4.1 Transport process of Pb2+
Fig. 3 shows the breakthrough curves (BTCs) of only Pb2+ at the different injection concentrations (C M=100, 200 and 400 ng/mL) and Darcy velocities (v =0.087 and 0.260 cm/s). Clearly, the steady values increase with increasing injection concentration C M, and the times needed to reach stability also correspondingly increase. On the other hand, the outflow concentration slightly increases with increasing Darcy velocity (v =0.087 cm/s→0.260 cm/s), which actually reveals a small deposition effect at a higher velocity.
Using Eqs. (1)−(3), the BTCs of Pb2+ can be theoretically predicted (see Fig. 3), which are in good agreement with the test results in terms of the trend, with a coefficient of determination of R 2>0.90. The adopted parameters are summarized in Table 1 referring to the test results of the authors. According to the concept of the theoretical model, the parameters (β 1,κ d) are not related to the hydrodynamic process (Bai et al., 2019), and parameter α d is also simply set to a constant value (Bai et al., 2017; Bennacer et al., 2017). Thus, only the reaction rate constant λ varies due to the difference in seepage velocity. Therefore, determining the calculation parameters becomes very simple and clear. The transport processes are calculated using the PARDISO solver in COMSOL Multiphysics (COMSOL Co., Ltd.). The control parameters in the calculations are as follows: the temporal discretization step is 3 s, the spatial discretization step is 0.02 m, the damping factor is 0.9, the iteration number is 4, and the relative tolerance is 0.0001.
For the test results using the impulse-injection pattern obtained by the authors at a higher injection concentration (Pb2+,C M=100−400 mg/mL), the BTCs at v =0.087 and 0.260 cm/s are approximately the same, seemingly indicating that the Darcy velocity has a negligible effect on the transport of heavy metal ions. This phenomenon is slightly different from the test results shown in Fig. 3 (herein, C M=100−400 ng/mL). Actually, during heavy metal ion transport, a portion dissolves in water and is transported by it, while some is adsorbed onto the solid matrix. Clearly, at a high injection concentration, the heavy metal ions dissolved in water are dominant due to the relatively limited adsorption amount on the solid matrix, which will have little effect on the effluent concentration in a short time (e.g., the impulse-injection pattern or the initial period in Fig. 3). In contrast, a large influence is observed in the case of continuous injection (Fig. 3), which is manifested as a distinct deposition and subsequent release process with decreasing injection concentration. The theoretical results also confirm this characteristic (see Fig. 3).
Compared with the outflow concentration of Pb2+ in the absence of SPs (Fig. 3), the steady outflow concentration of Pb2+ in the presence of SPs (Figs. 4 and 5) is complex. In other words, the presence of SPs may promote or inhibit Pb2+ migration. The final results seem to be closely related to the concentration of injected Pb2+, the particle size and concentration of injected SPs, and the seepage velocity. For instance, the steady concentration of Pb2+ in the presence of SPs (C inj=0.5 mg/mL; Fig. 4(a)) for a slightly smaller particle size (e.g., D 50=13.4 μm) and at a lower injection concentration of Pb2+ (e.g.,C M=100 ng/mL) and higher seepage velocity (e.g.,v =0.260 cm/s) is nearly 1.1 times that in the absence of SPs. This indicates that SPs can significantly facilitate Pb2+ transport due to the size exclusion effect (Alem et al., 2015; Bai et al., 2017).
However, with increasing injection concentration of Pb2+ (e.g., C M=400 ng/mL; please compare Figs. 3 and 4(a)), the presence of SPs inhibits Pb2+ transport due to the accelerated deposition of SPs. For example, the steady concentration of Pb2+ in the presence of SPs (C inj=0.5 mg/mL; Fig. 4(a)) for a slightly smaller particle size (e.g.,D 50=13.4 μm) is nearly 0.5 times that in the absence of SPs (Fig. 3) at a Pb2+injection concentration of C M=400 ng/mL and a seepage velocity of v =0.260 cm/s. At this time, Pb2+adsorption onto SPs reduces the repulsive force between SPs and the solid matrix according to the DLVO theory due to the decrease in absolute zeta potential in the surface charge (Wang et al., 2012; Sugimoto et al., 2014; Chrysikopoulos, et al., 2017; Chen et al., 2018), resulting in an increase in the deposition amount of SPs onto the solid matrix. Hence, the coupling effect of Pb2+ and SPs should be considered, which is attributed to the decrease in the double electric layer on the SP surface (i.e., the decrease in surface potential energy). Clearly, the promotion effects of SPs increase with increasing injection concentration (please refer to the difference between Figs. 4(a) and 4(b)), while they significantly decrease with increasing particle size (please refer to the difference between Figs. 4 and 5).
