期刊
PHYSICS LETTERS A
卷 380, 期 35, 页码 2767-2773出版社
ELSEVIER
DOI: 10.1016/j.physleta.2016.06.032
关键词
Darcy law; Momentum diffusion; Fractal porosity; Permeability; Metric of flow; Inverse Menger sponge
资金
- Mexican Petroleum Company (PEMEX) [143927]
In this Letter, we report experimental and theoretical studies of Newtonian fluid flow through permeable media with fractal porosity. Darcy flow experiments were performed on samples with a deterministic pre-fractal pore network. We found that the seepage velocity is linearly proportional to the pressure drop, but the apparent absolute permeability increases with the increase of sample length in the flow direction L. We claim that a violation of the Hagen-Poiseuille law is due to an anomalous diffusion of the fluid momentum. In this regard we argue that the momentum diffusion is governed by the flow metric induced by the fractal topology of the pore network. The Darcy-like equation for laminar flow in a fractal pore network is derived. This equation reveals that the apparent absolute permeability is independent of L, only if the number of effective spatial degrees of freedom in the pore-network nu is equal to the network fractal (self-similarity) dimension D, e.g. it is in the case of fractal tree-like networks. Otherwise, the apparent absolute permeability either decreases with L, if nu < D, e.g. in media with self-avoiding fractal channels, or increases with L, if nu > D, as this is in the case of the inverse Menger sponge. (C) 2016 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据