.
In the ZR soil, eﬄuent concentrations of AgNPs from the saturated
and unsaturated soil columns were around the detection limit of AAS
during the entire experiments and no noteworthy breakthrough could
be observed (Fig. 3c). In the TR soil under saturated conditions, AgNPs
appeared in the eﬄuent after 2.5 PV and their concentrations gradually
increased to a maximum C/C0 of 0.005 after 5 PV (Fig. 3b). Following
the reintroduction of AgNP-free solutions, the eﬄuent concentrations of
AgNPs declined, approaching zero at approximately 7 and 9 PV undersaturated and unsaturated conditions, respectively.
Similar results have been reported by other researchers. Braun et al.
(2015) reported that no breakthrough of AgNPs occurred in the silty
loam soil at a ﬂow velocity of 0.0015 cm min−1 due to high retention
and that the RPs were strongly hyperexponential, compared to the exponential distribution of AgNPs in the loamy sand soil. Cornelis et al.
(2013) observed high retention and small eﬄuent concentrations of
AgNPs in 11 natural soil columns. Kasel et al. (2013b) also observed
almost complete retention of functionalized multi-walled carbon nanotubes (MWCNT) in two undisturbed soils at water contents close tosaturation (i.e., degree of saturation of 85–96%). They recovered >86% of MWCNT in the soil proﬁle and their experiments showed no
detectable breakthrough of MWCNT. Several reasons have been mentioned to explain the high retention of NPs in natural soils: sedimentation and straining of NPs on soil minerals following their aggregation and/or heteroaggregation (Cornelis et al., 2013), physicalﬁltration mechanisms (Kasel et al., 2013b), grain size eﬀects, mineralogical composition of the soil or long-term colloidal stability of NPs(Braun et al., 2015; Sagee et al., 2012), nanoscale chemical and physical heterogeneity on the soil surfaces and blocking eﬀects (Liang et al.,2013a), and attachment mechanisms (Bradford et al., 2004). It is reported that soil colloids containing Fe, Al, and Si (Liang et al., 2013a;
Neukum et al., 2014) could provide favorable attachment sites for
AgNPs.
The surfactant coatings on the AgNPs can also aﬀect the retention of
AgNPs. Lin et al. (2012) investigated the eﬃciency of AgNPs with two
diﬀerent polymer coatings (poly vinylpyrrolidone or Arabic gum) to

3.5

-1
-3
Depth (cm)-5
-7

saturated
fitted-saturated
unsaturated
fitted-unsaturated

-9
-11
-13
-15

b

S/C0 (cm3 g-1)
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-1

Depth (cm)

-3
-5
-7

saturated
fitted-saturaetd
unsaturated
fitted-unsaturated

-9
-11
-13
-15

Fig. 4. Observed and simulated retention proﬁles for silver nanoparticles in (a) TR and(b) ZR soil columns. The background electrolyte for leaching experiments was 6 mM Ca(NO3)2 and the AgNPs input concentration was 50 mg L−1. The arrows indicate the end of
the AgNPs pulse. Continuous curves represent the HYDRUS-1D simulations using the onesite kinetic attachment-detachment model, in which blocking is combined with depthdependent retention (M4).

Table 4Mass recoveries of AgNPs, ﬁltration coeﬃcients, and Peclet numbers in the sand and soilcolumns under saturated and unsaturated conditions.
Flow conditions

Saturated

Unsaturated

SampleSand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2

Meﬀ

Msoil

Mtotal

λf

%

%

%

m−1

88.90
0.60
0.02
0.70
0.20
84.90
1.10
0.01
0.10
0.10

ND
99.20
95.30
89.80
98.80
ND
99.00
94.30
99.10
60.90

88.90
99.80
95.32
90.50
99.00
84.90
100.10
94.31
99.20
61.00

0.86
34.47
26.17
32.91
40.10
0.85
28.11
30.85
46.63
43.78

Pe

170.84
2.21
2.66
1.77
1.50
22.16
7.50
6.00
2.43
1.33

Meﬀ, Msoil, and Mtotal are mass percentages recovered from eﬄuent, soil/sand samples,
and total (sum of both), respectively; ND - not detected. λf - ﬁltration coeﬃcient, Pe = νL/
D = L/λ - Peclet number, where v is the mean pore water velocity, L is the length of thecolumns (=15 cm), and D is the hydrodynamic dispersion coeﬃcient (D = λv, λ is dispersivity).

