1 Introduction

Biochar is produced via biomass pyrolysis and is rich in carbon and functional groups, which has raised increasing attention due to its multiple environmental functions, such as carbon sequestration and pollutant adsorption (Beesley et al. 2011; Lehmann et al. 2011; Lu et al. 2012; Woolf et al. 2010). Besides bulk biochar, nanoscale biochar (N-BC) has also received growing concerns for its potential environmental risks. N-BC can be formed by matrix fracture and pore collapse of bulk biochar during charring, grinding, and sonication, or weathering in the natural environment releasing fine biochar particles, subject to soil hydrology, solution chemistry, and climate (Kuzyakov et al. 2014; Liu et al. 2018; Spokas et al. 2014; Xu et al. 2017). The generated N-BC can migrate in soils and aquifers, eventually reaching the ocean via river and atmosphere (Qu et al. 2016). The potential environmental risk of N-BC originates from not only its transport in the subsurface releasing harmful internal components simultaneously (e.g., heavy metals, polycyclic aromatic hydrocarbons, and dioxins), but also from facilitating the transport of contaminants by acting as a carrier (Cao et al. 2021; Tong et al. 2020; Xiang et al. 2021; Zhu et al. 2021). The mobility of N-BC in laboratory and field scale has been conducted with great effort (Chen et al. 2017; Wang et al. 2019; Yang et al. 2020b). Physicochemical conditions such as solution chemistry, biochar property, flow velocity, and porous media were all reported to pose significant impacts on the mobility of biochar via altering the electrical double layer thickness, surface functional groups, collision efficiency, and straining (Shang et al. 2013; Wang et al. 2013a; Zhang et al. 2010). The coexisting substances of metals (Cao et al. 2021; Jin et al. 2020), microplastics (Tong et al. 2020; Wang et al. 2022), organic matters (Yang et al. 2017, 2019; Zhu et al. 2021), and soil colloids (Gui et al. 2021) have also been verified to pose significant effects on the N-BC mobility in porous media via forming homo-/hetero-aggregates altering the surface charge density, aggregate size and steric repulsion of N-BC.

Cd2+ is a highly toxic and mobile heavy metal that mainly exists as a divalent ion in soils and water (Roberts 2014; Wang et al. 2021a, b; Zhang et al. 2020), which can be absorbed and accumulated in crops to the food chain. Multiple remediation methods were employed to remove or reduce the bioavailability of Cd2+ from soils, such as adsorption, precipitation, electrokinetic remediation, and bioremediation (Debrassi et al. 2012; Robinson et al. 2001; Yu et al. 2013). Among these methods, immobilizing Cd2+ in soils with biochar has attracted growing interest for its simple operation, eco-safe, and low cost (Huang et al. 2015, 2017). Different forms of biochar were innovated to immobilize Cd2+ from soils, including pristine biochar (e.g., derived from rice straw (Tan et al. 2020), green peppers (Sun et al. 2020), poultry manure (Haider et al. 2021), metal/metal-oxide modified biochar (e.g., Fe, Fe3O4, and MgO modified (Tang et al. 2020a, b; Wan et al. 2020; Wang et al. 2021a, b), and other substance-amended biochar (e.g., plant growth-promoting bacteria and compost amended) (Ma et al. 2020; Tang et al. 2020a, b; Tu et al. 2020; Xu et al. 2020). Various immobilization mechanisms of Cd2+ by biochar in soils were involved, like surface complexation, precipitation, electrostatic attraction, and cation exchange (Xiao et al. 2020). The strong binding of biochar with Cd2+ may facilitate the transport of Cd2+ by cotransport inducing potential environmental risks. Cao et al. (2021) investigated the cotransport of Cd2+ with ball-milled biochar from ramie in terms of different Cd2+ and biochar concentrations, and injection sequence. The role of solution chemistry on the cotransport of Cd2+ with biochar, such as pH and ionic strength (IS), is still unknown, which might pose a significant effect on their cotransport.

Numerical models are often used to simulate the transport of biochars in quartz sands or natural soils by fitting their breakthrough curves with/without the retention profiles. For the steady-state flow condition, most studies adopted a two-site kinetic model coupled with the advection-dispersion equation, assuming one site was reversible with attachment-detachment and the other was irreversible only with attachment. For example, the two-site kinetic model has been applied for the cotransport modeling of biochar with U(VI) (Sun et al. 2022), humic acid and naphthalene (Yang et al. 2017), iron oxyhydroxide (Wang et al. 2013b), PAHs (Yang et al. 2021), chromate (Jin et al. 2020), sulfamethazine (Yang et al. 2020a), and proteins (Yang et al. 2019). A few studies employed a one-site kinetic model assuming first-order reversible attachment-detachment (e.g., cotransport of biochar with zwitterionic ciprofloxacin (Zhu et al. 2021) or only irreversible attachment (e.g., individual and cotransport of biochar with Cd2+) (Cao et al. 2021; Liu et al. 2021; Wang et al. 2013a). In transient chemical conditions, the release of biochar from the porous media was simulated by assuming equilibrium and kinetic release using the colloid release model during the cotransport with humic acid (Bradford et al. 2015; Wang et al. 2020). Unfortunately, all the above numerical models used for biochar transport only accounted for the attachment/detachment of biochar to/from the solid phase with Langmuir and/or depth-dependent blocking. Many essential processes that pose significant effects either on biochar or contaminants were ignored in the models for simplification, such as the Ostwald ripening of biochar that can be caused by the cations and the presence of mobile and immobile biochar controlling the coexisting contaminant mobility. Therefore, the descriptions of the current numerical models on the biochar individual transport and cotransport with other contaminants were insufficient, incapable of revealing the driving processes that control their mobility.

