# Rarefied gas flow in functionalized microchannels

## TL;DR

This paper studies how rarefied gases flow through microchannels with and without surface functionalization, focusing on the impact of geometry and surface effects.

## Contribution

The study introduces a methodology to reduce experimental uncertainty in micro flow experiments and compares results with theoretical models.

## Key findings

- Functionalization effects are likely obscured by experimental uncertainty in the tested geometry.
- The surface-to-volume ratio of 0.4 μm-1 appears too small for functionalization to strongly influence gas flow.
- Results provide insights into molecular reflection characteristics described by the TMAC.

## Abstract

The interaction of rarefied gases with functionalized surfaces is of great importance in technical applications such as gas separation membranes and catalysis. To investigate the influence of functionalization and rarefaction on gas flow rate in a defined geometry, pressure-driven gas flow experiments with helium and carbon dioxide through plain and alkyl-functionalized microchannels are performed. The experiments cover Knudsen numbers from 0.01 to 200 and therefore the slip flow regime up to free molecular flow. To minimize the experimental uncertainty which is prevalent in micro flow experiments, a methodology is developed to make optimal use of the measurement data. The results are compared to an analysis-based hydraulic closure model (ACM) predicting rarefied gas flow in straight channels and to numerical solutions of the linearized S-model and BGK kinetic equations. The experimental data shows that if there is a difference between plain and functionalized channels, it is likely obscured by experimental uncertainty. This stands in contrast to previous measurements in smaller geometries and demonstrates that the surface-to-volume ratio of 0.4 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\upmu$$\end{document}μm-1 seems to be too small for the functionalization to have a strong influence and highlights the importance of geometric scale for surface effects. These results also shed light on the molecular reflection characteristics described by the TMAC.