School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
DISMA "G. L. Lagrange", Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, Italy; DIATI, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, Italy.
J Contam Hydrol. 2018 May;212:3-13. doi: 10.1016/j.jconhyd.2017.09.002. Epub 2017 Sep 13.
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 typically rely on effective deposition rates defined by complex fitting procedures, neglecting the advection-diffusion interplay, the pore-scale flow complexity, and assuming slow reactions (or large Péclet numbers). Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to several conceptual inconsistencies and significant errors. To study more accurately the dependence of deposition on the flow parameters, in this work we advocate a clear distinction between the surface processes (that altogether defines the so-called attachment efficiency), and the pore-scale processes. With this approach, valid when colloidal particles are small enough, we study Brownian and gravity-driven deposition on a face-centred cubic (FCC) arrangement of spherical grains, and define a robust upscaling based on a linear effective reaction rate. The case of partial deposition, defined by an attachment probability, is studied and the limit of perfect sink is retrieved as a particular case. We introduce a novel upscaling approach and 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 Péclet numbers, when larger physical times are needed to reach the asymptotic regime and thus, equivalently, 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 Péclet numbers; it also is consistent with the classical heat and mass transfer literature.
在从孔隙到连续体（达西）尺度的扩展中，多孔介质固液界面处的反应和沉积现象必须用宏观反应源项来表示。在周期性介质的情况下，可以从周期性单元的三维微观模拟中计算有效速率。在胶体过滤领域已经研究了几种计算和半分析模型来描述这个问题。它们通常依赖于通过复杂的拟合程序定义的有效沉积速率，忽略了对流-扩散相互作用、孔隙尺度流动的复杂性，并假设反应速度较慢（或大的佩克莱特数）。因此，当这些速率被插入到一般的宏观输运方程中时，它们可能会导致几个概念上的不一致和显著的误差。为了更准确地研究沉积对流动参数的依赖关系，在这项工作中，我们提倡在表面过程（共同定义了所谓的附着效率）和孔隙尺度过程之间进行明确区分。当胶体颗粒足够小时，我们采用这种方法，研究布朗运动和重力驱动在面心立方（FCC）排列的球形颗粒上的沉积，并基于线性有效反应速率定义一个稳健的扩展。部分沉积的情况，由附着概率定义，也被研究，并作为一个特例得到了完美汇的极限。我们引入了一种新的扩展方法和一个特别方便的计算设置，允许直接计算有效速率的渐近稳态值。这使得计算域可以大大缩小到单个重复周期单元的尺度。当需要更大的物理时间来达到渐近状态时，即在更高的佩克莱特数的情况下，这种节省更为明显，因此，在传统设置中，需要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是如何更稳健和可扩展到整个佩克莱特数范围的；它也与经典的热和传质文献一致。
