# Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis

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## Abstract

The molecular tagging velocimetry (MTV) is a well-suited technique for velocity field measurement in gas flows. Typically, a line is tagged by a laser beam within the gas flow seeded with light emitting acetone molecules. Positions of the luminescent molecules are then observed at successive times and the velocity field is deduced from the analysis of the tagged line displacement and deformation. However, the displacement evolution is expected to be affected by molecular diffusion, when the gas is rarefied. Therefore, there is no direct and simple relationship between the velocity field and the measured displacement of the initial tagged line. This paper addresses the study of tracer molecules diffusion through a background gas flowing in a channel delimited by planar walls. Tracer and background species are supposed to be governed by a system of coupled Boltzmann equations, numerically solved by the direct simulation Monte Carlo (DSMC) method. Simulations confirm that the diffusion of tracer species becomes significant as the degree of rarefaction of the gas flow increases. It is shown that a simple advection–diffusion equation provides an accurate description of tracer molecules behavior, in spite of the non-equilibrium state of the background gas. A simple reconstruction algorithm based on the advection–diffusion equation has been developed to obtain the velocity profile from the displacement field. This reconstruction algorithm has been numerically tested on DSMC generated data. Results help estimating an upper bound on the flow rarefaction degree, above which MTV measurements might become problematic.

## Keywords

Molecular tagging velocimetry Microflows Direct simulation Monte Carlo## Mathematics Subject Classification

47N55## Notes

### Acknowledgments

This research obtained financial support from the European Community Seventh Framework Program (FP7/2007-2013) under Grant Agreement No. 215504, from the Fédération de Recherche Fermat, FR 3089, and from the Project 30176ZE of the PHC GALILEE 2014 Program. The latter is supported by the Ministère des Affaires Etrangères et du Développement International (MAEDI) and the Ministère de l’Enseignement Supérieur et de la Recherche (MENESR).

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