A conceptual mathematical model was developed to simulate the transport of migrating nanoparticles in homogeneous, water saturated, 1-dimensional porous media. The model assumes that nanoparticles can collide with each other and aggregate. Nanoparticles can be found attached reversibly and/or irreversibly onto the solid matrix of the aquifer or suspended in aqueous phase. Attached particles may either contribute to the acceleration of subsequent particle deposition or hinder it, leading to the ripening or blocking process, respectively. The aggregation process was simulated based on the Smoluchowski Population Balance Equation (PBE) and was coupled with the advection-dispersion-attachment equation (ADA) to form a family of partial differential equations that govern the migration of nanoparticles in porous media. For the solution of the PBE, an efficient finite volume solver was employed that significantly accelerated computation times, by reducing the number of participating equations, while maintaining the required accuracy. The developed model was applied to nanoparticle transport experimental data available in literature. The model successfully matched the breakthrough concentration curves, and estimated the corresponding nanoparticle diameter, proving its ability to capture the physical processes participating in nanoparticle transport.

中文翻译：

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使用非线性连接聚集纳米粒子传输：建模和实验验证


开发了一个概念数学模型来模拟迁移纳米颗粒在均质、水饱和、一维多孔介质中的传输。该模型假设纳米粒子可以相互碰撞和聚集。纳米颗粒可以可逆地和/或不可逆地附着在含水层的固体基质上或悬浮在水相中。附着的颗粒可能有助于加速后续颗粒沉积，也可能阻碍后续颗粒沉积，分别导致成熟或阻塞过程。聚集过程基于 Smoluchowski 种群平衡方程 （PBE） 进行模拟，并与平流-分散-附着方程 （ADA） 耦合，形成一个偏微分方程系列，控制纳米颗粒在多孔介质中的迁移。对于 PBE 的求解，采用了高效的有限体积求解器，通过减少参与方程的数量，同时保持所需的精度，显著加快了计算时间。开发的模型应用于文献中可用的纳米颗粒传输实验数据。该模型成功匹配了突破性的浓度曲线，并估计了相应的纳米颗粒直径，证明了它能够捕捉参与纳米颗粒传输的物理过程。