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.