Despite the comprehensive research on the interactions between Cd2+ and biochar, the studies on the cotransport of Cd2+ with N-BC are still limited, especially for the unknown influence from the solution chemistry (e.g., pH and IS) and the unclear critical processes driving the mobility of Cd2+ and N-BC during the cotransport. Thus, the objectives of our study were to (1) investigate the individual transport behaviors of Cd2+ and N-BC under different solution pH and IS, respectively; (2) demonstrate the interactive mechanisms between Cd2+ and N-BC and their cotransport behaviors under different solution pH and IS; (3) reveal the underlying key processes controlling the mobility of Cd2+ and N-BC during the cotransport with a process-based cotransport numerical model by incorporating the Ostwald ripening of N-BC and the adsorption between Cd2+ and mobile/immobile N-BC.

2 Materials and methods

2.1 Preparation of N-BC colloids

Wheat straws sampled from Panzhihua City (China) were carbonized at 500 ℃ for 6 h in an N2-supported muffle furnace. The produced pristine biochars (P-BCs) were washed with deionized water under an ultrasonication bath and then stood still for 12 h to remove the dissolved impurities in the supernatant. The above cleaning procedure was repeated for 3 times, and then the biochars were dried at 105 ℃. The P-BCs were milled and sieved by a 200-mesh screen for the following dispersion. 15 g P-BCs in 500 ml deionized water were ultrasonicated for 4 h, then centrifugated at 3800 r min− 1 for 30 min. The supernatants were filtered by 0.45 μm polycarbonate membranes (Whatman, UK) to obtain colloidal solutions with a colloid diameter < 0.45 μm. The colloidal solution was then used as the stock solution. Its concentration was calculated by subtracting the precipitated biochar weighed after drying in the centrifuge tube from 15 g biochar. The obtained nanoscale wheat biochars were labeled as N-BC. The zeta potentials and hydrodynamic diameters of N-BC were determined in KCl solution under different pH (4, 5, 6, and 7) and IS (1, 50, 100, and 150 mM) (Zetasizer Nano ZS, Malvern Panalytical), respectively. The morphology and element analysis of the P-BC and N-BC were conducted using a field emission scanning electron microscope (FESEM) with energy dispersive X-ray spectroscopy (EDX) (SU8220, HITACHI, Japan) and a transmission electron microscope (TEM) with EDX (Talos F200S G2, Thermo Fisher Scientific).

2.2 Porous medium

0.2–0.5 mm quartz sands (Shengli quartz sand factory, China) were washed with deionized water for 3 times before being soaked with 20% HCl. Afterward, the sands were washed with deionized water and dried at 105 ℃. The quartz sand suspension was prepared using 5 g milled and 200 mesh screened quartz sand with deionized water followed by ultrasonication for 20 min. The supernatant solution containing colloidal quartz sand fraction was then collected and dispersed in KCl solution at different pH (4, 5, 6, and 7) and IS (1, 50, 100, and 150 mM) and used for the zeta potential measurement of quartz sand (Zetasizer Nano ZS, Malvern Panalytical) (Sun et al. 2022).

2.3 Column experiments

Acrylic columns with a height of 12 cm, an inner diameter of 3 cm, and porous mesh screens on both ends were used to wet-pack the quartz sand homogenously. The column bulk density and porosity were adjusted to 1.5 ± 0.1 g cm− 3 and 0.45 ± 0.02. The columns were initially saturated with KCl solutions for 10 pore volumes (PV) at the designated pH and IS in each scenario with a bottom-up steady-state flow at a Darcy velocity of 0.488 cm min− 1. Then 1 mM KBr of 1.5 PVs was injected into each column as a conservative tracer to determine the dispersion coefficient. Ion chromatography was adopted to measure the breakthrough curve (BTC) concentration of Br− (Metrohm Compact IC 861, Switzerland). For the individual transport experiments, 1.5 PVs of 500 mg L− 1 N-BC solutions or 10 mg L− 1 Cd2+ solutions were injected, followed by 4 PVs KCl solutions under different pH (4, 5, 6, and 7) and IS (1, 50, 100, and 150 mM), respectively. For the cotransport experiments, 1.5 PVs mixture solutions (500 mg L− 1 N-BC + 10 mg L− 1 Cd2+) were also injected in different pH (4, 5, 6, and 7) and IS (1, 50, 100, and 150 mM), respectively. After each column experiment, the quartz sands were collected in 3 layers of each 4 cm into centrifuge tubes to calculate the recovery. 20 mL deionized water was added, followed by an ultrasonic bath for 20 min. The supernatants were collected to determine the retained concentrations of N-BC and Cd2+, respectively. An automatic collector collected the effluents per minute (BS-100 N, Huxi, China). The N-BC concentrations were determined by UV spectrophotometer (UV-2800, Unico Instrument Company, China) at 550 nm. The correlation between absorbance and colloid concentration is shown in Fig. S1. The Cd2+ concentrations were determined by ICP-MS (ELAN DRC-e, PerkinElmer, US).