conditions, respectively, see Table 4), suggesting low retention in thesand columns. This is consistent with other studies, indicating that thesand surfaces are unfavorable for particle deposition (Fang et al., 2013).
Straining is also unlikely to be involved in the retention of AgNPs in95

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

heteroaggregation, and homoaggregation had a negligible eﬀect(Cornelis et al., 2013; Liang et al., 2013a; Braun et al., 2015).
In calcareous soils, the AgNPs transport may be aﬀected by surface
interactions with the carbonates. Moreover, our previous experimentsthat were conducted in a batch system for nine diﬀerent calcareous soils(Rahmatpour et al., 2017) suggested signiﬁcant and positive correlations between sorption isotherm parameters of AgNPs and pH due tothe increased hydrolysis/precipitation of Ag+ ions released from the
PVP-AgNPs. In addition, using electrolyte solution [i.e., 6 mM Ca(NO3)2] and the presence of Ca2+ in solution could aﬀect the AgNPs
behavior in our transport experiments. The results of Braun et al.
(2015) indicated that the presence of Ca2+ aﬀected AgNPs transporteven at low concentration (i.e., 1 mM). The divalent cation Ca2+ could
aﬀect the AgNPs transport by creating nanoscale chemical heterogeneity on the solid surfaces that can neutralize or reverse the surface
charges at speciﬁc locations (Bradford et al., 2015) and/or can induce
cation bridging between functionalized NPs and negatively-charged
sites on the clay surfaces (Liang et al., 2013a).
Hyperexponential retention proﬁles (RPs) were observed in bothsoils (Fig. 4). Retention of AgNPs decreased gradually along the travel
distance, with a maximum concentration of 100–130 mg kg−1 near thecolumn inlet and a minimum solid-phase concentration of 5 mg kg−1
near the column outlet. The higher concentration of AgNPs near thecolumn inlet in ZR soil columns in comparison with TR soil columns(Fig. 4) can be related to higher EC (Table 2) and greater divalent cations (data not shown) in ZR soil. Similarly Zhang et al. (2017) reported
more retention of MWCNT in the presence of Ca2+ compared with K+
ions. They also observed that in the presence of Ca2+, the blocking
behavior enhanced and RPs exhibited a hyperexponential shape. In fact,
after leaching of the columns with distilled water for 20 pore volumes,
the percentages of input AgNPs retained in the soils are > 90% in bothsoils. A signiﬁcant fraction of retained AgNPs (approximately 90%) isrecovered in the top 0–4 cm (Fig. 4). Bradford et al. (2004) suggested
that the number of dead-end pores decreases with increasing distance,
which results in the colloid transport occurring mainly within the large
pores and bypassing smaller pores due to limited transverse dispersivity
or size exclusion. Surface roughness and straining at grain-grain contacts, chemical heterogeneities on colloid surfaces, nanoparticle aggregation (Kasel et al., 2013a), hydrodynamic forces, and variations in
the pore-scale velocity (Liang et al., 2013a) can provide a viable explanation for hyperexponential RPs in the soil columns. The physicalblocking of NPs in dead-end pores or straining of NP heteroaggregatesare other possible explanations for retention of NPs in soil columns(Cornelis et al., 2013). Straining is also suggested to be a process thatcan explain hyperexponential retention proﬁles (Fig. 4) when most
AgNPs are retained in the upper ﬁrst centimeters of the columns.
However, straining is more important for relatively large particles oraggregates with larger drag coeﬃcients (Bradford and Torkzaban,2008).
The BTCs of AgNPs for saturated and unsaturated columns show no
signiﬁcant diﬀerence and they almost overlap (Fig. 3). Fang et al.
(2013) also reported that the presence of air under the unsaturated
conditions had only a limited eﬀect on the transport of TiO2 NPs at low
IS. The light microscope observations of Chen and Flury (2005) indicated that colloids did not adhere to the air–water interface underunsaturated conditions. Moreover, in the current study, the large hydrodynamic diameter of AgNPs (i.e., 157.59 nm) in comparison withthe thickness of the thin water ﬁlm (~50 nm) during steady-state waterﬂow conditions (Torkzaban et al., 2008) excluded the possibility of ﬁlm
straining under unsaturated conditions as suggested by Fang et al.
(2013).
