Jung Y, Torquato S
Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 2):056319. doi: 10.1103/PhysRevE.72.056319. Epub 2005 Nov 17.
It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. The multifunctionality of such two-phase systems has been further established by demonstrating that they are also extremal when a competition is set up between the effective bulk modulus and electrical (or thermal) conductivity of the bicontinuous composite. Here we compute the fluid permeabilities of these and other triply periodic bicontinuous structures at a porosity using the immersed-boundary finite-volume method. The other triply periodic porous media that we study include the Schoen gyroid (G) minimal surface, two different pore-channel models, and an array of spherical obstacles arranged on the sites of a simple cubic lattice. We find that the Schwartz P porous medium has the largest fluid permeability among all of the six triply periodic porous media considered in this paper. The fluid permeabilities are shown to be inversely proportional to the corresponding specific surfaces for these structures. This leads to the conjecture that the maximal fluid permeability for a triply periodic porous medium with a simply connected pore space at a porosity is achieved by the structure that globally minimizes the specific surface.
最近的研究表明，具有施瓦茨原始（P）和菱形（D）极小曲面界面的三重周期两相双连续复合材料不仅在几何上是极值的，而且在热和电的同时传输方面也是极值的。通过证明当在双连续复合材料的有效体积模量与电导率（或热导率）之间建立竞争时它们也是极值的，进一步确立了这种两相系统的多功能性。在这里，我们使用浸入边界有限体积法计算这些以及其他三重周期双连续结构在一定孔隙率下的流体渗透率。我们研究的其他三重周期多孔介质包括舍恩螺旋面（G）极小曲面、两种不同的孔道模型以及排列在简单立方晶格位点上的球形障碍物阵列。我们发现，在本文考虑的所有六种三重周期多孔介质中，施瓦茨P多孔介质具有最大的流体渗透率。这些结构的流体渗透率与相应的比表面积成反比。这导致了一个猜想，即在一定孔隙率下具有单连通孔隙空间的三重周期多孔介质的最大流体渗透率是由全局最小化比表面积的结构实现的。