2.4 Numerical modeling

The numerical models of the individual and cotransport of N-BC and Cd2+ were set up using the Hydrus-1D code with Phreeqc mode (Jacques et al. 2008). The model domain was composed of 121 nodes with 0.1 cm intervals. The upper and lower boundary conditions were designated as constant pressure heads. For the conservative transport of Br−, a concentration flux boundary was set as the upper boundary condition where 1 mM Br− was injected for 1.5 PVs. A zero concentration gradient boundary was assigned for the lower boundary condition. The reactive transport of N-BC and Cd2+ applied the same boundary conditions as the conservative transport but with different injected solution concentrations.

2.4.1 Colloid transport modeling

The reactive transport of N-BC was simulated by a first-order kinetic sorption model in a one-dimensional form (Šimůnek et al. 2006):

$$\frac{\partial \theta {C}_{b}}{\partial t}+\rho \frac{\partial {S}_{b}}{\partial t}= \frac{\partial }{\partial x}\left(\theta D\frac{\partial {C}_{b}}{\partial x}\right)- \frac{\partial q{C}_{b}}{\partial x}$$
(1)
$$\rho \frac{\partial {S}_{b}}{\partial t}=\theta {\psi }_{b}{k}_{a}^{b}{C}_{b}-\rho {k}_{d}^{b}{S}_{b}$$
(2)
$${\psi }_{b}=1-{S}_{b}/{S}_{max}^{b}$$
(3)

where \({C}_{b}\) (mol L− 1) is the aqueous concentration of N-BC, \(\theta\) (-) is the volumetric water content, \({S}_{b}\) (mol mol− 1) is the attached concentration of N-BC on the sand surface, \(t\) (min) is time, \(\rho\) (g cm− 3)   is the bulk density, \(D\) (cm2 min− 1)   is the dispersion coefficient, \({\psi }_{b}\) (-)   is the blocking function, and \(q\) (cm min− 1) is the water flux. \({k}_{a}^{b}\) (min− 1) and \({k}_{d}^{b}\) (min− 1) are the attachment and detachment coefficients for N-BC adsorption to quartz sand, respectively. \({S}_{max}^{b}\) (mol mol− 1) is the maximum attainable N-BC concentration on the sand surface.

2.4.2 Cd2+ transport modeling

The reactive transport of Cd2+ was simulated based on the modified one-dimension advection-dispersion equation with first-order kinetic sorption (Šimůnek et al. 2006):

$$\frac{\partial \theta {C}_{c}}{\partial t}+\rho \frac{\partial {S}_{c}}{\partial t}= \frac{\partial }{\partial x}\left(\theta D\frac{\partial {C}_{c}}{\partial x}\right)- \frac{\partial q{C}_{c}}{\partial x}$$
(4)
$$\rho \frac{\partial {S}_{c}}{\partial t}=\theta {\psi }_{c}{k}_{a}^{c}{C}_{c}-\rho {k}_{d}^{c}{S}_{c}$$
(5)
$${\psi }_{c}=1-{S}_{c}/{S}_{max}^{c}$$
(6)

where \({C}_{c}\) (mol L− 1) is the aqueous concentration of Cd2+, \({S}_{c}\) (mol mol − 1) is the attached concentration of Cd2+ on the sand surface, \({\psi }_{c}\) (-) is the blocking function, \({k}_{a}^{c}\) (min− 1) and \({k}_{d}^{c}\) (min− 1) are the attachment and detachment coefficients for Cd2+ adsorption to quartz sand, respectively. \({S}_{max}^{c}\) (mol mol− 1) is the maximum attainable Cd2+ concentration on the sand surface.

2.4.3 Cotransport modeling

The cotransport modeling of N-BC with Cd2+ was also based on the modified advection-dispersion equations. A ripening term was added into Eq. (2) to fit the potential ripening BTCs of N-BC in the presence of Cd2+ (Wang et al. 2015):

$$\rho \frac{\partial {S}_{b}}{\partial t}=\theta {\psi }_{b}{k}_{a}^{b}{C}_{b}-\rho {k}_{d}^{b}{S}_{b}+\theta {S}_{b}{C}_{b}{k}_{rip}$$
(7)

where \({k}_{rip}\) (min− 1) is the ripening coefficient accounting for the enhanced particle deposition on the sand surface due to the attractive particle-particle interaction.

The mass balance equation for Cd2+ was given by (Šimůnek et al. 2006):

$$\frac{\partial \theta {C}_{c}}{\partial t}+\rho \frac{\partial {S}_{c}}{\partial t}+\frac{\partial \theta {C}_{b}{S}_{c}^{m}}{\partial t}+\rho \frac{\partial {S}_{b}{S}_{c}^{im}}{\partial t}= \frac{\partial }{\partial x}\left(\theta D\frac{\partial {C}_{c}}{\partial x}\right)- \frac{\partial q{C}_{c}}{\partial x}+\frac{\partial }{\partial x}\left(\theta D\frac{\partial {C}_{b}{S}_{c}^{m}}{\partial x}\right)- \frac{\partial q{C}_{b}{S}_{c}^{m}}{\partial x}$$
(8)
$$\frac{\partial \theta {C}_{b}{S}_{c}^{m}}{\partial t}=\frac{\partial }{\partial x}\left(\theta D\frac{\partial {C}_{b}{S}_{c}^{m}}{\partial x}\right)- \frac{\partial q{C}_{b}{S}_{c}^{m}}{\partial x}+\theta {\psi }^{m}{k}_{a}^{m}{C}_{b}-\theta {k}_{d}^{m}{C}_{b}{S}_{c}^{m}$$
(9)
$$\rho \frac{\partial {S}_{b}{S}_{c}^{im}}{\partial t}=\theta {\psi }^{im}{k}_{a}^{im}{C}_{b}-\rho {k}_{d}^{im}{S}_{b}{S}_{c}^{im}$$
(10)
$${\psi }^{m}={C}_{b}/{C}_{b}^{ref}$$
(11)
$${\psi }^{im}={S}_{b}/{S}_{b}^{ref}$$
(12)

