**3. Results and Discussion**

## *3.1. The Curve of Adsorption and Desorption Kinetics*

Figure 3 shows the curves of adsorption and desorption kinetics of Pb. The adsorption and desorption capacities of Pb2+ in the three sand media were significantly dissimilar. The adsorption and desorption quantity reached equilibrium in 1440 min. The maximum adsorption capacity of fine sand, medium sand, and coarse sand were 2366.6 mg·kg−1, 1847.6 mg·kg−1, and 1543.8 mg·kg−1, respectively. The maximum desorption capacity of coarse sand, medium sand, and fine sand were 81.6 mg·kg−1, 62.38 mg·kg−1, and 29.18 mg·kg<sup>−</sup>1, respectively. Compared to the hyperbolic diffusion model, pseudo-secondorder model and Weber–Morris model, the data fit well to the Elovich model against various time ranges because the minimum *R*<sup>2</sup> value was 0.90. The fitting parameters are shown in Table 2. Based on the adsorption kinetics experiment data, Pb2+ in the contaminated solution was adsorbed rapidly onto the sampling sand within 240 min. The adsorption quantity gradually was stable from 240 to 1440 min in the experiment; this implies several points that adsorbed Pb2+ quickly on the medium surface at the initial stage. The effective points that adsorb Pb2+ gradually decreased with increasing reaction time, which gradually weakened the adsorption capacity until it reached equilibrium. The experiment's result aligned with the study of Ren, L. [33]. The same conditions occurred in the desorption kinetics experiment.

Figure 4 illustrates the effects of pH on the adsorption and desorption of sand medium. The adsorption capacity of Pb2+ in three sand media gradually increased at pH range of 4 to 6. The desorption capacity gradually decreased with increasing pH and the desorption quantity steadily approached equilibrium when the pH was between 8 and 9. Fine sand's adsorption and desorption capacities showed almost no change at different pH levels compared with medium and coarse sand. When the pH increased, the competitive adsorption sites of hydrogen ions in the medium decreased, and heavy metals mainly existed in the combined state of hydroxide or carbonic acid. This state is not conducive to their migration in the medium and increases adsorption capacity. These experimental conclusions are consistent with the literature [30,34].

**Figure 3.** Curves of adsorption and desorption kinetics of Pb in different media: (**a**) the adsorption quantity variation of Pb based on adsorption kinetics; (**b**) the desorption quantity variation of Pb based on desorption kinetics.


**Table 2.** Kinetic parameters for adsorption and desorption of Pb in different media.

Note: The data were fitted to the Elovich equation: *Q* = *a*<sup>1</sup> + *b*<sup>1</sup> ln*t*, the hyperbolic diffusion equation: *Q*/*Q*max = *a*<sup>2</sup> + *b*<sup>2</sup> *t* 1/2, the pseudo-second-order equation: *Q* = *k*<sup>1</sup> *Q*max<sup>2</sup> *t*/(1 + *k*<sup>1</sup> *Q*max *t*) and the Weber–Morris equation: *Q* = *k*<sup>2</sup> *t* 1/2 + *c*, respectively, where *Q* is the adsorption/desorption capacity; *t* is time; *a*<sup>1</sup> and *a*<sup>2</sup> refer to constant associated with maximum adsorption/desorption amount for the Elovich equation and the pseudosecond-order equation, respectively, *b*<sup>1</sup> and *b*<sup>2</sup> refer to adsorption/desorption rate coefficient, *k*<sup>1</sup> and *k*<sup>2</sup> refer to adsorption/desorption rate coefficient for pseudo-second-order model and Weber–Morris model, respectively, *c* is constants related to the medium for Weber–Morris model, *Q*max refers the equilibrium adsorption/desorption capacity for coarse sand, medium sand and fine medium.
