Gevertz Jana, Torquato S
Program in Applied and Computational Mathematics, Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011102. doi: 10.1103/PhysRevE.80.011102. Epub 2009 Jul 1.
Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical, and biological sciences. Using a first-passage time method, we compute the mean survival time tau of a Brownian particle among perfectly absorbing traps for a wide class of triply periodic porous media, including minimal surfaces. We find that the porous medium with an interface that is the Schwartz P minimal surface maximizes the mean survival time among this class. This adds to the growing evidence of the multifunctional optimality of this bicontinuous porous medium. We conjecture that the mean survival time (like the fluid permeability) is maximized for triply periodic porous media with a simply connected pore space at porosity phi=1/2 by the structure that globally optimizes the specific surface. We also compute pore-size statistics of the model microstructures in order to ascertain the validity of a "universal curve" for the mean survival time for these porous media. This represents the first nontrivial statistical characterization of triply periodic minimal surfaces.
从微观结构知识来理解多孔介质的输运性质是物理、化学和生物科学中一个备受关注的问题。我们使用首次通过时间方法，针对包括极小曲面在内的一大类三重周期多孔介质，计算了布朗粒子在完全吸收陷阱中的平均存活时间(\tau)。我们发现，具有施瓦茨(P)极小曲面界面的多孔介质在这类介质中平均存活时间最长。这进一步证明了这种双连续多孔介质具有多功能最优性。我们推测，对于孔隙率(\phi = 1/2)且具有单连通孔隙空间的三重周期多孔介质，通过全局优化比表面积的结构，平均存活时间（如同流体渗透率）会达到最大值。我们还计算了模型微观结构的孔径统计量，以确定这些多孔介质平均存活时间的“通用曲线”的有效性。这代表了对三重周期极小曲面的首次重要统计表征。
