考虑非线性吸附时污染物在半无限黏土中的一维扩散解

Analytical solution of contaminant diffusion through semi-infinite clay under non-linear adsorption condition

在考虑分段吸附等温模式的基础上,建立了污染物在黏土中的一维扩散模型。并得到了简化求解条件下的解析解。模型引入了移动边界以说明当污染物在黏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。通过该解分析了黏土颗粒对污染物的这种非线性吸附特征对其在黏土中扩散的影响。算例分析表明本文解得到的计算结果介于不考虑吸附情形和考虑线性吸附情形得到的结果之间。对于文中算例,考虑线性等温线得到的污染物击穿时间为按本文解得到的击穿时间的2.2倍。因此,在浓度较大时,采用线性吸附等温模线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。

An analytical solution of contaminant diffusion through soil was presented based on the assumption of simplified non-linear adsorption isotherm. The moving boundary was introduced to indicate the notable change of retardation factor of clay with the increase of contaminant concentration level. The breakthrough curve obtained from the present solution was found to be between the two curves obtained from the analytical solution for one-dimensional diffusion considering no adsorption and linear adsorption. As for the present example, the breakthrough time of the contaminant obtained from the linear adsorption solution was 2.2 times greater than that obtained from the nonlinear adsorption solution presented here. The present method was relatively simple to apply and could be used for evaluating experimental results and verifying more complex numerical models.