where \({S}_{c}^{m}\) (mol mol− 1) and \({S}_{c}^{im}\) (mol mol− 1) are the adsorbed Cd2+ concentration on the mobile and immobile N-BC, respectively. \({\psi }^{m}\) (-) and \({\psi }^{im}\) (-) adjust the sorption rate of Cd2+ to the present mobile and immobile N-BC, respectively. \({k}_{a}^{m}\) (min− 1) and \({k}_{d}^{m}\) (min− 1) are the attachment and detachment coefficients of Cd2+ to the mobile N-BC, while \({k}_{a}^{im}\) (min− 1) and \({k}_{d}^{im}\) (min− 1) are the attachment and detachment coefficients of Cd2+ to the immobile N-BC, respectively. \({C}_{b}^{ref}\) (mol L− 1) and \({S}_{b}^{ref}\) (mol mol− 1) were the reference concentrations of mobile and immobile N-BC for which the attachment rates were valid, respectively.

2.4.4 Model calibration

The dispersion coefficient (\(D\)) was assigned as the same value for each model, which was estimated by inversing the BTCs of Br−. The reactive transport parameters related to the N-BC transport (\({k}_{a}^{b}\), \({k}_{d}^{b}\), and \({S}_{max}^{b}\)), Cd2+ transport (\({k}_{a}^{c}\), \({k}_{d}^{c}\), and \({S}_{max}^{c}\)), and cotransport (\({k}_{a}^{b}\), \({k}_{d}^{b}\), \({S}_{max}^{b}\) and \({k}_{rip}\) of N-BC; \({k}_{a}^{c}\), \({k}_{d}^{c}\), \({S}_{max}^{c}\), \({k}_{a}^{m}\), \({k}_{d}^{m}\), \({k}_{a}^{im}\), \({k}_{d}^{im}\), \({C}_{b}^{ref}\), and \({S}_{b}^{ref}\) of Cd2+), were estimated by their BTCs using PEST with the Marquardt-Levenberg method (Doherty 2015). The composite parameter sensitivity of each model under different scenarios was also calculated by PEST with the following relation (Doherty 2015):

$$cs{p}_{i}=\frac{{\left[{\mathbf{J}}^{\text{t}}\mathbf{Q}\mathbf{J}\right]}_{ii}^{1/2}}{n}$$
(13)

where \(cs{p}_{i}\) was the composite sensitivity of parameter \(i\). \(\mathbf{J}\), \(\mathbf{Q}\), and \(n\) were the Jacobian matrix, weight matrix, and observation numbers of non-zero weights. The parameter sensitivity analysis can reveal the dominant process by evaluating how the model responded to the parameter change. The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory and isothermal adsorption models (i.e., Freundlich, Langmuir, and Temkin models) were are employed to investigate the interaction of N-BC with quartz sand and Cd2+ with N-BC, respectively (Text S1 and S2).

3 Results and discussion

3.1 Characteristics of N-BC

Figure 1a and c show that the milling treatment produced more nanoparticles in N-BC than P-BC (Fig. 1a and c). The diameter of the single N-BC nanoparticle was 22.21 ± 13.22 nm that was calculated based on the TEM image (Fig. S2). The elemental composition of the N-BC was C (70.86%), O (17.93%), Si (5.53%), K (3.4%), Ca (0.77%), Mg (0.34%), P (0.15%) and Al (0.12%), which did not show significant difference from P-BC (Fig. 1b and d). FTIR results revealed that the oxygen-containing functional groups, i.e., -OH, C = O, COO−, and C-O, increased after grinding (Fig. S3) (Balaz 2018; Cao et al. 2021). The average pore size, pore volume, and specific surface area also increased (Table S1).

Fig. 1
figure 1

The FESEM and EDX images of P-BC (a, b), and the TEM and EDX images of N-BC (c, d), respectively

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The varying hydrodynamic diameters of N-BC in different concentrations with time are presented in Fig. S4. The insignificant fluctuation of hydrodynamic diameter indicated good colloid stability of N-BC. The average hydrodynamic diameters of 200 and 500 mg L− 1 N-BC solutions were 226.2 nm and 215.3 nm, respectively. The zeta potentials of N-BC and quartz sand decreased with the decrease in IS or increase in pH (Table S2). The hydrodynamic diameters of N-BC varied little at different pH around 250 nm, but increased with IS from 228 nm  at 1 mM to 1107 nm at 150 mM due to the compressed double-layer leading to colloid aggregation. Fig. S5 shows that the Langmuir model fitted the isothermal adsorption experiments well with an R2 of 0.975 and 112 mg g− 1 maximum adsorption capacity (Table S3), indicating the adsorption mode of Cd2+ on N-BC was a reversible adsorption process with limited adsorption sites.

