Koza Zbigniew, Matyka Maciej, Khalili Arzhang
Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204 Wrocław, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 2):066306. doi: 10.1103/PhysRevE.79.066306. Epub 2009 Jun 16.
Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes in transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is a/L , being the ratio of the obstacle to system size. Distribution of the angle alpha between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of alpha is found to decay with the system size as (a/L);{d/2} , where d is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume. For porous media types studied here, the anisotropy effect becomes negligible only if a/L < or = 0.01 . This constraint was apparently violated in many previous computer simulations that need now to be recalculated.
研究了典型计算机模拟中使用的尺寸的统计均匀多孔介质中渗透率张量的各向异性。尽管默认情况下此类系统被假定为各向同性，但我们表明，实际上它们的各向异性渗透率会导致诸如渗透率和曲折度等传输参数发生显著变化。控制各向异性的主要参数是a/L，即障碍物与系统尺寸的比率。发现外力与体积流体流之间的夹角α的分布近似为正态分布，并且α的标准差随系统尺寸以(a/L)^(d/2)的形式衰减，其中d是空间维度。这些特性可用于估计大规模模拟中与各向异性相关的统计误差以及代表性单元体积的大小。对于此处研究的多孔介质类型，仅当a/L≤0.01时，各向异性效应才可以忽略不计。许多先前的计算机模拟显然违反了这一限制，现在需要重新计算。