The ﬁltration coeﬃcients (λf) and the Peclet numbers (Pe) are alsopresented in Table 4. It is expected that much larger λf values should beobserved in natural soil columns compared with the homogenous sandcolumns. The key role of soil structure and texture in the transport andretention of particles has been demonstrated in several studies (e.g.,aggregate and deposit on a silica surface. They reported that polymericcoatings could not necessarily stabilize AgNPs against deposition unlessthe collector surfaces are also coated with the polymer. The lower
mobility of AgNPs in the soil columns compared to the sand columns
can be explained by a high ratio of the surface area to the volume of the
ﬁne-grained soils, the mechanical straining of AgNPs, or by the enhanced availability of favorable attachment sites (Braun et al., 2015).
Moreover, repulsive interactions arising from the surfactant on the
AgNPs were more pronounced in the sand medium than in natural soils(Liang et al., 2013a).
The transport of AgNPs was highly retarded in comparison with theinert tracer (Br) in the TR soil (see Figs. 2b and 3b). The similar retardation-type behavior of engineered NPs has been previously reported(Torkzaban et al., 2010; Liang et al., 2013a; Kumahor et al., 2015).
Torkzaban et al. (2010) reported delays in the breakthrough ofquantum dot NPs (QDNPs) due to high initial rates of particle deposition. They suggested that a high diﬀusive mass transfer rate of QDNPs
from the bulk solution to the sand surfaces and the QDNPs mass transfer
to the unfavorable regions of the sand surfaces can explain this behavior. Also, coatings of the natural organic material (NOM) may result in
more hydrophobic AgNPs in soil (Kumahor et al., 2015). Hence, a reversible attachment process would occur and the BTCs would be observed with retardation.
Our results indicated that despite signiﬁcant diﬀerences in dispersivities and porosities between the two studied soils (seeTable 3), > 90% of AgNPs were recovered in the RPs of these soils andshapes of RPs were very similar (Fig. 4). In fact, the AgNPs retention in
the ZR soil was slightly stronger than in the TR soil, which may be
attributed to the smaller grain sizes and higher electrical conductivityof the ZR soil (see Table 1). Bradford et al. (2002, 2004) also reported adecreasing trend in eﬄuent colloid concentrations and increasing colloid retention in heterogeneous systems with decreasing median grain
size (d50).
In general, the higher retention of AgNPs in the soil columns compared to the sand columns can be attributed to the properties of thesoils, such as the presence of NOM, greater surface charges, and a wider
particle size distribution. Liang et al. (2013a,b) also observed lower
eﬄuent concentrations in a soil with smaller d50 in comparison to sand.
They suggested that soil heterogeneity decreased the energy barrier for
NP aggregation in comparison to the same homogeneous situation.
Filtration theory provides an explanation for this behavior because it
predicts that with a decrease in the grain size (or an increase in thespeciﬁc surface area), the mass transfer rate to the collector surface is
expected to increase (Liang et al., 2013a; Braun et al., 2015). Additionally, the presence of NOM and calcium carbonate in the alkaline
soils may have a stabilizing or destabilizing eﬀect on the AgNP retention in natural soils compared to sand. The soil organic matter exists as
solid particles (humins) or as dissolved compounds in the soil solution(fulvic and humic acids). Electrostatic attraction due to variable charges
on NOM surfaces can eﬀectively adsorb charged NPs (Peralta-Videa
et al., 2011), which can remove NPs to the solid phase. On the other
hand, the dissolved organic matter in soil may be sorbed on NPs surfaces and through charge alteration (reduction in the pHPZC) or stericforces may increase hydrophilicity of the surfaces (Espinasse et al.,2007), which may decrease aggregation of NPs and increase their mobility in natural soils (Peralta-Videa et al., 2011). However, due to thelack of information on the properties of NOM in the studied soils, their
speciﬁc contributions to the retention of AgNPs cannot be predicted.
Pore-water chemistry can aﬀect the mobility of AgNPs in soils (ElBadawy et al., 2010). The high activity of Ca2+ cations probably plays
an important role in AgNPs retention in the calcareous soils. Retentionof AgNPs is enhanced at higher IS due to compression of the electrostatic double layer and a decrease in the magnitude of the surface potentials of both NP and collector surfaces (Bradford et al., 2006). Previous studies have demonstrated that deposition phenomenon
enhanced with an increase in IS or cation valence due to96Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