3.2 Individual transport of N-BC

The transport of N-BC was retarded by the quartz sand as compared to the conservative transport of Br−, and was decreased with the increasing solution IS (Fig. 2a). The maximum C/C0 of N-BC was reduced from 0.85 at 1 mM to 0.4 at 150 mM, and the recovery rate of the effluent N-BC was also reduced from 96.2% at 1 mM to 37.1% at 150 mM (Table S4). The retarded transport of N-BC with increasing IS was attributed to the elevated electrostatic attraction indicated by the increased zeta potentials of N-BC and quartz sand (Table S2), which promoted the deposition of N-BC on the sand surface. As illustrated in Fig. 2c and Table S4, the calculated maximum energy barrier (\({{\Phi }}_{max}\)) was as high as 879.67 kT (i.e., k is Boltzmann constant and T is absolute temperature) at 1 mM but reduced 3 times to 287.92 kT at 150 mM. On the contrary, the secondary minimum (\({{\Phi }}_{sec}\)) decreased from − 0.005 kT at 1 mM to -7.45 kT at 150 mM, which might promote the deposition of N-BC at the secondary minimum. The model results well fitted the observed data with R2 > 0.96, indicating that the first-order kinetic sorption assumption was valid for N-BC transport without considering the straining process (Table S4). The model-fitted \({k}_{a}^{b}\) was observed to increase with IS but \({k}_{d}^{b}\) decreased, which means the attachment process became increasingly faster while the detachment became slower as IS increased. Meanwhile, \({S}_{max}^{b}\) also increased with IS providing more sorption sites. Positive values of \({{\Phi }}_{pri}\) were observed at 1, 50, and 100 mM IS, suggesting that the deposition at the primary minimum was impossible due to the electrostatic repulsive force. The attachment of N-BC on the sand surface was via the deposition at the secondary minimum, which could be reversible since the absolute value of \({{\Phi }}_{sec}\) was comparable to 1.5 kT (i.e., the average Brownian diffusion thermal energy) (Shen et al. 2007). At 150 mM IS, although \({{\Phi }}_{pri}\) was reduced to -237.85 kT, it was still unlikely for N-BC to deposit at the primary minimum due to the high primary energy barrier. The main process was still the attachment at the secondary minimum since \({{\Phi }}_{sec}\) was reduced to -7.45 kT. The parameter sensitivity analysis showed that the transport of N-BC was very sensitive to \({k}_{a}^{b}\) in all conditions, indicating that attachment was the dominant process (Fig. 2e).

Fig. 2
figure 2

a, b The measured and fitted BTCs of N-BC. c, d The calculated total interaction energy curves. e, f The calculated parameter sensitivities. a, c, e are at different IS under pH 7, and b, d, f are at different pH under 50 mM IS

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Figure 2b shows that the mobility of N-BC was enhanced with the increase in pH. The recovery rate of the effluent N-BC was increased from 53.0% at pH 4 to 63.7% at pH 7 (Table S4). The increase of pH promoted the transport of N-BC due to the elevated electrostatic repulsive force proved by the decreased zeta potentials (Table S2). Based on the DLVO calculations, \({{\Phi }}_{max}\) was enhanced significantly as pH increased (Fig. 2d), hampering the deposition at the primary minimum. Although negative values of \({{\Phi }}_{pri}\) were observed at pH 4 and 5, only \({{\Phi }}_{max}\) at pH 4 was less than 25 kT which was the threshold for colloid stability (Tadros 2014), indicating the possibility of deposition at the primary minimum at pH 4. The deposition at pH 5, 6, and 7 at the primary minimum was non-existent. The absolute values of \({{\Phi }}_{sec}\) were all less than 1.5 kT (the Brownian diffusion thermal energy), resulting in a weak deposition at the secondary minimum. Thus, the retardation at pH 4 was attributed to the deposition both at the primary and secondary minimum, while the retardation at pH 5, 6, and 7 resulted from the deposition at the secondary minimum. Figure 2f shows that the transport of N-BC was still very sensitive to \({k}_{a}^{b}\) while the influence of \({S}_{max}^{b}\) was nonnegligible under acid conditions. It means that the variation of sorption sites induced by the pH change can significantly impact the transport of N-BC in porous media.

3.3 Individual transport of Cd2+

Figure 3a shows the measured and simulated individual transport of Cd2+ under different IS. At 1 mM, the BTC started to elute at 1.4 PVs and reached a peak of 0.85. While at 150 mM, the elution time advanced to 1.2 PV and reached a peak of 0.95. The effluent recovery rate increased from 73.1% at 1 mM to 96.7% at 150 mM (Table S5), demonstrating the facilitating role of increasing IS on Cd2+ mobility. The Cd2+ transport model with an assumption of first-order kinetic sorption showed an excellent description of the observed BTC data with R2 > 0.93. \({k}_{a}^{c}\) decreased from 1.77 × 10− 1 to 3.90 × 10− 3 min− 1, \({k}_{d}^{c}\) increased from 4.09 × 10− 5 to 1.03 × 10− 4 min− 1, and \({S}_{max}^{c}\) decreased from 3.22 × 10− 9 to 2.85 × 10− 9 mol mol− 1 as IS increased from 1 to 150 mM. The model parameter sensitivity analysis revealed that the model responses to \({k}_{a}^{c}\), \({k}_{d}^{c}\), and \({S}_{max}^{c}\) were very sensitive at 1 mM, but the sensitivity dramatically decreased as IS increased (Fig. 3c). All the above results demonstrated that the sorption process weakened as IS increased, suggesting the promoted effect of IS on Cd2+ transport. The enhanced mobility of Cd2+ was due to the increased competition with the coexisting K+ at high IS and the increased zeta potential of quartz sand enhancing the electrostatic repulsive force with Cd2+ (Table S2) (Park et al. 2017).

