Journal of Hydrology 625 (2023) 129909

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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

Research papers

Divalent cation contributions to the co-transport and deposition offunctionalized multi-walled carbon nanotubes in porous media in thepresence of bentonite or goethite nanoparticles: Experiment and simulation
Miaoyue Zhang a, b, Scott A. Bradford c, Erwin Klumpp d, Jiří Šimůnek e, Yijun Mo a,
Kengbo Ding a, Quan Wan b, f, Shizhong Wang a, Chao Jin a, b, *, Rongliang Qiu a, b, f, *aSchool of Environmental Science and Engineering, Guangdong Provincial Key Laboratory of Environ. Pollut. Control and Remediation Technology, Sun Yat-sen
University, Guangzhou 510006, Chinab
Guangdong Laboratory for Lingnan Modern Agriculture, Guangzhou 510642, Chinac
USDA, ARS, Sustainable Agricultural Water Systems (SAWS) Unit, 239 Hopkins Road, UC Davis, Davis, CA 95616, USAd
Agrosphere Institute (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, GermanyeDepartment of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USAf
Guangdong Provincial Key Laboratory of Agricultural & Rural Pollution Abatement and Environmental Safety, College of Natural Resources and Environment, South
China Agricultural University, Guangzhou 510642, China

A R T I C L E I N F O

A B S T R A C T

This manuscript was handled by Corrado Cor­
radini, Editor-in-Chief, with the assistance ofSimone Di Prima, Associate Editor

This work investigates the influence of cation type (Ca2+ as compared to K+) on the co-transport and depositionof functionalized multi-walled carbon nanotubes (MWCNTs) with negatively (bentonite nanoparticles, BNPs) or
positively (goethite nanoparticles, GNPs) charged natural nanoparticles under the same ionic strength(IS = 1 mM) conditions. In packed column tests with quartz sand (QS), the co-transport of MWCNTs was slightly
increased by BNPs and inhibited by GNPs in both CaCl2 and KCl solutions, whereas the co-transport of BNPs or
GNPs was facilitated by MWCNTs in both solutions. However, the co-transport of MWCNTs in the presence of
BNPs or GNPs exhibited a different dependency on the cation type in quartz crystal microbalance with dissi­
pation (QCM-D) tests. No deposition of MWCNTs and BNPs was observed in QCM-D studies in the presence ofKCl, while enhanced deposition of MWCNTs and GNPs occurred in this same solution. In contrast, the depositionof both MWCNTs and BNPs or MWCNTs and GNPs increased in QCM-D in the presence of CaCl2. In both column
and QCM-D studies, Ca2+ exhibited a more significant impact on co-transport than K+, especially for MWCNTs
with GNPs than BNPs. Results from molecular dynamic simulations, aggregation studies, and interaction energy
calculations indicate that non-DLVO interactions (e.g., H-bonding and cation-π interaction) between two nano­particles (MWCNTs with BNPs or GNPs) played a non-negligible role in interpreting the deposition and cotransport in the presence of the divalent cation Ca2+. Mathematical modeling of breakthrough curves andretention profiles and aggregation results suggest that both straining and competitive blocking were enhanced
and played dominant roles in the co-transport of MWCNTs in the presence of BNPs or GNPs in QS, especially inthe presence of Ca2+. This work sheds novel insights on the contribution of divalent cations to interactions
between two colloids and their co-transport in porous media. This information is needed to assess the envi­
ronmental fate and risks of engineered nanoparticles (ENPs) and natural nanoparticles in aquatic and soil en­
vironments with abundant divalent cations.

Keywords:
Multi-walled carbon nanotubes
Goethite and bentonite nanoparticles
Non-DLVO interaction
Divalent cations
And competitive blocking

1. Introduction
Carbon nanotubes (CNTs), which are allotropes of carbon with acylindrical-shaped nanostructure (Iijima, 1991), have been employed innumerous commercial applications (Gohardani et al., 2014), including
electrical cables and wires (Janas et al., 2014), solar cells (Guldi et al.,2005), radar absorption (Lin et al., 2008), and adsorbents for environ­mental remediation and water treatment (Camilli et al., 2014; Li et al.,* Corresponding authors at: School of Environmental Science and Engineering, Guangdong Provincial Key Laboratory of Environ. Pollut. Control and Remediation
Technology, Sun Yat-sen University, Guangzhou 510006, China.
E-mail addresses: jinchao3@mail.sysu.edu.cn (C. Jin), eesqrl@mail.sysu.edu.cn (R. Qiu).
https://doi.org/10.1016/j.jhydrol.2023.129909
Received 31 March 2023; Received in revised form 13 June 2023; Accepted 3 July 2023
Available online 7 July 2023
0022-1694/© 2023 Elsevier B.V. All rights reserved.

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

2012; Mauter and Elimelech, 2008; Pan and Xing, 2012; Zhang et al.,2010). Such widespread applications of CNTs will undoubtedly result intheir release into the subsurface and water environment. The cylindrical(non-spheric) shape of multi-walled CNTs (MWCNTs) exhibited repre­
sentative transport behavior in porous media and interactions withmedia surfaces (Shen et al., 2018). Current studies have investigated theco-transport behavior of CNTs in porous media under various physicaland chemical conditions, including: input concentration of soil nano­particles, surfactant, organic matter, and contaminants (Tian et al.,2012; Yang et al., 2013; Zhang et al., 2022; Zhang et al., 2019; Zhang
et al., 2017b). However, information on the co-transport of CNTs andnatural colloids, interactions of CNTs with natural colloids, and thepotential for colloid-facilitated transport of CNT is still limited.
Cations such as Ca2+ and K+ are ubiquitous in the water and soil
systems due to rainfall, irrigation, fertilization, or artificial groundwater
recharge. Previous studies indicated that divalent cations played a moresignificant role in inhibiting colloid transport than monovalent cations.
First, the double layer thickness and magnitude of the surface potential
are decreased in the presence of divalent cations (Elimelech et al.,1998). Second, adsorbed divalent cations can create nanoscale chemical
heterogeneity on the solid surface that can neutralize or reverse thesurface charge at specific locations (Torkzaban et al., 2012). Third,
divalent cations can produce cation bridges between negatively charged
sites on the surface of two colloids or colloids and a collector (Torkzaban
et al., 2012). Forth, heteroaggregation and straining were enhanced in
the presence of divalent cations (Zhang et al., 2017a; Zhu et al., 2022).
Clay particles (e.g., bentonite and kaolinite) and iron oxides (e.g.,goethite and hematite) are typically the most abundant natural inor­
ganic colloids or nanoparticles in the water and soil. Since they can havecharge heterogeneities on their surface and interact with other sub­stances (e.g., engineered nanoparticles, heavy metals), clay particles andiron oxides have been demonstrated to have a high affinity for othercolloids and can influence their transport behavior (Syngouna andChrysikopoulos, 2013; Syngouna et al., 2017; Yang et al., 2012). Lianget al. (2013) and Zhang et al. (2017a) provided further experimental
evidence that the release of soil colloids with ionic strength (IS) reduc­tion and cation exchange can facilitate the transport of silver nano­particles and CNTs, respectively. Therefore, knowledge of theinteraction and association between engineered nanoparticles (ENPs)
and natural colloids/nanoparticles is needed to better understand thefate of ENPs in water and soil. Furthermore, most previous studies(Chrysikopoulos et al., 2017; Li et al., 2014) mainly focused on the cotransport of negatively charged clay particles and ENPs under unfa­
vorable conditions for their retention, e.g., in quartz sand under ambient
pH values. In this case, competitive blocking of deposition sites has beenreported to contribute to the enhanced transport of colloids under cotransport conditions (Cai et al., 2016; He et al., 2018). However, natu­
ral water and soil environments possess chemical heterogeneity underambient pH conditions, which includes both negatively charged col­loids, such as clay particles, and positively charged colloids, such as ironoxides. In addition, Derjaguin–Landau–Verwey–Overbeek (DLVO) the­ory is extensively used to interpret surface interactions between two
nanoparticles (e.g., ENPs and natural nanoparticles), and/or porous
media, which are used to assess environmental risk and transport
behavior of ENPs. However, a few recent studies indicated that ENPs can
exhibit different aggregation or transport behaviors from DLVO theory(Liu et al., 2017; Zhang et al., 2020). For example, our previous study on
the co-transport of CNTs in the presence of both negatively and posi­
tively charged natural nanoparticles (BNPs and GNPs, respectively)
under monovalent cation conditions in porous media indicated that nonDLVO interactions between CNTs and BNPs or between CNTs and GNPs
played a significant role during their co-transport. The relative impor­tance of cation type on the co-transport, deposition, and surface in­teractions (e.g., non-DLVO interaction) of ENPs in the presence of
natural colloids/nanoparticles is therefore expected although thesecomplexities have not yet been fully resolved.

