Poisson-Boltzmann与Donnan模型计算压实膨润土孔隙水与外部溶液间离子平衡的差异性比较

Comparison of the Poisson-Boltzmann and Donnan Models for Calculating the Ion Equilibrium between Compacted Bentonite Porewater and External Solution

压实膨润土孔隙水与外部溶液之间的离子平衡是影响离子在压实膨润土中扩散的影响因素之一,表征这一平衡的离子平衡系数可用压实膨润土的宏观属性参数通过Donnan模型计算得到.通过对膨润土主体矿物蒙脱石的TOT层结构单元进行简化,构建了一个压实膨润土的单类孔隙结构模型,辅以一个尺度变量H,用Poisson-Boltzmann(PB)理论模型计算上述离子平衡系数.对比计算结果,发现PB模型计算的离子平衡系数总是大于Donnan模型的结果,而参数H是联系这两种模型之间的桥梁.通过对参数H取极限H→0,实现了从PB模型到Donnan模型的数学变换,并从机理上讨论了两种模型之间的差异及其在实际扩散问题中的应用.分析表明PB模型更符合离子在压实膨润土中扩散的实际情况,更适于处理实际扩散问题.

The ion equilibrium at the interface of solution within compacted bentonite, and the external solution is an important factor influencing the diffusion of ionic species in the compacted bentonite. The ion equilibrium can be calculated by the Donnan model using macroscopic compacted bentonite parameters. By constructing a single pore type structure model for compacted bentonite, where the montmorillonite TOT-layers are depicted as a parallel array of rectangles, the ion equilibrium can also be calculated by the Poisson-Boltzmann （PB） model with a scale-defining variable H. We demonstrated that the ion equilibrium coefficients calculated by the PB model are always larger than those calculated by the Donnan model, and the models are linked by the factor H. The mathematical transition from the PB model to the Donnan model occurs in the limiting case H→0. The application of the two models to diffusion problem is also discussed, and the PB model is shown to be more realistic and suitable for solving actual diffusion problems.