标题： 多孔介质中有效颗粒沉积率的鲁棒性提升方法 显示英文标题

标题： A robust upscaling of the effective particle deposition rate in porous media

摘要： 在从孔隙尺度到连续体（达西）尺度的放大过程中，多孔介质固-液界面处的反应和沉积现象必须通过宏观反应源项来表示。 在周期性介质的情况下，有效速率可以通过周期单元的三维微观模拟计算得出。 在胶体过滤领域，已经研究了多种计算和半解析模型来描述这个问题。 它们通常依赖于由简单线性反应常微分方程定义的有效沉积速率，忽略了对流扩散的相互作用，并假设反应缓慢。 因此，当这些速率被插入到一般的宏观传输方程中时，会导致概念上的不一致，从而常常得到定性错误的结果。 在本工作中，我们研究了使用由体积平均定义的线性有效反应速率以及宏观对流-扩散-反应方程的面心球形排列的布朗沉积的放大问题。 研究了由附着概率定义的部分沉积情况，并将理想沉积作为特殊情况进行了回顾。 我们利用了一个特别方便的计算设置，可以直接计算有效速率的渐近稳态值。 这使得计算域可以大幅缩小到单个重复周期单元的尺度：在较高佩克莱特数的情况下，节省尤为明显，因为在这些情况下需要更长的物理时间才能达到渐近状态，因此在传统设置中需要一个更大的计算域和模拟时间。 我们展示了这种新的沉积速率定义在更广泛的佩克莱特数范围内更具鲁棒性和可扩展性；它也与经典的传热和传质文献一致。 显示英文摘要

摘要： In the upscaling from pore- to continuum (Darcy) scale, reaction and deposition phenomena at the solid-liquid interface of a porous medium have to be represented by macroscopic reaction source terms. The effective rates can be computed, in the case of periodic media, from three-dimensional microscopic simulations of the periodic cell. Several computational and semi-analytical models have been studied in the field of colloid filtration to describe this problem. They often rely on effective deposition rates defined by simple linear reaction ODEs, neglecting the advection-diffusion interplay, and assuming slow reactions. Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to conceptual inconsistencies and, therefore, often qualitatively wrong results. In this work, we study the upscaling of Brownian deposition on face-centred spherical arrangements using a linear effective reaction rate, defined by volume averaging, and a macroscopic advection-diffusion-reaction equation. The case of partial deposition, defined by an attachment probability, is studied and the limit of ideal deposition is retrieved as a particular case. We make use of a particularly convenient computational setup that allows the direct computation of the asymptotic stationary value of effective rates. This allows to drastically reduce the computational domain down to the scale of the single repeating periodic unit: the savings are ever more noticeable in the case of higher Peclet numbers, when larger physical times are needed to reach the asymptotic regime, and thus, equivalently, a much larger computational domain and simulation time would be needed in a traditional setup. We show how this new definition of deposition rate is more robust and extendable to the whole range of P\'eclet numbers; it also is consistent with the classical heat and mass transfer literature.