The main objective of this study is to better understand the roles ofnegatively (BNPs) and positively (GNPs) charged nanoparticles (4 mg
L− 1) on the transport and deposition of functionalized MWCNTs (1 mg
L− 1) in the presence of monovalent (IS = 1 mM KCl) and divalent(IS = 1 mM CaCl2) cations in porous media. Breakthrough curves andretention profiles for MWCNTs, BNPs, and GNPs were determined incolumn experiments. Numerical models were employed to simulate
their co-transport and competitive blocking behaviors. It should be
mentioned that similar co-transport and DLVO calculations of MWCNTs
in the presence of BNPs or GNPs at an IS = 1 mM KCl have been pre­viously discussed by (Zhang et al., 2022). While data presented in thecurrent paper exhibit similar trends to our earlier paper, this informa­tion is used for a novel purpose to identify the relative contribution ofdivalent cations. In addition, other aggregation experiments, quartz
crystal microbalance with dissipation (QCM-D), batch experiments, andmolecular dynamic (MD) simulations were conducted to further inves­tigate the deposition and associations of BNPs-MWCNTs or GNPsMWCNTs. Results provide valuable insight into the roles of natural
nanoparticles in facilitated or inhibited transport and deposition of
MWCNTs under divalent cation conditions. This knowledge is essential
to help researchers better design their filtration system, optimize themaintenance strategies, and effectively quantify the risk of ENPs while
divalent cations are available.
2. Materials and methods
2.1. Materials
Radioactively (14C) labeled MWCNTs (Bayer Technology Services
GmbH, Leverkusen, Germany) with a specific radioactivity of
3.2 MBq mg− 1 and a specific density of 1.641 g cm− 3 (Pauluhn, 2010)
were used in this study. The median diameter and length of function­
alized MWCNTs were 10–15 and 200–1000 nm, respectively. The sur­face of MWCNTs was functionalized (e.g., carboxylic groups) to enhancetheir stability. BNPs and GNPs were prepared from bentonite andgoethite colloids (Sigma-Aldrich Chemie GmbH, Munich, Germany).
BNPs had a diameter of 5–200 nm, and GNPs had a diameter of
5–120 nm and a length of 60–800 nm. More information on the syn­thesis, functionalization, and preparation of MWCNTs, BNPs, and GNPs
has been given in previous studies (Kasel et al., 2013; Zhang et al.,2022).
Suspensions of 14C-labeled MWCNTs (1 mg L− 1) with different BNPs
(0 and 4 mg L− 1) or GNPs (0 and 4 mg L− 1) concentrations at an
IS = 1 mM CaCl2 (molar concentration 0.33 mM L− 1 CaCl2) or IS = 1 mM
KCl (molar concentration 1 mM L− 1 KCl) were prepared and ultra­
sonicated 15 min at 65 W. The input concentrations of MWCNTs, BNPs,
and GNPs, as well as the IS = 1 mM CaCl2 and KCl, were selected basedon the preliminary aggregation experiments and high accuracy formeasurement (data not shown). All the suspensions of MWCNTs and/or
natural nanoparticles (BNPs or GNPs) were ultrasonicated again for an
additional 10 min before the experiments. The pH (Mettler Toledo
MP230 pH meter) of these suspensions was adjusted to 5.4 by incre­
mentally adding HCl or NaOH.
The zeta potentials and hydrodynamic diameters of the MWCNTs
suspensions at different concentrations of BNPs or GNPs (0 and 4 mg
L− 1) in IS = 1 mM CaCl2 were measured using a Zetasizer Nano (Malvern
Instruments GmbH, 71,083 Herrenberg, Germany) immediately aftersuspension preparation. The total interaction energies (Φ) between aplanar quartz surface and a spherical colloid with similar properties to
MWCNTs in the presence of BNPs or GNPs in IS = 1 mM CaCl2 solution
were calculated based on the approach of (Bradford and Torkzaban,2013). More details are given in Section S1 of the Supporting Informa­tion (SI).

2

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

2.2. Batch experiments(PerkinElmer, Rodgau, Germany). Concentrations of BNPs or GNPs in
effluent samples were determined as follows: 1 mL of effluent sample
was added to 1 mL aqua regia, digested for 30 min at 70 ℃, and Fe andAl concentrations were determined using an inductively coupled plasma
mass spectrometry (ICP-MS, PerkinElmer, NexIon 350D, USA) (Zhang
et al., 2022). The release of Al and Fe ions by BNPs or GNPs wasdetermined and found to be neglected in the time frame of the experi­ments performed. The BTCs of MWCNTs, BNPs, and GNPs are plotted as
normalized effluent concentrations (C/Co; where Co is the influent
concentration) versus pore volumes (PVs).
The retention profiles (RPs) of MWCNTs, BNPs, and GNPs were
determined following the excavation of the quartz sand in the packed
column in 1 cm increments. The sands were then dried and crushed.
Triplicate samples of approximately 0.5 g sand were combusted using a
biological oxidizer at 900 ◦ C (OX 500, R.J. Harvey Instrumentation
Corporation, Tappan, NY, USA) and measured by LSC to determine theconcentrations of MWCNTs on the sand. Triplicate 2 g samples of sandwere added to 4 mL aqua regia and digested for 30 min at 70 ℃ todetermine the concentrations (Al and Fe) of BNPs or GNPs in the solid
phase by ICP-MS. The RPs are given as normalized solid-phase con­centration (S/Co) as a function of distance from the column inlet. All theexperiments were replicated and exhibited good reproducibility. A
summary of the experimental conditions is provided in Table 1.
The net mass of MWCNTs that was retained due to BNPs or GNPs (rC/S) in QS at IS = 1 mM CaCl2 or KCl were quantified to evaluate mutual
contributions during their co-transport. rC/S was calculated using Eq.
(Adamczyk et al., 1994) as:

Batch experiments were conducted under quasi-equilibrium condi­
tions (Zhang et al., 2016) in IS = 1 mM CaCl2 solution using BNPs or
GNPs with MWCNTs (OECD, 2006; Zhang et al., 2022). The adsorptionof Ca2+ (IS = 0–5 mM) onto MWCNTs (1 mg L− 1) in the presence of BNPs
or GNPs (4 mg L− 1) was also determined in batch studies. The binding
energies between MWCNTs (1 mg L− 1) and BNPs (4 mg L− 1), and be­
tween MWCNTs (1 mg L− 1) and GNPs (4 mg L− 1) in IS = 1 mM CaCl2
were calculated by molecular dynamics (MD) simulations. More detailsof batch experiments and MD simulations are provided in sections S2and S3 of the SI, respectively.
2.3. Deposition and aggregation experiments
The deposition of MWCNTs (1 mg L− 1) in the presence and absenceof 4 mg L− 1 BNPs or GNPs under different cation types (IS = 1 mM CaCl2
or KCl) was quantified using a QCM-D system (Q-Sense Explorer, Biolin
Scientific AB, Sweden) with a crystal sensor (SiO2, QSX 303). QCM-D isconducted on a plate medium, not a porous medium, which has beenused to investigate the situ interactions between nanoparticles andmedia surfaces (Chen et al., 2016; Liu et al., 2012). The same flow ve­
locity as the column experiments (Darcy velocity ~ 0.7 cm min− 1) wasused in the QCM-D at room temperature using a peristaltic pump
(REGLO Digital ISM 596, ISMATEC, Switzerland) (Jin et al., 2022; Jinet al., 2021). MWCNT and BNP, and MWCNT and GNP suspensions were
either mixed by ultrasonication or not mixed before injection into the
QCM-D to further investigate their mutual interactions during deposi­tion. Note that the mixed system has more contact time between two
nanoparticles (MWCNTs with BNPs or GNPs) than the no mixed system.
The aggregation kinetics of MWCNTs (1 mg L− 1) in the presence andabsence of 4 mg L− 1 BNPs or GNPs at IS = 1 mM CaCl2 or KCl were
determined by time-resolved DLS measurements. All suspensions were
ultrasonicated before initiating aggregation experiments. Next, 1 mL
suspension was then transferred to the DLS cell to monitor changes in
the hydrodynamic diameter of MWCNTs with/without BNPs or GNPs
every 30 s for 40 min. All the QCM-D and aggregation experiments werereplicated and exhibited good reproducibility.

rC/S =

ΔrC
rS

[1]

where ΔrC is the difference (between co-transport and the corresponding
single-specie transport) in the retained mass of MWCNTs in the presence
and absence of BNPs or GNPs. rS is the injected mass of BNPs or GNPs.
2.5. Numerical modeling
A modified version of the HYDRUS-1D computer code (Šimůnek
et al., 2008) was employed to simulate both the transport and retentionof MWCNTs, BNPs, and GNPs in quartz sand. The mass balance equa­tions in the aqueous and solid phases for MWCNTs are given as:
(
)
∂CC ∂
∂CC
∂(vCC )
ρ[2]=D−
− ψ C kaC CC + b kdC SC
∂z
∂t
∂z
∂z
θ

2.4. Co-transport experiments
Single-species transport and co-transport experiments were con­ducted using a stainless-steel saturated column (3 cm inner diameter and12 cm length) with uniform quartz sand (QS, median grain size of
240 µm). QS was purified following a protocol in the literature (Kasel
et al., 2013) and wet-packed in the column. A pump (MCP V 5.10,
Ismatec SA, Glattbrugg, Switzerland) was used to inject backgroundelectrolyte solution and MWCNTs and/or natural nanoparticles (BNPs or
GNPs) suspensions into the column on the inlet side with the flow di­rection from the bottom to the top at a constant Darcy velocity of
0.71–0.72 cm min− 1 (Zhang et al., 2019). The columns were initiallyequilibrated with approximately 30 pore volumes (PVs) of backgroundelectrolyte solution (IS = 1 mM CaCl2 or KCl solution). Afterward, a nonreactive (conservative) tracer experiment (1 mM Br− ) was conducted tocharacterize the column’s hydraulic conditions. Concentrations of bro­mide in the effluent were collected using a fraction collector (FoxyJr.®,
Teledyne Isco Inc., Lincoln, USA) every 30 s (e.g., approximately 2.5 mL
per vial) and determined using a high-performance liquid chromato­graph (STH 585, Dionex, Sunnyvale, CA, USA) equipped with a UV
detector (UV2075, Jasco, Essex, UK).
Transport experiments using MWCNTs (0 and 1 mg L− 1) and natural
nanoparticles (0 and 4 mg L− 1 BNPs or GNPs) in electrolyte solution at
an IS = 1 mM CaCl2 or KCl were performed similarly to the conservative
tracer. The suspension of MWCNTs in the presence of BNPs or GNPs was
mixed and sonicated before injection into column tests. The concen­
trations of MWCNT in the effluent were determined using the LSC∂(ρb SC )= θψ C kaC CC − ρb kdC SC∂t[3]

where CC [N L− 3, N denotes the number of MWCNTs] is the concen­
tration of MWCNT in the aqueous phase, t is time [T, T denotes timeunits], D [L2T− 1, L denotes units of length] is the hydrodynamic
dispersion coefficient of the column experiment, v [L T− 1] is the porewater velocity, z [L] is the distance from the column inlet, θ [–] is thevolumetric water content, ψ C [–] is a dimensionless function to accountfor time- and depth-dependent retention, kaC and kdC [T− 1] are the firstorder retention coefficient and detachment coefficient, respectively, ρb[M L− 3, M denote units of mass] is the sand bulk density, and SC [N M− 1]
is the concentration of MWCNT in the solid phase. The first and second
terms on the right-hand side of Eq. (Akaike, 1974) account for thedispersive and advective transport of MWCNTs, respectively. The thirdand fourth terms in Eq. (Akaike, 1974) are used to describe retention andrelease to/from the solid phase, respectively. The value of ψ C is given inthis work as:
)(
)− β
(
S +Γ S
d50 + zψ C = 1 − C maxC S
(4)
d50
SC

3

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Journal of Hydrology 625 (2023) 129909

Table 1
Experimental conditions and mass recoveries from effluent for all column experiments.
RC

RS

Co (C)[mg L− 1]

Co (B)[mg L− 1]

Co (G)[mg L− 1]q[cm min− 1]

IS
[mM]

Por.

Me_C
[%]

Ms_C
[%]

Mt_C
[%]

Me_S
[%]

Ms_S
[%]

Mt_S
[%]

1.1
NA
NA
1.13
1.18
1.09
NA
NA
1.12
1.18

NA
1.17
1.33
1.26
1.35
NA
1.09
1.21
1.12
1.18

1
0
0
1
1
1
0
0
1
1

0
4
0
4
0
0
4
0
4
0

0
0
4
0
4
0
0
4
0
4

0.71
0.71
0.71
0.72
0.71
0.72
0.72
0.71
0.72
0.71

1 Ca2+
1 Ca2+
1 Ca2+
1 Ca2+
1 Ca2+
1 K+
1 K+
1 K+
1 K+
1 K+

0.43
0.44
0.45
0.46
0.45
0.43
0.44
0.44
0.43
0.43

0.1
NA
NA
0.4
0.03
16.2
NA
NA
19.6
1.0

98.5
NA
NA
95.5
100.5
82.4
NA
NA
79.1
102.3

98.6
NA
NA
95.9
100.6
98.6
NA
NA
98.7
103.3

NA
5.4
1.2
12.1
3.5
NA
26.7
8.7
30.3
19.9

NA
96.4
102.2
82.7
98
NA
67.5
85.1
65.5
78.8

NA
101.9
103.4
94.8
101.5
NA
94.2
93.8
95.8
98.8

NA denotes not applicable. RC is the retardation factor of MWCNTs, and RS is the retardation factor of BNPs or GNPs. Co (C), Co (B), and Co (G) are the input concentrationsof MWCNTs, BNPs, and GNPs, respectively. q is the Darcy velocity. Por. is the porosity. Me_C, Ms_C, and Mt_C are the effluent percentage, the retained percentage, and thetotal percentage of MWCNTs recovered from the column experiment, respectively. Me_S, Ms_S, and Mt_S are the effluent percentage of BNPs or GNPs recovered from thecolumn experiment. The ionic strength is 1 mM CaCl2 or KCl. The grain size of the QS is 240 μm.

where SS [NS M− 1; NS denotes the number of BNP or GNP] is the solid− 1phase concentration of the BNPs or GNPs, Smax
C [N M ] is the maximum
solid phase concentration of MWCNTs, ΓC [–] is the area conversion
factor between BNPs and MWCNTs, or between GNPs and MWCNTs, d50[L] is the median sand grain diameter, and β [–] is an empiricalparameter that controls the depth-dependency of the retention rate co­efficient. The value of β was set to 0.765 for MWCNTs, BNPs, and GNPs

based on our previous study with MWCNTs in quartz sand (Zhang et al.,2016; 2017a). The standard HYDRUS-1D code was modified to consider
competitive blocking described by Eq. (Bradford et al., 2017).
Similar to the MWCNT, the mass balance equations in the aqueousand solid phases for the BNPs or GNPs are given in this model as:

Fig. 1. Aggregation of MWCNTs (1 mg L− 1) in the presence of BNPs or GNPs (4 mg L− 1) in 1 mM CaCl2 (a) or KCl (b); QCM-D frequency (Δf) and dissipation (ΔD)
shift of 3rd overtone as a function of attachment time on silica surface (c-d);Δf of MWCNTs (1 mg L− 1) in the presence of BNPs or GNPs (4 mg L− 1) in 1 mM CaCl2 orKCl (c), Δf (d) and ΔD/Δf (e and f) of MWCNTs (1 mg L− 1) in the presence of BNPs or GNPs (4 mg L− 1) in 1 mM CaCl2 under mixed (ultrasonication after mixed) andno mixed MWCNTs with BNPs or GNPs suspension (ultrasonicated) before injection into QCM-D;
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M. Zhang et al.