Safadoust et al., 2011). However, in our study, λf is not signiﬁcantly
aﬀected by soil texture and saturation conditions (Table 4). Under saturated conditions, the λf values are larger in the ZR soil than in the TR
soil (an average of two replications; 30.32 ± 5.87 and36.50 ± 5.08 m−1 for the TR and ZR soils, respectively). Under unsaturated ﬂow conditions, a similar trend is observed (an average of
two replications; 29.48 ± 1.50 and 45.21 ± 1.94 m−1 for the TR andZR soils, respectively). It seems that the potential for a larger contact of
AgNPs with soil particles and adsorption sites helps to explain the larger
values of λf in the ZR soil columns. As mentioned above, the greater EC
could also increase the ﬁltration coeﬃcients as well as more retention
sites were present in this soil. Moreover, slight diﬀerences are observed
among the λf data for the two ﬂow conditions in the ZR soil. The
averaged λf under unsaturated ﬂow conditions (45.21 ± 1.94 m−1) islarger than under saturated ﬂow conditions (36.50 ± 5.08 m−1) in the
ZR soil. However, this diﬀerence is negligible in the TR soil
(30.32 ± 5.87 and 29.48 ± 1.94 m−1, respectively). This tiny diﬀerence in sandy loam soil may be explained by a weak structure or theoccurrence preferential ﬂow in this soil.
The pore water velocity is an important factor aﬀecting the NP ﬁltration in soils. A signiﬁcant power relationship was derived between
the ﬁltration coeﬃcient (λf) and the pore water velocity (v) using alldata (Fig. 5). The relation indicates that as the average pore watervelocity increases, AgNPs ﬁltration decreases, which is in agreementwith Safadoust et al. (2011) who reported that the ﬁltration coeﬃcientfor E. coli in soil columns increased as a result of a reduced ﬂow rate.
The data points in Fig. 5 may be divided into two groups; a group whichcorresponds to data for natural soils and another one (with very low λfvalues) which corresponds to data for sand. The nonlinear relation canalso be represented by two linear relations if we consider the twogroups separately. In other words, a linear relation between λf and v forthe soil columns would have a much greater slope than for the sandcolumns, indicating that the pore water velocity has a dominant eﬀect
on the AgNPs transport through natural soils.
The Peclet number (Pe) indicates a relative importance of the masstransport (advection) in comparison with diﬀusion (see Eq. (6)). According to the ﬁltration theory, the dominant mass transfer process forparticles smaller than 1 μm is the diﬀusion process (Braun et al., 2015).
Generally, Pe decreases faster with a decrease in the grain size andwater content (Table 4). For instance, Pe decreased from 170 for thesand columns to 2.4 and 1.6 for the TR and ZR soil columns in saturated
ﬂow conditions, respectively. The corresponding Pe values for unsaturated ﬂow also decreased from 22 for the sand columns to 6.7 and
1.9 for the TR and ZR soil columns, respectively. These results indicatethat for the sand columns the role of diﬀusion/dispersion relative toadvection is much more signiﬁcant under unsaturated conditions.
Braun et al. (2015) suggested that an increased deposition of AgNPs at
low ﬂow rates is related to an increasing impact of diﬀusion becausesome soil pores are empty and the ability of soil to conduct water decreases. It seems that for undisturbed soils, saturation conditions haveno remarkable eﬀect on the Pe value (Table 4). This may be due to nearsaturated conditions used in this study.
