Adsorption characteristics play a crucial role in solute transport processes, serving as a fundamental factor for evaluating the performance of clay liners. Nonlinear adsorption isotherms are commonly found with metal ions and organic compounds, which introduce challenges in obtaining analytical solutions for solute transport models. In this study, analytical solutions are proposed for a fully coupled hydraulic‐mechanical‐chemical (HMC) model that accounts for both the Freundlich and Langmuir isotherms. To mitigate the difficulties arising from the variable coefficients, the system of second‐order partial differential equations involving three variables is linearized. The method of separation of variables, theory of integration, and Fourier series are utilized to derive analytical solutions. The analytical method presented can potentially be extended to a broad spectrum of nonlinear adsorption isotherms. The results reveal a 56.5% reduction in solute breakthrough time under the Freundlich isotherm and a remarkable 2.6‐fold extension under the Langmuir isotherm when compared to the linear isotherm. The adsorption constants of the Freundlich and Langmuir isotherms exhibit a positive correlation with breakthrough time, while the exponent of the Freundlich isotherm and the maximal adsorption capacity in the Langmuir isotherm demonstrate a negative association with breakthrough time. This study enhances the precision of solute transport prediction and provides a more scientific assessment of clay liner performance.

中文翻译：

---

非线性吸附全耦合水力-机械-化学模型的解析解


吸附特性在溶质传输过程中起着至关重要的作用，是评估粘土衬垫性能的基本因素。非线性吸附等温线常见于金属离子和有机化合物，这给获得溶质输运模型的分析解决方案带来了挑战。在本研究中，提出了一个完全耦合的液压-机械-化学 (HMC) 模型的解析解，该模型同时考虑了弗罗因德利希 (Freundlich) 和朗缪尔 (Langmuir) 等温线。为了减轻因变量系数带来的困难，涉及三个变量的二阶偏微分方程组被线性化。利用分离变量的方法、积分理论和傅立叶级数来导出解析解。所提出的分析方法有可能扩展到广泛的非线性吸附等温线。结果表明，与线性等温线相比，Freundlich 等温线下的溶质突破时间缩短了 56.5%，而 Langmuir 等温线下的溶质突破时间显着延长了 2.6 倍。 Freundlich和Langmuir等温线的吸附常数与突破时间呈正相关，而Freundlich等温线的指数和Langmuir等温线的最大吸附容量与突破时间呈负相关。这项研究提高了溶质运移预测的精度，并为粘土衬垫性能提供了更科学的评估。