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)).