(

Journal of Hydrology 625 (2023) 129909

)

∂CS ∂
∂CS
∂(vCS )
ρ=D−
− kaS ψ s Cs + b kdS SS
∂z
∂t
∂z
∂z
θ

(5)

∂(ρb SS )= θkaS ψ S CS − ρb kdS SS∂t(6)

that interactions of MWCNTs with BNPs or GNPs were continuously
enhanced, especially for GNPs.
The zeta potentials and hydrodynamic diameters (Table S1) of the
MWCNT suspensions in the presence of BNPs or GNPs were measured tobetter assess the potential effects of MWCNTs-BNPs or MWCNTs-GNPs
associations on transport processes. The zeta potentials of mixed
MWCNTs-BNPs or MWCNTs-GNPs suspension were more negative in thepresence of BNPs and less negative in the presence of GNPs compared to
MWCNT suspensions without BNPs or GNPs at IS = 1 mM CaCl2(Table S1). The zeta potential of the sand was negative (-25.6 mV,
IS = 1 mM CaCl2). Similar to the electrostatic interaction between
MWCNTs and QS, the electrostatic interaction between the MWCNTsBNPs or MWCNTs-GNPs suspension and QS is still unfavorable. How­ever, the zeta potentials of MWCNTs-BNPs or MWCNTs-GNPs suspen­sion decreased compared to BNPs or GNPs without MWCNTs at
IS = 1 mM CaCl2. Therefore, the electrostatic interaction between
MWCNTs-BNPs and QS, and between BNPs and QS is unfavorable,
whereas the electrostatic interaction between GNPs and QS is favorable,
and between MWCNTs-GNPs and QS is unfavorable. Fig. S2 presents
plots of Φ as a function of separation distance (h) when a sphericalcolloid (with properties similar to MWCNTs in the presence or absenceof BNPs or GNPs) approaches the surface of QS in CaCl2 solution at
IS = 1 mM. An energy barrier to the primary minimum is present as thecolloid approaches the QS as expected based on electrostatics. However,
the height of the energy barrier and the depth of the primary minimum isa strong function of the presence of BNPs or GNPs. The presence of BNPs
produced a rapid increase in the energy barrier and the primary mini­
mum of MWCNTs on the QS in CaCl2. The presence of GNPs alsoenhanced the energy barrier, whereas it decreased the primary mini­
mum of MWCNTs in CaCl2 (Fig. S2a). Consequently, these observations
indicate that positively charged GNPs or negatively charged BNPs might
not completely result in “unfavorable” and “favorable” conditions forthe attachment of MWCNTs to QS as expected based on only electro­
static considerations. In addition, the presence of MWCNTs enhanced
the energy barrier of BNPs or GNPs on the QS in CaCl2, especially for
GNPs (Fig. S2a and S2b). The energy barrier between two nanoparticles(MWCNTs with BNPs or GNPs) in Fig. S2c also suggested that hetero­aggregation occurred much easier between MWCNTs and GNPs thanbetween MWCNTs and BNPs. Note that the presence of Ca2+ decreased
the energy barrier and primary minimum between MWCNTs-BNPs or
MWCNTs-GNPs aggregates and QS compared to the monovalent cationof K+ (Fig. S2d and S2e).

where the subscript S parameters indicate that they are associated with
the BNPs or GNPs. The value of ψ S is given as:
(
)(
)− β
S +Γ S
d50 + z
ψ S = 1 − S maxS C
(7)
d50
SS
Eqs. (Bradford et al., 2017) and (Bradford et al., 2002) describe thepossibility of single species and competitive Langmuirian blocking.
Three model formulations for MWCNTs, BNPs, and GNPs retention wereconsidered in this study. The single species transport (model M1) of
MWCNTs, BNPs, or GNPs with Langmurian blocking (Adamczyk et al.,1994) is accounted for using the first term on the right-hand side of theseequations when ΓC and ΓS are set to zero (including both time- anddepth-dependent blocking, β = 0.765), respectively, whereas competi­
tive blocking (Becker et al., 2015; Zhang et al., 2019) is considered whenΓC and ΓS are greater than zero (model M2). The M3 model considers
only time-dependent (Langmuirian blocking) retention by setting β, ΓC ,and ΓS equal to zero. More details of numerical modeling are given in the
Section S4 of the SI.
3. Results and discussion
3.1. Interactions and aggregation of MWCNTs in the presence of BNPs or
GNPs at IS = 1 mM CaCl2
The aggregation kinetics of MWCNTs in the presence and absence of
BNPs or GNPs at IS = 1 mM CaCl2 and KCl were performed and areshown in Fig. 1a and 1b, respectively. In the absence of BNPs or GNPs,
MWCNTs were not aggregated in both CaCl2 and KCl solutions due torepulsive forces between negatively charged MWCNTs, indicating thathomoaggregation of MWCNTs could be neglected during the transportand deposition of MWCNTs in both CaCl2 and KCl solutions. In thepresence of BNPs or GNPs, the hydrodynamic diameters of MWCNTsBNPs were stable in KCl solution and showed slight increases in CaCl2
solution, whereas the hydrodynamic diameters of MWCNTs-GNPs
exhibited slight and rapid increases in KCl and CaCl2 solutions, respec­tively. Such results demonstrated that divalent Ca2+ compared tomonovalent K+ induced a significantly stronger impact on the in­teractions between MWCNTs and BNPs, especially between MWCNTsand GNPs. This observation indicated that heteroaggregation could
occur during the co-transport and deposition of MWCNTs in the pres­ence of BNPs or GNPs at IS = 1 mM CaCl2 in this study (Li et al., 2019).
Several studies have reported that heteroaggregation quickly occurred
between engineered nanoparticles and clay minerals or iron oxides due
to cation bridging, electrical interaction, hydrogen bonding, andchemical bonding (Huynh et al., 2012; Labille et al., 2015; Lenhart et al.,2015; Sarpong et al., 2017; Wang et al., 2015). The divalent Ca2+
compared to monovalent K+ could induce heteroaggregation of
MWCNTs in the presence of BNPs or GNPs by cation bridging andelectrical interaction. Other mechanisms that likely contributed to theseobservations will be discussed later.
A much higher association was observed between MWCNTs and
GNPs than BNPs (Fig. S1). Furthermore, much higher sorption of
MWCNTs on BNPs or GNPs occurred in the presence of Ca2+ (e.g., nearlycomplete adsorption) than K+ (Zhang et al., 2022). The concave
isotherm shape under quasi-equilibrium conditions indicated a low
MWCNTs-BNPs or MWCNTs-GNPs affinity at low concentrations.
However, adsorption was enhanced with increasing concentration of
MWCNTs in the suspension. Our previous studies (Zhang et al., 2022)
showed convex, L-shape isotherms of MWCNTs with BNPs or GNPs in
1 mM KCl. In comparison to K+, isotherms in the presence of Ca2+ show

