Analysis of Gas Molecule Mean Free Path and Gaseous Thermal Conductivity in Confined Nanoporous Structures

Abstract

This study comprehensively analyzes the mean free path of gas molecules and gaseous thermal conductivity in confined nanoporous structures through a wide range of temperatures and pressures. A simplified unit cell cubic array structure of nanospheres is used to correlate microstructure features with specific surface area and density of nanoporous materials. Zeng’s model is used to describe the mean free path of the gas molecules and the gaseous thermal conductivity in confined nanoporous structures, and experimental gaseous thermal conductivity data from the literature is used to validate the model. The results show that a material’s nanoporous structure features are directly related to specific surface area and density. The mean free path of gas molecules in a confined nanoporous structure decreases with increasing specific surface area and density. Thus, nanoporous materials with a relatively high specific surface area and a higher density are more favorable for confining gaseous thermal conductivity in nanopores. This work shows that $p=10^{4}\hbox { Pa}$ and $10^{6}\hbox { Pa}$ are two characteristic pressures at ambient temperatures for the investigated silica aerogel materials. When $p<10^{4}\hbox { Pa}$, the mean free path of the gas molecules remains constant with varying pressure, while gaseous thermal conductivity approaches zero due to the restrictive effect of the nanoporous structure and the diluted gas molecules. When $\hbox {p}>10^{6}\hbox { Pa}$, the limiting effect of the nanoporous structure on the movement of gas molecules can be ignored, and so the mean free path of gas molecules in the nanoporous material approaches the mean free path of gas molecules in free space, while the gaseous thermal conductivity approaches the gaseous thermal conductivity in free space. As temperature increases, there exists a maximum value for gaseous thermal conductivity in confined nanoporous materials, but this maximum increases as pressure increases. The maximum gaseous thermal conductivity for the material is also determined in the paper.