Molecular diameters of rarefied gases

S Kunze,J Thöming,R Groll,B Besser

doi:10.1038/s41598-022-05871-y

S Kunze, J Thöming + Show 2 more

Open Access

https://doi.org/10.1038/s41598-022-05871-y

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Journal: Scientific Reports	Publication Date: Feb 8, 2022
Citations: 17	License type: open-access

Affiliation: University of Bremen, SpaceTech (Germany)

Abstract

Molecular diameters are an important property of gases for numerous scientific and technical disciplines. Different measurement techniques for these diameters exist, each delivering a characteristic value. Their reliability in describing the flow of rarefied gases, however, has not yet been discussed, especially the case for the transitional range between continuum and ballistic flow. Here, we present a method to describe gas flows in straight channels with arbitrary cross sections for the whole Knudsen range by using a superposition model based on molecular diameters. This model allows us to determine a transition diameter from flow measurement data that paves the way for generalized calculations of gas behaviour under rarefied conditions linking continuum and free molecular regime.

Highlights

Molecular diameters are an important property of gases for numerous scientific and technical disciplines
The proposed analytical description for rarefied gas flow is composed of models for convective and diffusive flow
The method presented here can determine a molecular diameter that is sensitive to the region around Kn = 1 and represents a diameter that is valid in the transitional regime

Summary

Introduction

Molecular diameters are an important property of gases for numerous scientific and technical disciplines. The van der Waals diameter is obtained by crystallographic experiments such as X-ray diffraction, zero point density data[5] or the molar volume of s olids[6] This diameter is applied in the van der Waals equation of state to account for the nonideal behaviour of gases under high pressure[7,8]. Transport processes such as the absorption of oxygen in the lungs or gas transport through a membrane are strongly influenced by diffusion effects. Usually obtained at normal pressure, can be used to estimate molecular diameters These diameters are typically utilized to calculate the mean free path λ9, which plays a crucial role in gas kinetics:

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