The concept of the representative elementary volume (REV) is often associated with the notion of hydrodynamic dispersion and Fickian transport. However, it has been frequently observed experimentally and in numerical pore-scale simulations that transport is non-Fickian and cannot be characterized by hydrodynamic dispersion. Does this mean that the concept of the REV is invalid? We investigate this question by a comparative analysis of the advective mechanisms of Fickian and non-Fickian dispersions and their representation in large-scale transport models. Specifically, we focus on the microscopic foundations for the modeling of pore-scale fluctuations of Lagrangian velocity in terms of Brownian dynamics (hydrodynamic dispersion) and in terms of continuous-time random walks, which account for non-Fickian transport through broad distributions of advection times. We find that both approaches require the existence of an REV that, however, is defined in terms of the representativeness of Eulerian flow properties. This is in contrast to classical definitions in terms of medium properties such as porosity, for example.

中文翻译：

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异常色散是否有具有代表性的基本体积？

代表性基本体积 (REV) 的概念通常与流体动力分散和菲克输运的概念相关联。然而，在实验和数值孔隙尺度模拟中经常观察到，传输是非 Fickian 的，不能用流体动力学分散来表征。这是否意味着 REV 的概念无效？我们通过比较分析 Fickian 和非 Fickian 色散的平流机制及其在大型传输模型中的表示来研究这个问题。具体来说，我们专注于根据布朗动力学（流体动力学弥散）和连续时间随机游走对拉格朗日速度的孔隙尺度波动进行建模的微观基础，通过广泛的平流时间分布来解释非 Fickian 传输。我们发现这两种方法都需要存在一个 REV，然而，它是根据欧拉流动特性的代表性来定义的。这与介质属性（例如孔隙率）方面的经典定义形成对比。