Analytical solutions for one-dimensional contaminant ion transport through electro-kinetic barriers

Analytical model for electrokinetic remediation of contaminated soil

“…When ∇ is less than 1 V/m, the effect of ∇ on contaminant transport is not obvious, which may be attributed to the minimum electric field intensity required to drive HMI transport. As depicted in figure 4(b), when ∇ increases from 1 V/m to 10 V/m, the mass flux in the middle of the soil increases rapidly, which agrees with the results obtained by Wang et al [10] As evidenced by the variation in mass flux depicted in figure 4(b), ∇ accelerates the migration speed of HMIs in soil and the amount of migrating HMIs.…”

“…The finite difference method is adopted to calculate the model proposed in this study. To facilitate thorough comparison and analysis, the parameters presented in table 1 used in numerical simulations by Narasimhan and Ranjan [5], Kim et al [15], and Wang et al [10] are adopted. Based on the governing equations and the initial and boundary conditions given by equations ( 7)-( 10), the model is numerically solved using MATLAB 2020b using the finite difference method.…”

“…Analytical approaches offer enhanced insights into the fundamental physical mechanisms underlying EKR processes, thereby improving computational efficiency. Analytical solutions also tend to produce more precise outcomes owing to their mathematical rigor, which provides theoretical benchmarks and enables the verification of intricate numerical models [9,10]. Moreover, these solutions, noted for their simplicity, can be directly applied to practical experiments or engineering applications, and have garnered increasing attention in recent years.…”

Analysis of Factors for Compacted Clay Liner Performance Considering Isothermal Adsorption

“…Many studies have been performed on mathematical simulations of pollutant migration [8][9][10][11][12][13][14][15][16][17][18]. The effect of boundary conditions on the simulation results has been discussed through theoretical analysis [8][9][10]. Solute transport experiments have been conducted to study suitable boundary conditions [1,4,[15][16][17][18].…”