• 关键词：非线性吸附  简化的吸附模型  溶质扩散  粘土  解析解  有限厚度边界  移动边界

• 基金项目：国家杰出青年科学基金项目(No50425825);国家自然科学基金重点资助项目(No50538080)

• 谢海建
• 浙江大学岩土工程研究所, 杭州 310027

• 陈仁朋
• 浙江大学岩土工程研究所, 杭州 310027

• 陈云敏
• 浙江大学岩土工程研究所, 杭州 310027

• 柯瀚
• 浙江大学岩土工程研究所, 杭州 310027

• 摘要：在采用非线性分段式吸附等温模式的基础上,建立了溶质在粘土中的一维扩散模型,在考虑有限厚度边界及土中溶质背景浓度的条件下得到了相应的解.模型引入了移动边界以说明当溶质在粘土孔隙水中的浓度达到某一较高值后,阻滞因子将发生显著变化.算例分析表明,该模型和考虑经典非线性吸附等温线得到的结果相差不大,这进一步说明了该模型的合理性.考虑非线性吸附效应对溶质迁移有重要影响.在较高溶质浓度下采用线性吸附等温模式会得到偏不安全的结果.该解相对较简单,并可用于验证各种数值模型、拟合试验数据等.

• Abstract：An analytical solution of solute diffusion through soil is presented based on a simplified non-linear adsorption isotherm. The adsorption of solute on the clay minerals is accurately reflected by the present isotherm. The finite depth boundary condition and initial concentration condition are considered in the model. The moving boundary is introduced to indicate the notable change in the clay retardation factor with the increase of solute concentration. No great difference was observed between the results obtained from the presented solution and those obtained from numerical solutions considering classic non-linear adsorption isotherms. It is also shown that nonlinear adsorption plays an important role in solute diffusion through clay liners. The solute diffusion models grossly overestimate retardation of contaminants at high solute concentration by assuming linear adsorption. The method presented in this paper is relatively simple to apply and can be used for evaluating experimental results, and verifying more complex numerical models.

• Key words：nonlinear adsorption  simplified nonlinear adsorption isotherm  solute diffusion  clay  analytical solution  finite depth boundary  moving boundary

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