Fig. 3
figure 3

a, b The breakthrough and fitting curves of Cd2+. c, d The calculated parameter sensitivities. a, c are at different IS under pH 7, and b, d are at different pH under 50 mM IS

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Figure 3b shows the measured and simulated individual transport of Cd2+ under different pH. The BTCs under pH 4, 5, and 6 almost started to elute at the same time from 1.2 PVs. The BTC under pH 7 eluted from 1.4 PVs. The effluent recovery rate decreased from 99.1% at pH 4 to 89.4% at pH 7. The BTC data was well fitted with R2 > 0.95. The calibrated \({k}_{a}^{c}\), \({k}_{d}^{c}\), and \({S}_{max}^{c}\) were all increased from 2.93 × 10− 3 min− 1, 1.06 × 10− 6 min− 1, and 6.65 × 10− 12 mol mol− 1 at pH 4 to 1.54 × 10− 2 min− 1, 5.94 × 10− 5 min− 1, and 3.14 × 10− 9 mol mol− 1 at pH 7, respectively (Table S5). The attachment of Cd2+ to quartz sand was still the dominant process, and its influence on the model results also increased with pH (Fig. 3d). All these results revealed the retardation of Cd2+ by the increasing pH. This retardation was attributed to (1) the enhanced electrostatic attraction force with the increase of pH indicated by the zeta potentials (Table S2); (2) less H+ to compete with Cd2+ for the sorption sites leading to more retained Cd2+ in the column.

3.4 Effect of solution IS on the cotransport

The cotransport BTCs of N-BC with Cd2+ under different solution IS are illustrated in Fig. 4. The mobility of N-BC in the presence of Cd2+ was decreased by the increase of IS with effluent recovery reduced from 94.7% at 1 mM to 7.7% at 150 mM (Table 1). These effluent recoveries of N-BC in the cotransport scenarios were less than those in the individual transport, indicating the retardation effect of Cd2+ on N-BC mobility. It might be due to the previously attached Cd2+ on the quartz sand providing positively-charged favorable sorption sites for the negatively-charged N-BC and facilitating the deposition of N-BC on the sand surface. This can be proved by the enhanced \({S}_{max}^{b}\) of N-BC in the cotransport models, which were all greater than those in the individual transport experiments (Table 1). Fig. S6a shows that the adsorption capacity of N-BC for Cd2+ decreased with the increase of IS due to the ion competition, which might promote N-BC retention in low IS by forming cation bridges between N-BC and quartz sand. However, the retained recovery of N-BC in the cotransport at 1 mM IS only increased by 3% from 1.9% to 4.9% compared to its individual transport, less than that at 150 mM IS increased by 27.6% from 56% to 83.6%. These results indicated that the interaction between quartz sand and N-BC was still the dominant process, while the Cd2+-induced N-BC retention became significant as the IS increased. The decline of C/C0 at the plateau of the BTCs was observed in the BTCs at 100 and 150 mM, where C/C0 decreased with PV after the first BTC peak at 1.6 and 1.5 PV (Fig. 4c and d). This phenomenon did not exist in the individual transport scenarios under all conditions but existed in the cotransport due to (1) the deposition of N-BC on the previously attached N-BC on the sand surface, namely Ostwald ripening, promoted by the cation bridging of Cd2+; (2) the straining of greater aqueous N-BC homo-aggregates in the pores induced by aggregation, which can be more significant as the pores became more plugged; (3) the compressed double layer of N-BC in the high IS at 100 and 150 mM facilitating the above two processes. Both aggregation and ripening might be occurring simultaneously, however, it was not possible to separate these effects from the collected data (Liang et al. 2019; Xu et al. 2021). Therefore, this phenomenon induced by aggregation and/or ripening was all referred to as ripening in the following text for simplification. The simulated retention profiles of N-BC also showed that the retention at the column inlet of N-BC at 100 and 150 mM was 2 to 3 times higher than at 1 and 50 mM IS due to the ripening of N-BC at the inlet (Fig. 5a). This process posed a significant influence on N-BC transport as illustrated by the parameter sensitivity that the model response to \({k}_{rip}\) was after \({k}_{a}^{b}\) (Fig. S7a). It is worth mentioning that the ripening was highly related to the colloidal property. It can be observed at 100 mM IS in a ramie-derived ball-milled biochar transport but without Cd2+, of which particle size was 1167 nm at 100 mM larger than 589 nm of this study (Cao et al. 2021). The preparation and characteristics of nanoscale biochar determined the particle size under different solution chemistry.

Fig. 4
figure 4

The cotransport breakthrough curves and fitting curves of Cd2+ and N-BC at different IS under pH 7. The total Cd2+ concentration (Cd_tot) was the sum of the aqueous free Cd2+ (Cd_aqu) and the Cd2+ adsorbed on the mobile N-BC (Cd_mob) in the effluent

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Table 1 The cotransport fitting parameters and recovery of N-BC at different IS and pH
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Fig. 5
figure 5

The simulated vertical profiles of a the immobile N-BC on sand surface and b retained Cd2+ on the sand surface (solid line) and on the immobile N-BC (dashed line) at 1 mM (black), 50 mM (red), 100 mM (blue), and 150 mM (green) IS, respectively

