Numerical modelling of the insect respiratory system and gas flow

Simelane, Simphiwe
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The understanding of uid ow at microscale geometrics is an increasingly important eld in applied science and mechanics, especially in bioinspiration and biomimetics. These elds seek to imitate processes and systems in biology to design improved e cient engineering devices. In this thesis, inspired by the e ciency of the insect tracheal system in transporting respiratory gases at microscale, mathematical models that both mimic and explain the gas exchange process are developed. Models for the simultaneous movement of respiratory gases across the insect spiracle, gas transfer from one respiratory chamber to the next, end di usion and tissue absorption at the tracheole tips, and tracheal uid transport are presented. Expressions for tracheal partial pressures of the respiratory gases, rate of change of gas concentrations, rate of tracheal volume change, spiracle behaviour on net gas ow, cellular respiration and tissue absorption, and global gas movement within the insect are presented as well. Two versions of bioinspired pumping mechanism that is neither peristaltic nor belongs to impedance mismatch class of pumping mechanism are then presented. A paradigm for se- lectively pumping and controlling gases at the microscale in a complex network of channels is presented. The study is inspired by the internal ow distributions of respiratory gases produced by rhythmic wall contractions in dung beetle tracheal networks. These networks have been shown to e ciently manage uid ow compared to current produced micro uidic devices. The insect-like pumping models presented are expected to function e ciently in the microscale ow regime in a simple or complex network of channels. Results show the ability to induce a unidi- rectional net ow by using an inelastic channel with at least two moving contractions. These results might help in explaining some of the physiological systems in insects and may help in fabricating novel e cient micro uidic devices. In this study, both theoretical and the Di erential Transform Method are used to solve the exible trachea with gas exchange problem as well as the 2D viscous ow transport with or without prescribed moving wall contractions problem. Both Lubrication theory and quasi- steady approximations at low Reynolds number are used in the derivation of theoretical analysis. ii Moreover, an analytical investigation into the compressible gas ow with slight rarefactions through the insect trachea and tracheoles is undertaken, and a complete set of asymptotic analytical solutions is presented. Then, estimation of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver the respiratory gases to the cells is obtained by comparing the magnitude of the di erent forces in the compressible gas ow. The 2D Navier-Stokes equations with a slip boundary condition are used to investigate the compressibility and rare ed e ects in the respiratory channels.
A thesis submitted in fulflment of the requirements for the degree of Doctor of Philosophy in the School of Computer Science and Applied Mathematics. November 2015