3.4. Modeling AgNP transport and retention in saturated and unsaturated
columns
Four models (M1 to M4) based on the original attachment-detachment model were ﬁtted to the AgNP transport (BTCs) and retention(RPs) data. Table 5 summarizes the values of the ﬁtted parameters formodels M1, M2, M3, and M4, as well as statistical indices indicating thegoodness of ﬁt such as the coeﬃcient of determination (R2), RMSE, andAIC. The AIC (Eq. (5)) is a criterion to select the best model with thelowest RSS and the lowest number of ﬁtting parameters (i.e., K); thebest model is the model with the smallest AIC. All four model formulations (M1, M2, M3, and M4) described the AgNPs transport andretention quite well with R2 > 0.80 (Table 5).
A good agreement between measured and modeled BTCs was obtained using the M1 model (i.e., a conventional attachment-detachment
model) for the sand columns. However, the BTCs for the natural soilcolumns were not successfully simulated using the M1 model because offavorable deposition sites in the soils with high clay and calcium carbonate contents (Table 1). Also, for undisturbed soil columns, a decrease in the colloid concentration with depth simulated with the M1
model was generally steeper than that shown by the experimental data.
The smallest AIC values for soil columns were obtained for the M2 or
M4 models (Table 5), indicating that the models that included theLangmuirian blocking term provided the best agreement with the observed data. However, since experimental RPs were hyperexponential
with distance, indicating that the retention coeﬃcient exhibited adepth-dependency, and since large values of SE were observed for theM2 parameters, it is unlikely that this model (i.e., M2) is the best model
for simulating the AgNPs behavior in the soil columns. The improved
description may be attributed to the increased ﬂexibility (i.e., moreadjustable parameters) of the M2 model as also mentioned by Bradford
et al. (2003).
The M3 model described the experimental data (BTCs and PRs)
fairly well. However, some deviations were observed between the experimental and simulated RPs. Model M3 tended to underestimate thehigh concentrations near the column inlet. On the other hand, with the
exception of the second saturated columns of the ZR soil, the smallest
R2, and highest RMSE were obtained using this model.
Finally, since model M4 includes a depth-dependency in the retention coeﬃcient, the spatial distributions of colloids were more consistent with the M4 simulations than with the other models when both
BTCs and RPs were considered. The values of R2 for the M4 model werelarger than 0.92 (see Table 5).
Modeling of each replication of a particular soil column experimentindicates that the transport parameters are highly variable (Table 5).
However, high retention of NPs in all replications is pronounced (seeTable 4 and Fig. 4). Cornelis et al. (2013) also reported highly variabletransport parameters and mass recoveries for AgNPs in natural soilcolumns. Greater physical and chemical heterogeneities of intact soilcolumns (i.e., a pore size distribution and pore continuity) could explain such variability compared to homogenous sand columns(Table 5).
Symmetrical BTCs of AgNPs for the sand column experiments underboth saturated and unsaturated ﬂow conditions, in which no data wasavailable on RPs, could be best ﬁtted using the conventional attachment-detachment model (M1) (R2 of 0.987 and 0.972, respectively) (seeFig. 3a and Table 5). Accordingly, other researchers also reported good

