A unified numerical framework for quantifying diffusion behavior in TPMS structures for solar thermochemical applications

Abstract

This study investigates the effective diffusion coefficient in Schwarz-P triply periodic minimal surface structures across the continuum, transition, and Knudsen regimes. A hybrid numerical approach, combining finite volume methods and random walk simulations, is utilized to assess how geometric parameters (power, curvature, and periodicity) affect porosity, tortuosity, specific surface area, and diffusion behavior at both macro and micro scales. In the continuum regime, the effective diffusion coefficient is primarily influenced by porosity and tortuosity. Structures with odd power values show reduced pore connectivity and porosity with increasing power or curvature, leading to decreased diffusion coefficients. Even power values result in dual-pore configurations that maintain higher porosity and specific surface area, with diffusion behavior mainly affected by throat dimensions. At the microscale, increasing periodicity reduces pore and throat sizes, prompting a transition from continuum to non-continuum transport behavior. The study also analyzes the sensitivity of the effective diffusion coefficient to pressure and temperature. In the continuum regime, the diffusion coefficient increases with decreasing pressure, while in the Knudsen regime, it becomes pressure-independent. Elevated temperatures enhance the diffusion coefficient across all regimes, with a more pronounced effect in the continuum regime. These findings provide a framework for optimizing triply periodic minimal surface-based porous media to improve gas-phase diffusion, with practical implications for enhancing the efficiency of solar thermochemical reactors.