4.2 Deposition of Pb2+ and SPs along the migration distance
As a typical result, Fig. 6 shows the measured Pb2+deposition concentrations along the migration distance when the particle size of the co-injected SPs is D 50=13.4 μm, including the results in the absence of SPs (i.e.,C inj=0). The test results reveal that the Pb2+ deposition concentration on the solid matrix rapidly decreases with increasing migration distance. When the migration distance is reduced to x =90 cm (i.e., the length of the sand column), the deposition concentrations are already very low. In addition, with increasing seepage velocity of the water flow (e.g.,v =0.087→0.260 cm/s), due to the continuously increased hydrodynamic forces, the Pb2+ deposition concentration also notably decreases with decreasing suspended SPs in the water flow (please compare Figs. 6 and 7). Similar results are also obtained whenD 50=24.7 μm, which is not shown herein due to the limited space. However, the test photos in Fig. 1(b) clearly show the transport evolution of SPs over time. On the whole, with increasing particle size of the SPs, the SP deposition amount will increase significantly (Fig. 1(b)), while the Pb2+ deposition amount will conversely decrease. In other words, when the SP particle size is larger than a certain value, SP adsorption onto heavy metal ions will be weakened, namely, the inhibition effect will be significantly reduced.
Fig. 6 shows that Pb2+ deposition increases with increasing injection concentration (e.g., CM=100 ng/mL → 400 ng/mL). At this time, more Pb2+ will be adsorbed onto the surface of SPs and migrate or be deposited in the form of coupled Pb2+ and SPs with the flowing water, which is reflected by the SP deposition distribution with the migration distance, as shown in Fig. 7. It should be noted that the concentration of the injected Pb2+ in this test is arguably low (i.e., CM=100−400 ng/mL), so most Pb2+ will be adsorbed onto the surface of SPs, thus forming a combination of coupled Pb2+ and SPs. However, when the Pb2+ injection concentration notably increases, Pb2+ will not only occur in combined form but will also occur as free Pb2+ in water and be transported by the flowing water. At this time, as shown in Figs. 4 and 5, the Pb2+ concentration in the leachate will notably increase.
Generally, the heavy metal ions adsorbed onto SPs will change the dielectric properties of the SPs, resulting in positively charged surfaces. As such, the adsorption of SPs onto the porous medium matrix increases, and the deposition probability of SPs also increases. However, in this study, it seems that the Pb2+injection concentration has little effect on SP deposition during the migration process (see the green and red test dots in Fig. 7), which is probably related to the low Pb2+ injection concentration (i.e., CM=100−400 ng/mL). In other words, adsorption of a small amount of heavy metal ions is not enough to significantly change the surface charge characteristics of SPs. At this time, the migration process of SPs can still be described by the transport theory of a single suspension (i.e., Eqs. (1)−(3)). In contrast, the coupling effect of SPs on heavy metal ion transport must be considered. Hence, heavy metal ions will migrate and be deposited in two forms, i.e., dissolved in the flowing water and absorbed onto the SPs.
Using Eqs. (1)−(4), the BTCs of SPs can be theoretically predicted, and furthermore, the distributions of the deposited SPs along the migration distance are also obtained (see the solid lines in Fig. 7). The adopted parameters are listed in Table 1 according to the test results. Fig. 7 also shows the predicted curves of the deposited SPs during transport of only SPs (i.e., dashed lines). Clearly, there is a good agreement between the predicted and experimental results denoted by the dots, with a coefficient of determination ofR 2>0.91. These suitable agreements indicate that the deposition-release model proposed in this paper can well reflect the migration process of a single suspended substance by seepage. Clearly, the reaction rate constant of SPs interacting with the solid matrix is far larger than that of Pb2+interacting with the solid matrix (Table 1), which essentially reflects a more notable hysteretic effect of the SPs attached on the matrix by the clogging effect. It can be deduced that heavy metal ion transport is closely related to SP transport due to the strong adsorption on heavy metal ions with positive charges. In other words, the magnitude of the mutual influence between two types of suspended matter on their transport and deposition characteristics depends on the physical and chemical properties.
Based on the test results in Fig. 6, the Pb2+deposition rate in the whole column with the SP injection concentration, Cinj, can also be given by Eq. (4) (see Fig. 8). Clearly, with increasing SP injection concentration (e.g., Cinj=0, 0.5, 2, 4 mg/mL), the Pb2+deposition amount gradually increased. Here,C inj=0 indicates the Pb2+deposition rate in the absence of SPs. Apparently, with increasing Pb2+ injection concentration (C M=100, 400 ng/mL), the Pb2+deposition amount decreases. Moreover, heavy metal ions will be dissolved in water and migrate with the water flow. Therefore, the deposition rate of heavy metal ions decreases slightly with increasing seepage velocity, and the heavy metal ions dissolved in water will gradually become dominant with increasing injection concentration.
As mentioned before, with increasing SP particle size (e.g.,D 50=13.4→ 24.7 µm), the SP deposition amount increases. However, due to the reduction in the specific surface area of SPs, their adsorption capacity of Pb2+ will be weakened, resulting in a decrease in the Pb2+deposition rate. In addition, the increasing trend of the Pb2+ concentration with increasing SP injection concentration will also be weakened, which results in a decreasing trend in the Pb2+ deposition rate (Fig. 8(a)).