Filtration cofficient (m-1)

60
50
y = 4.282x-0.969
R² = 0.9272

40
30
20
10
0
0

1

2
3
Pore water velocity (cm min-1)

4

5

Fig. 5. Overall relationship between the ﬁltration coeﬃcient (λf) and the pore watervelocity (v).

97

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

Table 5
Parameters obtained by ﬁtting diﬀerent transport models to the experimental AgNPs breakthrough curves and retention proﬁles using HYDRUS-1D.
Flow conditions

Sample

Model

RMSE

AIC

β

R2

katt
h−1

Saturated

Unsaturated

Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2
Sand
TR soil-1
TR soil-2
ZR soil-1
ZR soil-2

M1
M1
M1
M1
M1
M2
M2
M2
M2
M2
M3
M3
M3
M3
M3
M4
M4
M4
M4
M4
M1
M1
M1
M1
M1
M2
M2
M2
M2
M2
M3
M3
M3
M3
M3
M4
M4
M4
M4
M4

0.01650.180
0.08420.028
0.02640.0183
0.037
0.082
0.013
0.02980.01850.954
0.137
0.07290.062
0.017
0.01510.08290.024
0.02492.16 × 10−2
0.062
0.055
0.028
0.017
0.023
0.052
0.041
0.013
0.0166
0.022
0.104
0.102
0.08090.0845
0.22
0.055
0.042
0.02060.0165−417.7−222−271.3−725−1133−405.1
−425
−271
−1358
−713.5
−406
−506
−218
−533.2−864.9−414.4−542.3−270.9−755.1−1148−459.2
−416
−433
−671
−761
−449
−440.2−475.2−806.8−767.6−459−338.5−341.9−471.7−463.5−456.6−430.4−471.2−726.7−763.4

0.987
0.983
0.960
0.959
0.922
0.984
0.968
0.965
0.983
0.956
0.983
0.940
0.849
0.887
0.841
0.986
0.986
0.961
0.964
0.921
0.973
0.975
0.937
0.972
0.973
0.976
0.936
0.969
0.988
0.979
0.972
0.949
0.818
0.897
0.868
0.972
0.968
0.968
0.962
0.980

0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765

0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765

4.30 × 10−2
52.96
11.36
7.328
12.41
0.042
110.1425.50
123.925.78
0.399
338.72689.7
637.51628.191.53
4013.43026.41633.52839.5
1.15 × 10−2
7.35
8.69
11.35
9.21
5
35.22
76.47
103.6413.07
0.416
128.81200.33368.88296.380.440
1118.87517
1400.12874.6SE
katt

0.33 × 10−2
4.21
2.96
0.456
0.819
0.36 × 10−2
33.53
13.73
11.35
0.403
0.13
990.11
244.89371.35536.140.12
288.671285.3140.57304.250.28 × 10−2
2.85
2.494
0.858
0.509
2.286
19.36
42.96
10.56
1.33
0.099
567.92
182.71319
245.360.287
514.97225.45115
257.7

Smax/C0cm3 g−1SE
Smax/C02596.2
5.88
2.50
3.043
1.0 × 10+5

3.62 × 10−14
0.724
0.813
0.04
4.11 × 10+7

0.33 × 10+6
11.33
2.085
3.59
182.490.34 × 10−18
0.423
0.245
0.227
9.799

0.765
2.02
1.606
2.603
4.62

0.239
0.204
0.0706
0.045
0.983

3.21
2.09
1.60
8.03
2.33

37.03
0.284
0.05
0.858
0.06

Diﬀerent models were used in simulations: attachment and detachment (M1); attachment, detachment, and blocking (M2); depth-dependent retention (M3); and blocking combined withdepth-dependent retention (M4). katt - ﬁrst-order attachment rate, β - empirical parameter, Smax - the maximum solid phase concentration of deposited AgNPs, AIC - Akaike Information
Criterion, RMSE - root mean square errors, and SE - standard error.

ﬁts for the NP transport in the soil and sand columns using a similar
model (Cornelis et al., 2013; Liang et al., 2013a,b; Braun et al., 2015).
Low attachment on the sand surfaces, as quantiﬁed by a small value ofkatt, explains the high eﬄuent concentrations. Liang et al. (2013a) reported that when katt is too small, the breakthrough occurs with noretardation and the eﬄuent concentrations slowly increase with time as
the favorable retention locations are gradually ﬁlled. Overall, theblocking eﬀects were not observed to play a signiﬁcant role in thequartz sand columns.
Lower values of katt for the sand columns compared to the soilcolumns may be attributed to the eﬀect of a collector particle size on
the AgNPs transport and retention (Table 5). However, the same trend
was not observed between the two soil columns. The katt values for the
TR soil with a higher median grain size (see Table 1) were larger thanthe corresponding values for the ZR soil. However, Smax/Co values for
the ZR soil were higher than the corresponding values for the TR soil
(Table 5).
Detachment is mostly interpreted by the deposition of AgNPs in thesecondary minimum and their subsequent removal due to changes inhydrochemical conditions (Braun et al., 2015). In our study, experimental data was described only as an attachment process, while assuming that detachment was negligible. A detachment of nanoparticles

