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 / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/19347 |
| Date | January 2015 |
| Creators | Simelane, Simphiwe |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf |
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