3.2. QCM-D deposition kinetics of MWCNTs with BNPs or GNPs in thepresence of different cations
QCM-D was used to measure the deposition kinetics during the cotransport of MWCNTs with BNPs or GNPs in IS = 1 mM CaCl2 or KCl
on a silica surface. The QCM-D frequency (Δf) and dissipation (ΔD) shiftof the 3rd overtone are shown in Fig. 1 and S3 as a function of attach­ment time on the silica surface. Both MWCNTs, BNPs, and GNPs were
not deposited on the silica surface during single-species transport under
IS = 1 mM CaCl2 or KCl (QCM-D tests, Fig. S3a and b). No deposition of
MWCNTs and BNPs was also observed on the silica surface in IS = 1 mM
KCl (Fig. 1c), whereas the deposition of MWCNTs and GNPs wasenhanced in this same electrolyte solution during their co-transport. The
lack of deposition (close to zero) of MWCNTs in the presence of BNPs
(IS = 1 mM KCl) was attributed to the large energy barrier (Fig. 1c andS3e). The slightly enhanced deposition (close to − 1, Fig. 1c) of MWCNTsand GNPs in IS = 1 mM KCl was potentially due to heteroaggregation of
MWCNTs and GNPs, and/or nanoscale heterogeneities (e.g., variations
in charge and roughness) on particle surfaces.
The QCM-D deposition of MWCNTs with BNPs or GNPs wasenhanced (Fig. 1c) compared to single-species transport of MWCNTs,
BNPs, or GNPs in the presence of IS = 1 mM CaCl2 (compared with 1 mM
KCl), with GNPs exhibiting a more significant effect than BNPs on such5

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

Fig. 2. Observed and fitted (M1) BTCs (a, c, e, and g) and RPs (b, d, f, and h) of MWCNTs, BNPs, and GNPs in quartz sand. (a) BTCs and (b) RPs of MWCNTs withadding 0 and 4 mg L− 1 of BNPs in 1 mM CaCl2; (c) BTCs and (d) RPs of BNPs or GNPs with adding 0 and 1 mg L− 1 of MWCNTs in 1 mM CaCl2; (e) BTCs and (f) RPs of
MWCNTs with adding 0 and 4 mg L− 1 of BNPs in 1 mM KCl; (g) BTCs and (h) RPs of BNPs or GNPs with adding 0 and 1 mg L− 1 of MWCNTs in 1 mM KCl; The Darcy
velocity is 0.71–0.72 cm min− 1.

deposition. These results suggested that Ca2+, in comparison to K+,
enhanced the interaction between two nanoparticles (MWCNTs with
BNPs or GNPs), and between the two nanoparticles (MWCNTs with BNPs
or GNPs) and silica, promoting their deposition. However, the deposi­tion behavior of MWCNTs with BNPs or GNPs in IS = 1 mM CaCl2 so­lution also depended on the system mixing (Fig. 1d). The suspension of
MWCNTs and BNPs exhibited similar deposition behavior in IS = 1 mM
CaCl2 solution under both mixed and no-mixed conditions, whereas
more deposition occurred for MWCNTs and GNPs in the mixed systems(Fig. 1d). This result suggests that Ca2+ had a continuing effect on theinteraction between MWCNTs and GNPs.
The ΔD/Δf slopes were mainly close to zero in the single-species
deposition experiments of MWCNTs, BNPs, and GNPs under

IS = 1 mM CaCl2 (Fig. S3c) or KCl (Fig. S3d), suggesting that a depositedlayer was not formed during the single-species transport in the QCM-D.
The interaction between GNPs and silica surface might not be strong
enough to overcome the mechanical oscillations and shear forces fromthe flow field of QCM-D, resulting in limited deposition of GNPs under
IS = 1 mM CaCl2 or KCl. In the co-transport of MWCNTs and BNPs, theΔD/Δf slopes were still close to zero in IS = 1 mM KCl (Fig. S3e),
whereas slow- and fast-slope regions were obtained in IS = 1 mM CaCl2(Fig. 1e). The ΔD/Δf slopes mostly stayed constant in the co-transport of
MWCNTs and GNPs in IS = 1 mM CaCl2 (Fig. 1f) or KCl (Fig. S3f) so­lutions, suggesting that the viscoelasticity characteristics of the depos­
ited layer did not change during the deposition process (Marcus et al.,2012). The ΔD/Δf slopes included slow- and fast-slope regions in the6

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

non-mixed suspension with MWCNTs in the presence of BNPs or GNPs at
an IS = 1 mM CaCl2. In this case, the slow-slope region was close to zeroin the presence of BNPs (Fig. 1e), while it was slightly greater than zeroin the presence of GNPs (Fig. 1f). The deposition layer of two nano­particles (MWCNTs with BNPs or GNPs) apparently depended on theformation of MWCNTs-BNPs or MWCNTs-GNPs aggregates (Fig. 1e, 1f,
and S3e). In addition, the ΔD/Δf slopes of MWCNTs and GNPs are
consistently lower than those of MWCNTs and BNPs in both mixed andno-mixed conditions, suggesting that the deposited layer of MWCNTsand GNPs is relatively harder and denser than that of MWCNTs and BNPs
(Gutman et al., 2013; Jin et al., 2022). QCM-D results were consistent
with the aggregation and interaction energy between two nanoparticles(MWCNTs with BNPs or GNPs). In brief, divalent Ca2+ promoted acontinued effect on the formation of MWCNTs-BNPs or MWCNTs-GNPs
aggregates compared to monovalent K+, especially for MWCNTs-GNPs
aggregates, that resulted in their deposition.

criterion (AIC) (Akaike, 1974) for the goodness of fit.
The effect of Ca2+. MWCNTs exhibited limited breakthrough andsignificant retention in the presence and absence of BNPs or GNPs whenthe IS = 1 mM CaCl2. BNPs produce a slight increase in the mass per­centage recovered in the effluent for MWCNTs (Fig. 2a, e.g., from 0.1%
to 0.4% when the BNPs Co increased from 0 to 4 mg L− 1, respectively),
which is shown in Table 1. The asymmetric shape of the BTCs was welldescribed with the M1 model with Langmuirian blocking (R2 > 0.99)
shown in Eqs. (2)-(4), which attributes the increasing values of C/Co
with suspension injection to blocking or filling of a limited number ofretention sites. Retention sites are filled more rapidly for higher reten­tion rates, lower retention capacities, and higher input concentrations
max(Leij et al., 2015). Note that fitted values of kaC , kaS , Smax
C / Co, and SS /Co all decreased in the presence of BNPs (Table 1). The decreasing
retention rate and capacity with BNPs may be partially explained bygreater amounts of electrostatic repulsion. In addition, the presence of
BNPs also decreased Smax
C / Co and thereby enhanced its blocking. If
competitive blocking is considered, then retention of BNPs will also
contribute to the filling of the MWCNT Smax
(Becker et al., 2015; Zhang
C
et al., 2019). Collectively, these results indicate that the presence of
BNPs enhanced the transport of MWCNT by (i) altering the solid surface
chemistry to create more electrostatically repulsive conditions and (ii)increased blocking and/or competitive blocking. In this work, BTCs of
MWCNTs (Fig. 2a) and BNPs (Fig. 2c) were both enhanced during the cotransport in comparison to their individual transport. This mutuallyfacilitated transport of MWCNTs and BNPs in QS suggested thatcompetitive blocking was potentially the dominant mechanism. The M2
model (Fig. S4, Tables 2 and S2) with competitive blocking was there­
fore used in the further analysis. Values of R2 and AIC (Akaike, 1974)
also indicate that the M2 model exhibited good simulated results (Fig. S4
and Table 2). Both of ΓC and ΓS were>0, suggesting that competitive

