Tortuosity-porosity relation in porous media flow
Tortuosity-porosity relation in porous media flow
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DOI：
10.1103/physreve.78.026306
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发表时间：
2008-08-01
影响因子：
2.4
通讯作者：
Koza, Zbigniew
中科院分区：
文献类型：
--
作者：
Matyka, Maciej;Khalili, Arzhang;Koza, Zbigniew
我们用数值方法研究了多孔介质的微观模型中的弯曲度-孔隙度关系。结果表明，在以往的研究中忽略的有限尺寸、慢松弛和离散化误差可能会导致扭曲度的严重低估。本文提出的简单扭度计算方法消除了使用复杂的加权平均值的需要。本文给出的数值结果与其他实验在颗粒填料和沉积物中发现的弯曲度(T)与孔隙度（phi）之间的经验关系（T -1与ln phi成正比）很好地吻合。这种关系也可以写成T-1与RS/phi成正比，其中R和S分别表示颗粒的水力半径和比表面积。这些关系的适用性似乎仅限于具有相同形状和大小的随机分布障碍物的多孔系统。
We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity (T) and porosity (phi) given by T-1 proportional to ln phi, that was found by others experimentally in granule packings and sediments. This relation can be also written as T-1 proportional to RS/phi with R and S denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.