SIAM Journal on Applied Mathematics, Volume 80, Issue 1, Page 448-475, January 2020.
We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow, therefore reducing the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and, therefore, can provide estimates on the storage capacity of the porous matrix.

中文翻译：

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局部周期性演化的多孔介质中的胶体运输-一种放大运动

SIAM应用数学杂志，第80卷，第1期，第448-475页，2020年1月。
我们推导了一个高级模型，该模型描述了多孔介质中胶体颗粒的聚集和沉积，从而允许孔局部堵塞。在孔尺度上，我们扩展了胶体动力学的现有模型，包括将沉积在固体边界（固体球体）上的胶体颗粒与通过多孔介质的气态部分运输的胶体颗粒分开的自由界面的演化。由于沉积，固体球生长，因此减少了可用于气相运输的空间。应用了升级程序，并获得了几类宏观模型以及有效的传输张量，其中明确包含了固体球体的局部增长。对所得模型进行数值求解，并给出各种仿真。特别是，它们能够检测堵塞区域，因此可以提供对多孔基质储存能力的估计。