during deposition experiments is almost always negligible (Liang et al.,2013a,b). There is nearly no secondary energy minimum in their interactions with surfaces because of their small size (Petosa et al., 2010).
Moreover, detachment would manifest itself in the BTC as tailing,which was not very pronounced in soil columns. Kumahor et al. (2015)
suggested that the huge diﬀerence between katt and kdet indicates fastattachment to the SWI and slow detachment.
The model simulations conﬁrm that a Langmuir blocking model (Eq.
(4)) is suﬃcient to closely ﬁt the behavior of RPs in the soil columns.
Overall, it may be concluded that attachment of AgNPs is irreversible inmany cases. This ﬁnding is consistent with the experimental results, inwhich high retention and very little recovery (< 1%) of AgNPs in theeﬄuent were observed under both ﬂow conditions (see Fig. 3b,c andTable 4).
Retarded BTCs can be described using ﬁtted parameters katt andSmax/Co in Eqs. (3) and (4), which are related to the retention rate andthe AgNPs sorption capacity, respectively (Liang et al., 2013a). Lianget al. (2013a) suggested that a high value of katt produces a complete NP
retention until Smax/Co is ﬁlled. Consequently, when the values of kattand Smax/Co are large, more retarded BTCs are expected (Liang et al.,2013a). Hence, the stronger AgNP retention in the ZR soil comparedwith the TR soil can be explained by an increase in the ﬁtted values of98

Geoderma 322 (2018) 89–100

S. Rahmatpour et al.

Smax/Co in the ZR soil (Table 5), which occurs due to the enhancementof the eﬀects of nanoscale heterogeneities and a decreased grain size,
which is in agreement with Liang et al. (2013a,b) and Sagee et al.
(2012). On the other hand, greater katt for the TR soil when comparedwith the ZR soil may be attributed to the other soil physical properties
such as soil structure and dead-end and/or non-continuous pores,
which were probably formed in the weakly-structured TR soil (see the
MWD values in Table 1).

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4. Conclusions
1) Results of this study have several implications for the understandingof the transport and retention of AgNPs in the saturated and unsaturated sand and soils. Quartz sand surfaces are unfavorable for
the AgNP deposition and result in a high mobility of AgNPs throughthe sand columns. Moreover, the limited transport of PVP-stabilized
AgNPs in the undisturbed soil experiments suggests that AgNPs rapidly interact with the natural soils. The high retention of AgNPs in
soil may be a result of favorable deposition of AgNPs on soil colloids
and/or straining of AgNPs enhanced by the formation of heteroaggregates.
2) The eﬀects of soil texture and a degree of water saturation on thetransport and retention of AgNPs in soil have been investigated.
These variables, by aﬀecting the hydrodynamic factors, distribution
and continuity of pores, deposition, ﬁltration and sorption, complicate the description of the AgNPs transport in the soil. The ZR soil
with higher surface area ﬁlters AgNPs more than the TR soil does.
Despite its lower surface area and smaller Freundlich coeﬃcient, theretention of AgNPs in the TR soil is not signiﬁcantly diﬀerent fromthe more structured ZR soil. In addition, the presence of air underunsaturated conditions has only a small eﬀect on the retention andtransport of AgNPs in most experiments.
3) The one-site kinetic attachment model provides a good descriptionof the retention proﬁles (RPs) of AgNPs under both saturated andunsaturated ﬂow conditions. However, the model ﬁtting parameters
could not be successfully used to explain the BTCs of AgNPs undervarious saturation conditions in the natural soil columns, partly due
to very small values of eﬄuent concentrations. The results demonstrate that AgNPs transport studies in natural soils need to consider
retarded BTCs, hyperexponential RPs, and colloid associations,which are factors commonly neglected in repacked sand column
experiments.
4) The high retention and limited mobility of AgNPs in natural calcareous soil systems under saturated or unsaturated conditions observed in this study suggest that there is only a low risk of oﬀ-sitetransport vertically into the subsurface or laterally into nearby sites.
However, further research is needed to understand reactions andtransformations which may re-mobilize AgNPs in the soils. A morerobust model is also required to consider the transport and deposition behavior of AgNPs.
Acknowledgments
We expressed our appreciation to the Isfahan University ofTechnology for the ﬁnancial support of the research.
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