Mean survival times of absorbing triply periodic minimal surfaces

TL;DR

This paper calculates the mean survival time of Brownian particles in triply periodic minimal surface porous media, revealing the Schwartz P minimal surface maximizes survival time and suggesting universal structural properties.

Contribution

It introduces a first-passage time method to analyze survival times in triply periodic minimal surfaces, highlighting the optimality of the Schwartz P surface and providing the first statistical characterization of these structures.

Findings

Schwartz P minimal surface maximizes mean survival time.

A universal curve for survival time is proposed.

Pore-size statistics support structural optimization hypotheses.

Abstract

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.