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The experimental BTCs of Cd2+ in the presence of N-BC at different IS were distinct from the Cd2+ individual transport scenarios (Fig. 4). The experimental effluent recoveries decreased with the increase of IS from 78.14% at 1mM to 35.91% at 150 mM in the presence of N-BC (Table 2), which were contrary to the Cd2+ individual transport that the effluent recoveries increased with IS. It was observed that the experimental effluent Cd2+ concentrations were positively correlated with the effluent N-BC. The adsorption of Cd2+ on the immobile N-BC significantly reduced Cd2+ mobility. It is worth mentioning that both the effluent recoveries of N-BC and Cd2+ decreased in the cotransport compared to their individual transport, except that the effluent recovery of Cd2+ increased in the cotransport at 1 mM IS and pH 7 compared to its individual transport. In the former case, the co-presence of N-BC and Cd2+ promoted the retention of each other in the column. The potential effect of their competition for the adsorption sites on the sand surface was insignificant. In the latter case, the increased mobility of Cd2+ at 1 mM IS and pH 7 in the presence of N-BC could be due to the high adsorption capacity of N-BC for Cd2+ carrying Cd2+ for cotransport (Fig. S6a) and/or the competition of N-BC with Cd2+ for the adsorption sites on the sand surface, promoting the transport of Cd2+. The BTCs of Cd2+ at 100 and 150 mM IS displayed long tails compared to those at 1 and 50 mM, indicating the release of retained Cd2+ from the columns was due to the increased competition with the coexisting K+ at high IS.

Table 2 The experimental and model recoveries of Cd2+ in the cotransport experiments
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The cotransport models fitted the transport of Cd2+ well by considering the interactions of Cd2+ with N-BC and quartz sand in the columns (Fig. 4). Besides the simulated total effluent Cd2+ concentrations, the cotransport models also presented the concentrations of aqueous free Cd2+ and the Cd2+ adsorbed on the mobile N-BC in the effluents. The results showed that 59.1% and 54.86% of the total Cd concentrations adsorbed on the mobile N-BC in the effluents at 1 and 50 mM IS, respectively, which eluted along with 94.7% and 50.7% effluent N-BC (Tables 1 and 2). And the adsorbed Cd2+ on the mobile N-BC decreased to 0.36% and 0.32% along with the decrease of effluent N-BC to 17.3% and 7.7% at 100 and 150 mM IS, respectively (Fig. 4c and d). The distinct positive correlation of the adsorbed Cd2+ on the mobile N-BC with the effluent N-BC revealed the significant cotransport of N-BC with Cd2+ and high affinity of Cd2+ to N-BC at high IS (i.e., 100 and 150 mM). Figure 4c and d display long tails of the Cd2+ BTCs which were mainly the aqueous Cd2+ with 40.9% and 46.63% of the total Cd2+ concentration at 100 and 150 mM IS revealed by the cotransport models, respectively. The Cd2+ adsorbed on the mobile N-BC was only 0.36% and 0.32%, respectively (Table 2). The tails started from 3 PVs which corresponded to the effluent time of the background KCl solution. These results suggested that the Cd2+ in the long tails was in the form of aqueous Cd2+ and might originate from the desorption of the Cd2+ adsorbed on the immobile N-BC which remained only 5.85% and 3.73% at 100 and 150 mM IS in the columns after the experiments. The simulated vertical profiles revealed that the retained Cd2+ concentrations on the immobile N-BC were all lower than those on the sand surface under all conditions (Fig. 5b). The Cd2+ concentrations on the immobile N-BC increased with the column depth, contrary to the decrease of adsorbed N-BC with depth, demonstrating the release of Cd2+ from the immobile N-BC eluted by the background solution. The parameter sensitivity analysis illustrated that the responses of the cotransport model to the parameters followed the sequence of the parameters related to immobile N-BC (\({k}_{a}^{im}\), \({k}_{d}^{im}\), \({S}_{b}^{ref}\)) > quartz sand (\({k}_{a}^{c}\), \({k}_{d}^{c}\), \({S}_{max}^{c}\)) > mobile N-BC (\({k}_{a}^{m}\), \({k}_{d}^{m}\), \({C}_{b}^{ref}\)) (Fig. S7b). These results indicated that the dominant process was the interaction of Cd2+ with the immobile N-BC driving Cd2+ transport. The Cd2+ adsorption on and desorption from the immobile N-BC controlled the retention and release of Cd2+ during the cotransport scenarios. It is worth mentioning that the desorption of Cd2+ from the mobile N-BC was negligible since the parameter sensitivities of \({k}_{d}^{m}\) were zero under all conditions, and the calibration of \({k}_{d}^{m}\) showed very low confidence.

3.5 Effect of solution pH on the cotransport

The cotransport BTCs of N-BC with Cd2+ under different solution pH are illustrated in Fig. 6. The retained N-BC decreased from 79.5% at pH 4 to 44.0% at pH 7 (Table 1), which was due to enhanced electrostatic repulsive force via the expansion of the electrical double layer indicated by the decreased zeta potentials (Table S2). The retained concentrations of N-BC in the presence of Cd2+ were all greater than those in the absence of Cd2+ at different pH, suggesting the retardation of Cd2+ on N-BC transport. Fig. S6b shows that the adsorption capacity of N-BC for Cd2+ increased with the increase of pH due to the enhanced negatively charged N-BC (Table S2). However, the retained N-BC recovery in the cotransport at pH 4 increased by 37.3% from 42.2% to 79.5% compared to its individual transport, higher than that at pH 7 only increased by 13.1% from 30.9% to 44%. These results demonstrated that the Cd2+-induced N-BC retention was significant in low pH, while the interaction between N-BC and quartz sand became dominant as pH increased. The ripening phenomena were observed under all conditions and were more significant at lower pH. It can be proved by the simulated vertical profiles that the deposited N-BC concentrations decreased with column depth and the increase of pH (Fig. 7a). Large amounts of N-BC were retained in the upper layers at pH 4 and 5 due to the enhanced van der Waals attractive force between N-BC and quartz sand in acid pH indicated by the increased zeta potentials (Table S2), resulting in the significant ripening effect. The parameter sensitivity analysis demonstrated that the adsorption to the quartz sand surface was still the main process that controlled N-BC transport and the ripening effect was nonnegligible (Fig. S8a). The calibrated transport parameters showed that \({k}_{a}^{b}\) and \({S}_{max}^{b}\) were all increased in the presence of Cd2+, indicating that the adsorbed Cd2+ on the quartz sand provided additional sorption sites and enhanced the adsorption rate of N-BC (Table 1).

