Statistical assessment of tangential momentum accommodation coefficient using internal flow rate model based on rarefied gas conditions

Abstract

In this paper, we refer previously reported numerical data to design a new analytic equation for Poiseuille flow in a circular channel. Superposition of the continuum, slip, and free-molecular flow equations provides a versatile solution for the entire Knudsen range; however, it is not accurate in the transition regime. Adding correction factors and modifications to the existing flow-rate model enhances the precision and validity for wide flow ranges. Parameters of each equation are fitted for the collected data with Levenberg–Marquardt algorithm and compared in each regime; subsequently, the equation with the best accuracy and simplicity is selected. The newly suggested formula fits well for the referred data by correlating with the dimensionless flow rate, Knudsen number, and tangential momentum accommodation coefficient (TMAC). Furthermore, we calculate the TMAC using previous experimental data, which reflects the reflective interactions between the channel surfaces and gas molecules. Our newly suggested formula demonstrates effectively that the TMAC is significantly affected not only by the channel surface roughness but also by the molecular structure of gas.

Keywords

• Microchannel
• Rarefied gas
• Poiseuille flow
• Transition flow
• Tangential momentum accommodation coefficient