## 4 Results and Discussion  
### Dissolution and Diffusion Processes of a Single Electrolyte  
Figure 3 shows the changes in the concentration profile of various single-electrolyte salts at different times when they were dissolved in static water. Generally, although the dissolution of a soluble salt is slow, it does occur in static water. In static water, the dissolution equilibrium time of soluble salts may be as long as one year [9]. In the case of unsteady diffusion, the solute has a normal profile [27] that reflects the concentration gradient, and this is suitable for calculations made using [PERSON]'s second law [28]. Except for subtle differences, the diffusion trends of MgSO\({}_{4}\) and Na\({}_{2}\)SO\({}_{4}\) are roughly similar, as shown in Figure 3a,b, respectively. To directly compare the diffusion behaviors of MgSO\({}_{4}\) and Na\({}_{2}\)SO\({}_{4}\) in aqueous solution, Figure 3c shows the calculated results of their saturation degree profiles at different diffusion times. Because the change in solute concentration or saturation degree is mainly caused by solute diffusion, it is concluded from the saturation degree that the diffusion ability of Na\({}^{+}\) is slightly stronger than that of Mg\({}^{2+}\). Compared to Mg\({}^{2+}\), in the process of cation diffusion, the atomic weight of Na\({}^{+}\) is smaller, the atomic radius is smaller, and the valence is lower;  
thus, the hydration ability of Na+ is weaker than that of Mg2+, and this leads to the smaller diffusion resistance. From this rule, the Na2 SO4 components diffuse slightly faster than MgSO4, as shown in Figure 3c. This phenomenon is more obvious when the diffusion time is long.  
The difference between the experimental (Exp.) and calculated (Calc.) results in Figure 3a,b is due to the deviations in the calculation process. According to Equations (1)-(9), it is assumed that the parameters (e.g., \(D_{AB}\)) are not accurate as expected, which makes the makes the calculation error larger at longer durations of dissolution and diffusion. However, the calculation is still reliable in practice because the calculated results are close enough to the experimental data even after nearly 3000 h of diffusion.  
Figure 4 shows changes in saturation degree at different distances from the solid-liquid interface over time, and this indicates that the diffusion of soluble salts in static water is not stable. The process of static dissolution is roughly divided into three stages. The first stage is until about 720 h of dissolution. The saturation degree changes during this period of dissolution and diffusion processes are close to linear, and this indicates that the mass transfer is roughly steady. The second stage is from about 720 to 7000 h. During this period of the diffusion process, the saturation degree change is nonlinear and specifically has the form of a power function; the diffusion rate gradually decreased, and this indicates that the mass transfer entered an unsteady state. The third stage is after 7000 h, when the diffusion rate decreased further and the saturation degree change or the mass transfer process developed into a slow quasi-linear form and finally reached an unsaturated steady state. It is worth mentioning that such unsteady state mass transfer phenomena are common in molecular diffusion in condensed matter  
Figure 3: Profiles of saturation degree over time (in the dissolution and diffusion processes of single electrolyte in water): (**a**) MgSO4; (**b**) Na2 SO4; (**c**) calculated results of MgSO4 and Na2 SO4.  
systems, and this is similar to the transport [29] in cementitious materials. Among the three stages of dissolution and diffusion in Figure 4, the dissolution mining in practice mainly occurs in the first stage; hence, the law of diffusion at the first stage is the most important.