3.3. Column Co-Transport of MWCNTs with BNPs or GNPs in thepresence of different cations
Fig. 2a and b (IS = 1 mM CaCl2), and 2e and 2f (1 mM KCl) present
observed and simulated (M1 model) BTCs and RPs, respectively, for
MWCNTs in QS when the input concentrations of BNPs or GNPs were
0 and 4 mg L− 1. Fig. 2c and d, and 2 g and 2 h present corresponding
BTCs and RPs for BNPs and GNPs, respectively. The experimental con­ditions and mass balance information are presented in Table 1. The total
mass balance for MWCNTs (Mt_C), BNPs (Mt_S), and GNPs (Mt_S) in thecolumn experiments was very good (>93%, Table 1). Fitted model pa­
rameters and their standard error coefficients of M1 and M2 models are
given in Tables 2, S2 (dispersion coefficient, kdC , and kdS ), and S3, alongwith the Pearson correlation coefficient (R2) and Akaike information
Table 2Fitted model parameters.
Model

AICC

AICS

AICC+S
− 1

Smax
C /Co

ΓC

kaC

Smax
S /Co

ΓS

kaS

R2C

R2S

[cm3g− 1][–][min− 1][cm3g− 1][–][min− 1]

[–]

[–]

62.91

NF

NF

NF

0.997

NF

NF

2.603

NF

30.16

NF

0.999

NF

3.294

NF

45.00

NF

0.998

56.32
56.32
1.06

2.553
2.553
0.939

NF
5.88E-02
NF

22.98
22.98
0.591

0.995
0.998
0.920

0.988
0.972
0.748

63.98
63.98
1.107

3.051
3.051
1.493

NF
0.12
NF

29.14
29.14
0.687

0.995
0.998
0.994

0.977
0.951
0.795

16.47

NF

NF

NF

0.976

NF

NF

1.724

NF

11.80

NF

0.967

NF

2.796

NF

22.76

NF

0.988

15.19
15.19
0.373

1.397
1.397
0.706

NF
6.48E-04
NF

11.08
11.08
0.34

0.968
0.968
0.910

0.978
0.978
0.747

39.07
39.07
0.82

2.080
2.080
0.945

NF
1.56E-03
NF

13.92
13.92
0.41

0.910
0.910
0.987

0.970
0.970
0.702

− 1

Co (MWCNTs) = 1 mg L , Co (BNPs/GNPs) = 0 mg L , 1 mM CaCl2
M1− 112.2
NF
2.752
NF
Co (MWCNTs) = 0 mg L− 1, Co (BNPs) = 4 mg L− 1, 1 mM CaCl2
M1
NF− 155.9
NF
NF
Co (MWCNTs) = 0 mg L− 1, Co (GNPs) = 4 mg L− 1, 1 mM CaCl2
M1
NF− 119.3
NF
NF
Co (MWCNTs) = 1 mg L− 1, Co (BNPs) = 4 mg L− 1, 1 mM CaCl2
M1− 281.0
2.322
NF
M2− 295.4
2.322
4.63E-02
M3− 299.7
1.370
NF
− 1
− 1
Co (MWCNTs) = 1 mg L , Co (GNPs) = 4 mg L , 1 mM CaCl2
M1− 355.8
3.153
NF
M2− 358.5
3.153
0.21
M3
− 354.7
6.113
NF
Co (MWCNTs) = 1 mg L− 1, Co (BNPs/GNPs) = 0 mg L− 1, 1 mM KCl
M1
215.7
NF
1.621
NF
Co (MWCNTs) = 0 mg L− 1, Co (BNPs) = 4 mg L− 1, 1 mM KCl
M1
NF− 92.8NF
NF
Co (MWCNTs) = 0 mg L− 1, Co (GNPs) = 4 mg L− 1, 1 mM KCl
M1
NF
302.5
NF
NF
Co (MWCNTs) = 1 mg L− 1, Co (BNPs) = 4 mg L− 1, 1 mM KCl
M1− 226.1
1.354
NF
M2− 226.1
1.354
1.95E-04
M3− 105.4
0.822
NF
− 1
− 1
Co (MWCNTs) = 1 mg L , Co (GNPs) = 4 mg L , 1 mM KCl
M1− 253.1
1.733
NF
M2− 253.2
1.733
4.92E-02
M3− 262.1
1.271
NF

max
Smax
C /Co and kaC are the normalized maximum solid phase concentration and the first-order retention rate coefficient of MWCNTs, respectively; SS /Co and kaS, are thenormalized maximum solid phase concentration and the first-order retention rate coefficient of BNPs or GNPs, respectively; NF - denotes not fitted; R2C and R2S are thecorrelation of observed and fitted data for MWCNTs, and for BNPs or GNPs in the solid phase, respectively. AICC and AICS are the Akaike information criterion for
MWCNTSs, and for BNPs or GNPs in the M1 model, respectively. AICC+S is the Akaike information criterion for MWCNTSs in the presence of BNPs or GNPs in M1-M3
models. ΓC is the area conversion factor between BNPs and MWCNTs, or between GNPs and MWCNTs; ΓS is the area conversion factor between MWCNT and BNPs, or
between MWCNTs and GNPs. The fitted parameters of dispersion coefficient, kdC, and kdS are in Table S2.

7

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

blocking is expected to play a role in enhancing MWCNT transport in thepresence of BNPs.
The RPs for MWCNTs and BNPs all exhibited hyper-exponential
shapes that were well described with the M1 model (Fig. 2b and d)that included a depth-dependent retention function (Eq. 4)
withβ = 0.765. Several factors can contribute to particle retention underelectrostatically repulsive conditions and hyper-exponential RPs. The
presence of BNPs enhanced the energy barrier and the primary mini­
mum of MWCNTs on the QS, whereas particle interaction in a primary
minimum may occur for certain conditions that dramatically reduce
and/or eliminate the repulsive energy barrier. For example, the barrierheight and adhesive interaction have been reported to be sensitive to theparticle shape and orientation (Gomez-Flores et al., 2019; Shen et al.,2017), surface roughness and topography (Bradford et al., 2017;
Hamamoto et al., 2019; Zhang et al., 2016), and chemical heterogeneity(He et al., 2018; Wang et al., 2012). In addition, surface and porestraining processes have been shown to significantly contribute to par­ticle retention under electrostatically unfavorable conditions by altering
the lever arms (Treumann et al., 2014; Zhang et al., 2016). A detailed
determination of the relative importance of these factors has beenaddressed in previous works (Zhang et al., 2016; 2017a) but is beyond
the scope of the present study.
In contrast to BNPs, GNPs generally exhibit a positive charge innatural aquatic and soil environments. In this work, the zeta potential
for GNPs in IS = 1 mM CaCl2 was 27.2 mV (Table S1). Note that mostprevious co-transport studies have not considered colloids with net
positive charges. In contrast to the co-transport of MWCNTs and BNPs,
Fig. 2a shows that the transport of MWCNTs was slightly diminished(Me_M, from 0.1% to 0.03%, Fig. 2a, Table 1) in the presence (4 mg L− 1)
compared to the absence of GNPs. This resulted in a corresponding slightincrease in the solid phase mass percentage (e.g., 98.5% to 100.5%,
Table 1, Fig. 2b) for MWCNTs in the presence of GNPs. In contrast to
MWCNTs, the breakthrough of GNPs in the effluent slightly increased
from 1.2% to 3.5% (Me_C, Fig. 2c, Table 1) as the input concentration of
MWCNTs increased from 0 to 1 mg L− 1, resulting in a corresponding
decrease in the solid phase mass percentage of GNPs from 102.2% to98.0% (Ms_C, Fig. 2d, Table 1). The BTCs for MWCNTs in the presence of
GNPs (Fig. 2a) were well described using the M1 model (R2 > 0.99 inTable 2). Note that fitted values of kaC were very large in the presence of
GNPs (Table 2), which delays the breakthrough of MWCNT until
blocking decreases the number of available retention sites. Furthermore,
the values of kaC and Smax
C / Co for MWCNTs increased due to the presenceof GNPs (Table 2). This implies that the rate and capacity for MWCNT
retention increased with the GNPs concentration. In addition, some in­dividual GNPs could attach to the QS and apparently created positively
charged sites on the sand that were electrostatically favorable for theretention of negatively charged MWCNTs. Furthermore, the GNPs
associated with MWCNTs had free positive charges and thus interactedwith QS as solid bridges. The association between MWCNTs and GNPs
also created a less negatively charged suspension of MWCNTs(Table S1). The BTCs for GNPs (Fig. 2c) were also adequately describedusing the M1 model (R2 > 0.99 in Table 2). Fitted values of kaS and Smax
S /Co for GNPs were high but decreased due to the presence of MWCNTs.
The retention of positively charged GNPs on the negatively charged QS
surface is electrostatically favorable. However, the observed blocking
behavior for GNPs indicates that there was only a limited number ofretention sites for GNPs on the QS and that these sites were rapidly filled
due to nanoscale roughness that creates shallow primary minimum in­teractions (Zhang et al., 2022; Zhang et al., 2016). In addition, similar tothe co-transport of MWCNTs and BNPs, the M2 model with limitedcompetitive blocking also exhibited a good description for the cotransport of MWCNTs and GNPs (Fig. S4 and Table 2). Both ΓC and Γ S
were>0, suggesting that competitive blocking also plays a role inenhancing MWCNT transport in the presence of GNPs (Zhang et al.
2019; Zhang et al. 2022).