Fig. 6
figure 6

The cotransport breakthrough curves and fitting curves of Cd2+ and N-BC at different pH under 50 mM IS. The total Cd2+ concentration (Cd_tot) was the sum of the aqueous free Cd2+ (Cd_aqu) and the Cd2+ adsorbed on the mobile N-BC (Cd_mob) in the effluent

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Fig. 7
figure 7

The simulated vertical profiles of a the immobile N-BC on sand surface and b retained Cd2+ on the sand surface (solid line) and on the immobile N-BC (dashed line) at pH 4 (black), pH 5 (red), pH 6 (blue), and pH 7 (green), respectively

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The transport of Cd2+ in the presence of N-BC showed divergent BTCs compared to the absence of N-BC (Fig. 6). The experimental recoveries of the effluent Cd2+ decreased from 52.95% at pH 4 to 43.47% at pH 6, and then increased to 56.39% at pH 7 (Table 2). It was observed that the BTCs of Cd2+ before 2.8 PVs gradually increased with the effluent N-BC concentrations as pH increased from 4 to 7. A positive correlation between the BTCs of Cd2+ before 2.8 PVs and the BTCs of N-BC can be deduced, indicating a cotransport of Cd2+ with N-BC promoting the mobility of Cd2+. After 2.8 PVs, a high BTC peak of Cd2+ was observed at pH 4, which gradually decreased with the increase of pH. These phenomena can be attributed to the reduced competition of H+ with Cd2+ and the increased electrostatic attraction between the immobile N-BC and Cd2+ indicated by the decreasing zeta potential of N-BC (Fig. S6b and Table S2). This trend was consistent with the individual transport of Cd2+ that the BTCs of Cd2+ decreased with the increasing pH (Fig. 3b).

The BTCs of Cd2+ in the presence of N-BC were simulated well at different pH (Fig. 6). The model results revealed that the simulated BTCs of Cd2+ adsorbed on the mobile N-BC (i.e., the purple curves) were positively correlated to the BTCs of N-BC that were increased with pH. The effluent Cd2+ concentrations in the BTCs after 2.8 PVs (i.e., the blue curves) were mainly from the desorption of Cd2+ adsorbed on the immobile N-BC. It can be proved by the simulated vertical profiles that the retained Cd2+ concentrations on the immobile N-BC increased with pH but were still less than those on the sand surface (Fig. 7b; Table 2). The parameter sensitivity analysis revealed that the responses of the cotransport models to the parameters followed the sequence of the parameters related to immobile N-BC (\({k}_{a}^{im}\), \({k}_{d}^{im}\), \({S}_{b}^{ref}\)) > quartz sand (\({k}_{a}^{c}\), \({k}_{d}^{c}\), \({S}_{max}^{c}\)) > mobile N-BC (\({k}_{a}^{m}\), \({k}_{d}^{m}\), \({C}_{b}^{ref}\)) (Fig. S8b). The low parameter sensitives of \({k}_{a}^{m}\), \({k}_{d}^{m}\), and \({C}_{b}^{ref}\) indicated that the interaction of Cd2+ with mobile N-BC played a minor role. These results suggested that the driving process controlling Cd2+ transport at different pH was the interaction of Cd2+ with immobile N-BC. Despite the high affinity of Cd2+ with N-BC, the adsorption of Cd2+ to the immobile N-BC posed a more significant effect on Cd2+ transport than the adsorption to the mobile N-BC, which was due to the retardation effect of the immobile N-BC on Cd2+ transport.

4 Conclusion

This study demonstrated variable transport behaviors of Cd2+ and N-BC during their individual and cotransport scenarios under different pH and IS, which indicated the significant effects of solution chemistry on their transport patterns. For the individual transport scenarios, increasing IS and decreasing pH retarded the transport of N-BC but promoted the transport of Cd2+. For the cotransport scenarios, the presence of Cd2+ promoted the deposition of N-BC on the quartz sand surface with increasing IS and decreasing pH by providing additional sorption sites and led to the ripening of N-BC via cation bridging. In general, the presence of N-BC retarded the transport of Cd2+ under all conditions. However, lower pH and higher IS could facilitate the release of Cd2+ from the immobile N-BC. The process-based cotransport model with parameter sensitivity analysis revealed that the Cd2+ adsorption on and desorption from the immobile N-BC controlled the retention and release of Cd2+ at variable pH and IS, while the influence of mobile N-BC on Cd2+ transport was minor. Our findings demonstrated that despite the retardation effect of N-BC on the Cd2+ mobility, groundwater’s transient solution chemistry conditions could still lead to the release of Cd2+ from the immobile N-BC. It is worth mentioning that this study did not consider the influence of coexistent natural substances, such as multivalent ions, dissolved organic matters, and soil colloids. They may pose distinct impacts on the co-migration of Cd2+ with N-BC that need further investigations.