Anion exclusion is an important phenomenon in agricultural, environmental and engineering fields which still needs suitable quantitative models. In this work, a novel model is proposed which considers the porous media as parallel capillaries with negatively charged walls that cause total anion exclusion at a distance from the walls. By defining the ‘anion velocity coefficient’, ${\upsilon }_{\left(-\right)}$, as the ratio of anion velocity to pore fluid velocity, equations to estimate the value of ${\upsilon }_{\left(-\right)}$ at the injection inlet have been derived by three different methods, namely from the profiles' data, ${\upsilon }_{\left(-\right)}^{\text{data}}$, from the concentration ratio at the inlet, ${\upsilon }_{\left(-\right)}^{r_c}$, and from the electrical double layer thickness model, ${\upsilon }_{\left(-\right)}^{\mathrm{EDL}}$. Finally, a simple sensitivity analysis for the third method has been presented. The estimates of ${\upsilon }_{\left(-\right)}$ presented in this paper were examined versus 22 data points for nitrate solution flow in initially dry soil columns for various soil and salt types and solution concentrations. The coefficient of determination between ${\upsilon }_{\left(-\right)}^{\text{data}}$ and ${\upsilon }_{\left(-\right)}^{r_c}$ for the whole dataset was 0.7755. Also, the ${\upsilon }_{\left(-\right)}^{r_c}$ estimate could predict the ${\upsilon }_{\left(-\right)}$ value estimated from the breakthrough anion concentration curve for available data of an advective injection test in a clayey rock. As a result, when anion exclusion dominates, the anion flux decreases but the anion velocity increases. In the case of using nitrate fertilisers, this point may be used to regulate the amount of optimal irrigation and also to explain the extent of contamination of a distant groundwater body.

中文翻译：

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一种用于研究土壤和页岩中部分水饱和迁移的新型机械阴离子排斥模型：以硝酸盐溶液流动为例

阴离子排斥是农业、环境和工程领域的重要现象，仍需要合适的定量模型。在这项工作中，提出了一种新模型，该模型将多孔介质视为具有带负电荷的壁的平行毛细管，在远离壁的距离处导致完全的阴离子排斥。通过定义“阴离子速度系数”，${\upsilon }_{\left(-\right)}$, 作为阴离子速度与孔隙流体速度之比, 方程来估计${\upsilon }_{\left(-\right)}$进样口的位置已通过三种不同的方法得出，即从剖面数据，${\upsilon }_{\left(-\right)}^{\text{数据}}$，从入口处的浓度比，${\upsilon }_{\left(-\right)}^{r_C}$，从双电层厚度模型，${\upsilon }_{\left(-\right)}^{\mathrm{EDL}}$. 最后，对第三种方法进行了简单的敏感性分析。的估计${\upsilon }_{\left(-\right)}$本文介绍的硝酸盐溶液在最初干燥的土壤柱中的 22 个数据点对各种土壤和盐类型以及溶液浓度进行了检查。之间的决定系数${\upsilon }_{\left(-\right)}^{\text{数据}}$和${\upsilon }_{\left(-\right)}^{r_C}$整个数据集为 0.7755。此外，该${\upsilon }_{\left(-\right)}^{r_C}$估计可以预测${\upsilon }_{\left(-\right)}$根据粘土岩平流注入试验可用数据的穿透阴离子浓度曲线估计的值。结果，当阴离子排斥占主导地位时，阴离子通量减少但阴离子速度增加。在使用硝酸盐肥料的情况下，这一点可用于调节最佳灌溉量，也可用于解释远处地下水体的污染程度。