Fig. 2b and d show that the RPs for MWCNTs and GNPs, respectively,
were well described using the model that accounted for Langmuirian
blocking and depth-dependent (hyper-exponential) retention. Thisobservation suggests that similar retention mechanisms contributed to
the retention of both MWCNTs and GNPs, even though these colloids areoppositely charged. In addition to the retention mechanisms for
MWCNTs and BNPs (e.g., surface roughness, surface straining processes,
and charge heterogeneity) discussed in the previous section, GNPs
contribute to retention through favorable electrostatic interactions.
The effect of cation valence. Additional experiments were conducted toinvestigate the effect of cation valence (Ca2+ or K+) on the co-transportof MWCNTs (1 mg L− 1) in the presence of BNPs or GNPs (4 mg L− 1).
Fig. 2e–h present similar information to Fig. 2a–d when the backgroundelectrolyte solution was CaCl2 at IS = 1 mM. The enhancement (BNPs) or
reduction (GNPs) of MWCNT transport by BNPs or GNPs was more
obvious in the presence of IS = 1 mM KCl than CaCl2 (Fig. 2a and e).
Similarly, greater transport of BNPs occurred than GNPs, especially inthe presence of IS = 1 mM KCl than CaCl2 (Fig. 2c and g). These same
trends were reflected in the calculated mass balance values and fitted
model parameters. Differences in the interaction of GNPs and BNPs for
the MWCNTs and the sand grains were discussed in previous sections.
max
Table 2 indicates that fitted values of kaC , kaS , Smax
C / Co, and SS / Co
(Table 2) were higher in the presence of Ca2+ than K+. The retardation
factors of RC and RS (Table 1) were also greater in the presence of Ca2+
than K+. These observations indicate that Ca2+ produced a stronger
adhesive force than K+ due to localized neutralization and/or reversal of
surface charge (Grosberg et al., 2002; Zhang et al., 2017a), and/or
cation bridging (Torkzaban et al., 2012). These same factors can also
contribute to greater interactions between two nanoparticles (MWCNTs
with BNPs or GNPs) in the presence of Ca2+ than K+ (Torkzaban et al.,2012). Note that both of ΓC and ΓS were significantly greater in the cotransport of MWCNTs with BNPs or GNPs in presence of Ca2+ than K+,
suggesting that divalent Ca2+ cations strongly enhanced competitive
blocking in porous media compared to monovalent K+ cations.
The calculated values of rC/S (mg mg− 1) reflect the net mass of
MWCNTs that were retained due to attached BNPs or GNPs, which are
shown in Fig. S6 as a function of BNPs and GNPs concentrations. It was
found that values of rC/S were − 7.5E-03 and − 8.3E-03 mg mg− 1 when
the concentration of BNP was 4 mg L− 1 at IS = 1 mM CaCl2 and KCl,
respectively (Fig. S6), but changed to 5.0E-03 and 5.0E-02 mg mg− 1
when the concentration of GNP was 4 mg L− 1 at IS = 1 mM CaCl2 andKCl, respectively (Fig. S6). Negative values of rC/S reflect a decrease in
MWCNTs retention due to BNPs attachment, whereas positive values
indicate that attached GNPs on the MWCNTs increase the MWCNTs
retention. Note that MWCNT retention was more pronounced for GNPs
than BNPs in the presence of Ca2+than K+.
3.4. Potential mechanisms
The co-transport and deposition of MWCNTs with BNPs or GNPs
exhibited different behaviors in column and QCM-D systems. The
contribution of Ca2+ to retention was significantly greater than K+ whenthe IS = 1 mM, especially for MWCNTs and GNPs in both column and
QCM-D studies. Such phenomena could not be explained just by cation
bridging, charge heterogeneity, and heteroaggregation, so other mech­anisms likely contributed to these observations.
Straining and Competitive Blocking. Deposition trends for MWCNTs incolumn and QCM-D studies were similar when the IS = 1 mM KCl, while
differences were observed in IS = 1 mM CaCl2. Competitive blocking/deposition can occur in column and QCM-D tests, but straining, which isone mechanism of nanoparticle removal in porous media, can only occur
in column tests. Column results were simulated with M1 (Langmuirian
blocking and depth-dependent retention), M2 (Langmuirian competitive
blocking and depth-dependent retention), and M3 (Langmuiring
blocking) models to better identify the relative contributions ofcompetitive blocking and straining. The M1 and M2 models (Fig. 2 and8

