Matyka Maciej, Koza Zbigniew, Gołembiewski Jarosław, Kostur Marcin, Januszewski Michał
Faculty of Physics and Astronomy, University of Wrocław, 50-204 Wrocław, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):023018. doi: 10.1103/PhysRevE.88.023018. Epub 2013 Aug 19.
Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect: anisotropy of the permeability tensor. We show that a nonzero angle between the external body force and macroscopic flux vector exists in three-dimensional periodic models of sizes commonly used in computer simulations and propose a criterion, based on the ratio of the system size to the grain size, for this phenomenon to be relevant or negligible. The finite-size anisotropy of the porous matrix induces a pressure gradient perpendicular to the axis of a porous duct and we analyze how this effect scales with the system and grain sizes. We also analyze how the size of the representative elementary volume (REV) for anisotropy compares with the REV for permeability.
多孔介质模型通常应用于相对较小的系统，这不仅导致结果依赖于系统大小，还会产生在较大系统中不存在的现象。在此，我们研究一种这样的有限尺寸效应：渗透率张量的各向异性。我们表明，在计算机模拟中常用尺寸的三维周期性模型里，外力与宏观通量矢量之间存在非零夹角，并基于系统尺寸与颗粒尺寸之比提出了一个准则，用以判断该现象是相关还是可忽略的。多孔基质的有限尺寸各向异性会在垂直于多孔管道轴线的方向上诱导出一个压力梯度，我们分析了这种效应如何随系统尺寸和颗粒尺寸变化。我们还分析了各向异性的代表性单元体积（REV）的大小与渗透率的REV相比情况如何。
