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Microscale Gaseous Slip Flow in the Insect Trachea and Tracheoles

Microscale Gaseous Slip Flow in the Insect Trachea and Tracheoles An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier–Stokes equations with a slip boundary condition are used to investigate compressibility and rarefied effects in the trachea and tracheoles. Expressions for the velocity components, pressure gradients and net flow inside the trachea are then presented. Numerical simulations of the tracheal compressible flow are performed to validate the analytical results from this study. This work extends previous work of Arkilic et al. (J Microelectromech Syst 6(2):167–178, 1997) on compressible flows through a microchannel. Novel devices for microfluidic compressible flow transport may be invented from results obtained in this study. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Microscale Gaseous Slip Flow in the Insect Trachea and Tracheoles

Acta Biotheoretica , Volume 65 (3) – Jul 11, 2017

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-017-9312-9
pmid
28695410
Publisher site
See Article on Publisher Site

Abstract

An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier–Stokes equations with a slip boundary condition are used to investigate compressibility and rarefied effects in the trachea and tracheoles. Expressions for the velocity components, pressure gradients and net flow inside the trachea are then presented. Numerical simulations of the tracheal compressible flow are performed to validate the analytical results from this study. This work extends previous work of Arkilic et al. (J Microelectromech Syst 6(2):167–178, 1997) on compressible flows through a microchannel. Novel devices for microfluidic compressible flow transport may be invented from results obtained in this study.

Journal

Acta BiotheoreticaSpringer Journals

Published: Jul 11, 2017

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