M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

Table 2) showed a better description than the M3 model (Fig. S5 andTable 2). Depth-dependent retention has been associated with thestraining process (Lin et al., 2021), indicating that straining likely
played an important role in the co-transport of MWCNTs in the presenceof BNPs or GNPs in both IS = 1 mM CaCl2 and KCl solutions. The cation
Ca2+ enhanced MWCNTs-BNPs or MWCNTs-GNPs aggregation (Fig. 1a)and thus the deposition of MWCNTs with BNPs or GNPs in QCM-D(Fig. 1c). The ratio of particle diameter to sand grain diameter in theco-transport of MWCNTs with BNPs (0.0032 for MWCNTs-BNPs aggre­
gates) or GNPs (0.0045 for MWCNTs-GNPs aggregates) is much higher
than in single-species transport of MWCNTs (0.001). Therefore, heter­
oaggregation between two nanoparticles (MWCNTs with BNPs or GNPs)
produced larger hydrodynamic diameters (Fig. 1a, Table S1) that should
further enhance straining (the ratio of particle diameter to sand grain
diameter > 0.0017) processes even under unfavorable conditions(Bradford and Torkzaban, 2015; Bradford et al., 2002; Zhang et al.,2016). Increased straining in the presence of Ca2+ is also consistent withmore hyper-exponential RPs for both MWCNTs, BNPs, and GNPs (Fig. 2)
and higher values of Smax
and Smaxin the M1, M2, and M3 models
C
S(Table 1). Therefore, both straining and competitive blocking wereenhanced by Ca2+ compared to K+ in the co-transport of MWCNTs in thepresence of BNPs or GNPs in QS in column tests, while competitive
blocking and zeta potential alteration can only explain the enhanced
breakthrough in co-transport experiments in QS (e.g., MWCNT in thepresence of BNPs, and BNPs and GNPs in the presence of MWCNTs). To
summarize, different deposition behaviors of two nanoparticles(MWCNTs with BNPs or GNPs) in column and QCM-D systems suggested
that both straining and competitive blocking play dominant roles intheir co-transport in QS.
Cation Bridging and Non-DLVO Interaction. Ca2 produced stronger
interactions between two nanoparticles (MWCNTs with BNPs or GNPs)
than K+, especially for MWCNTs and GNPs, during their co-transportand deposition. Previous studies indicated that divalent Ca2+enhanced the interaction between negatively charged colloids due tocation bridging and alteration of zeta potentials (Shi et al., 2022; Zhu
et al., 2022). The adsorption isotherms of Ca2+ on MWCNTs, BNPs, and
GNPs are shown in Fig. S7. Results indicate that the adsorption capac­
ities of Ca2+ followed the order of MWCNTs > BNPs > GNPs. GNPs could
still adsorb a very small amount of Ca2+, probably due to the free hy­
droxy groups on the surface of GNPs (Zhang et al., 2022). Therefore,
while cation bridging may occur in the association between MWCNTsand GNPs, it plays a more dominant role in MWCNTs and BNPs.
Molecular dynamics (MD) simulations were conducted to investigate
the interactions between two nanoparticles (MWCNTs with BNPs or
GNPs) in IS = 1 mM CaCl2 (Fig. 3) and KCl (Zhang et al., 2022). The
binding energies of BNPs (Fig. 3a) and GNPs (Fig. 3b) with MWCNTs in
IS = 1 mM CaCl2 were − 125.9 ± -7.0 kJ mol− 1 and − 181.2 ± 7.5 kJ mol− 1, which is equivalent to − 50.8 and − 73.2 kT (1kT = 2.476 kJ mol− 1) (Gupta and Srivastava, 2020) respectively. In
addition, MD simulations show that MWCNTs can be completely
wrapped by GNPs with a smaller mean distance (0.45 nm, Fig. 3b) be­
tween the centroids of MWCNTs. Although MWCNTs were also wrappedby BNPs, much greater dispersion around MWCNTs than GNPs wasobserved, resulting in a larger mean distance (0.49 nm, Fig. 3a) between
the centroids of MWCNTs. The tiny difference of 0.45 and 0.49 nm wasin good agreement with the observation of enhanced hydrodynamic

Fig. 3. (a) and (b) are the MD simulations of MWCNTs with BNPs or GNPs. (a) The left side of the figure is the schematic molecular structure for BNPs, MWCNTs, and
GNPs. Red is oxygen (O), white is hydrogen (H), light blue is carbon (C), light pink is iron (Fe), yellow is silicon (Si), and purple is aluminum (Al). The solvents of
CaCl2 and water molecules have been hidden for better observation. d is the mean distance between the centroids of two MWCNTs. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version of this article.)9M. Zhang et al.

Journal of Hydrology 625 (2023) 129909

diameters of MWCNTs found in the presence of GNPs and BNPs in
IS = 1 mM CaCl2. Note that more negative binding energies and fewer
mean distances between two nanoparticles (MWCNTs with BNPs or
GNPs) were observed in IS = 1 mM CaCl2 than KCl, suggesting thatdivalent Ca2+ cations resulted in stronger interactions between two
nanoparticles (MWCNTs with BNPs or GNPs) than monovalent K+ cat­ions. Similar to the MD simulation between two nanoparticles (MWCNTs
with BNPs or GNPs) in IS = 1 mM KCl (Zhang et al., 2022), the MD
simulations in IS = 1 mM CaCl2 also demonstrate that non-DLVO in­teractions (e.g., H-bonding and cation-π interaction) between two
nanoparticles (MWCNTs with BNPs or GNPs) are thermodynamicallyfeasible (Dougherty, 2013; Patiño et al., 2020) and even stronger than in
IS = 1 mM KCl, which absolutely contributes to the deposition andinteraction behavior of MWCNTs with BNPs or GNPs during their cotransport. Therefore, Ca2+ could facilitate the non-DLVO interactions
between two nanoparticles (MWCNTs with BNPs or GNPs), and further
enhance the associations between MWCNTs-BNPs or MWCNTs-GNPs.
In sum, we found that divalent cations could play a more critical rolein mechanisms controlling the co-transport of two colloids than mono­valent cations, especially when colloids have opposite surface charges.
Previous studies indicated that divalent cations induce interactions be­
tween two colloids by cation bridging, charge heterogeneity, andalteration of zeta potentials. However, this study found that divalentcations can also enhance surface interactions between two colloids by
non-DLVO forces, especially for colloids with opposite surface charges.
Consequently, divalent cations can enhance heteroaggregation, strain­
ing, and competitive blocking of two colloids during their co-transport.
Such information can be further used to understand and assess the fate of
ENPs (e.g., MWCNTs) associated with natural nanoparticles (e.g., BNPs
and GNPs) in the soil and groundwater. It is also shown that DLVO
theory alone may not be an effective tool to assess the interaction be­
tween two colloids or nanoparticles (NPs). This may also partiallyexplain why colloids or NPs can still be retained even under unfavorable
conditions.

surface.

4. Conclusions

Supplementary data to this article can be found online at https://doi.
org/10.1016/j.jhydrol.2023.129909.

CRediT authorship contribution statement
Miaoyue Zhang: Methodology, Software, Formal analysis, Writing –original draft. Scott A. Bradford: Conceptualization, Formal analysis.
Erwin Klumpp: Conceptualization, Formal analysis. Jiří Šimůnek:Conceptualization, Formal analysis. Yijun Mo: Methodology. Kengbo
Ding: . Quan Wan: . Shizhong Wang: . Chao Jin: Conceptualization,
Project administration. Rongliang Qiu: Conceptualization, Funding
acquisition, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
Funding was provided by the National Natural Science Foundation ofChina (Project No. 42230707 and 42077342), Sino-German Mobility
Programme (Project No. M-0749), and the 111 Project (Project No.
B18060). The authors would like to acknowledge Stephan Köppchen forbromide measurement. Thanks to Herbert Philipp and Claudia Walraf
for their technical assistance.
Appendix A. Supplementary data

This study investigated the co-transport and deposition of MWCNTs
and representative natural nanoparticles (negatively charged BNPs andpositively charged GNPs) in packed quartz sand columns and QCM-D
systems when the IS = 1 mM CaCl2 or KCl. In QCM-D tests, in the KClsolution, no deposition of MWCNTs or BNPs was observed, while
enhanced deposition of MWCNTs and GNPs occurred in their cotransport. However, the deposition of both MWCNTs and natural
nanoparticles (BNPs or GNPs) was enhanced in the CaCl2 solution. In
column tests, the transport of MWCNTs was slightly enhanced or
inhibited due to the presence of BNPs or GNPs, respectively, whereas thetransport of BNPs or GNPs was facilitated in the presence of MWCNTs inboth CaCl2 and KCl solutions. In addition, Ca2+, in comparison to K+,
exhibited a much stronger impact on MWCNTs and GNPs than MWCNTs
and BNPs. Our comprehensive results indicate that divalent cations suchas Ca2+ compared to monovalent cation K+: (i) enhanced interactions of
MWCNTs with both positively charged GNPs and negatively charged
BNPs through non-DLVO (e.g., H-bonding and cation-π interaction) andDLVO interactions; (ii) increased the contribution of straining andcompetition blocking in the co-transport of MWCNTs in the presence of
BNPs or GNPs in QS; and (iii) induced different interaction mechanisms
between MWCNTs and negatively charged BNPs (e.g., cation bridging)or positively charged GNPs (e.g., heteroaggregation due to both DLVO
and non-DLVO interactions). All these results imply that divalent cations
play a more complex role than monovalent cations in the co-transport ofcolloids, and that significant non-DLVO interactions, competitive
blocking, and straining should be evaluated to better quantify environ­mental fate and risk assessment in the water and soil. QCM-D and col­umn tests are also proved to be a powerful tool for the colloid transportand deposition, and interactions between nanoparticles and media

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