A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Masters of Science. May 27, 2015. / Abstract The unsteady three-dimensional ow of a thin slender rivulet of incompressible Newtonian uid down an inclined porous plane is investigated. The leak-o velocity is not speci ed in the model but is determined in the process of deriving the invariant solution. A second order nonlinear partial di erential equation in two spatial variables and time and containing the leak-o velocity is derived for the height of the thin slender rivulet. Using Lie group analysis it is found that the partial di erential equation can be reduced in two steps to an ordinary di erential equation provided the leak-o velocity satis es a rst order linear partial di erential equation in three variables. An exact analytical solution with a dry patch in the central region is derived for a special leak-o velocity. Two models are considered, one with the leak-o velocity proportional to the height of the rivulet and the other with leak-o velocity proportional to the cube of the height. Numerical solutions are obtained for the height of the rivulet using a shooting method which also determines the two-dimensional boundary of the rivulet on the inclined plane. The e ect of uid leak-o on the height and width of the rivulet is investigated numerically and compared in the two models. The conservation laws for the partial di erential equation with no uid leak-o are investigated. Two conserved vectors are derived, the elementary conserved vector and a new conserved vector. The Lie point symmetry of the partial di erential equation associated with each conserved vector is obtained. Each associated Lie point symmetry is used to perform a double reduction of the partial di erential equation, but the solutions obtained are not physically signi cant.

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Poly(dimethylsiloxane) (PDMS) fluids containing magnetite nanoparticles stabilized with carboxylic acid-functionalized PDMS were prepared. PDMS-magnetite complexes were characterized using transmission electron microscopy, elemental analysis, and vibrating sample magnetometry. PDMS-magnetite complexes containing up to 67 wt% magnetite with magnetizations of ~52 emu gram-1 were prepared. The magnetite particles were 7.4 ± 1.7 nm in diameter. Calculations suggested that the complexes prepared using mercaptosuccinic acid-functionalized PDMS (PDMS-6COOH) complexes contained unbound acid groups whereas the mercaptoacetic acid-functionalized PDMS (PDMS-3COOH) complexes did not. Calculations showed that the PDMS-3COOH and PDMS-6COOH covered the same surface area on magnetite. Calculations were supported by molecular models and FTIR analyses. The complexes were dispersed into PDMS carrier fluids by ultrasonication, resulting in magnetic PDMS fluids with potential biomedical applications. Magnetite particles (100 nm to 1 mm in diameter) were prepared by crystallization from goethite/glycol/water solutions under pressure. Two methods for particle growth were investigated in which the crystallization medium was varied by adjusting the amount of water or by adding itaconic acid. Particle surfaces were analyzed by x-ray photoelectron spectroscopy (XPS). Particles with clean surfaces were coated with carboxylic acid-functionalized poly(e-caprolactone) stabilizers. Adding itaconic acid to the reactions afforded particles ~100 nm in diameter. The magnetite particles displayed magnetic hysteresis. The particles were dispersed into vinyl ester resins by ultrasonication and it was demonstrated that the ~100 nm particles remained dispersed for three days without agitation. These dispersions have applications in magnetic induction heating for composite repair. Living polymerizations of hexamethylcyclotrisiloxane were terminated with dimethylchlorosilane, phenylmethylchlorosilane, or diisopropylchlorosilane (DIPCS). Platinum-catalyzed hydrosilation of the hydrosilane-terminated PDMS with allyloxyethanol afforded a systematic series of hydroxyalkyl-terminated PDMS. The reactions were successful except for the hydrosilation of the sterically-hindered DIPCS-functionalized PDMS where no reaction was observed. Hydroxyalkyl-terminated PDMS oligomers were successful in initiating the stannous octoate-catalyzed copolymerization of e-caprolactone, which afforded PDMS-b-PCL diblock copolymers of controlled composition. / Ph. D.

The rheology and development morphology of textured fluids have been investigated. The first fluid considered in this work was a liquid crystalline polymer consisting of isotropic and anisotropic solutions of poly-p-phenyleneterephthalamide (PPT) in sulfuric acid. The second textured fluid considered in this work was an immiscible polymer blend consisting of poly(ethylene terephthalate) (PET) and nylon 6,6. The role played by liquid crystalline order (LCO) and a polydomain texture on the rheology of PPT solutions was investigated. It was found that several of the rheological phenomena commonly attributed to liquid crystalline order in polymers (e.g., three region flow curve, negative steady state first normal stress difference, and oscillatory behavior at the start up of shear flow) were not observed in the solution in its anisotropic state. The solution in both its anisotropic and isotropic state exhibited a two region flow curve (Newtonian plateau and shear thinning region at rates ranging from 10^-4 to 10² sec^-I), a positive steady state first normal stress difference which increased with shear rate, and a transient shear stress which displayed a single overshoot before reaching a steady state value. The rheology of PET/nylon 6,6 blends was found to be a function of both polymer degradation and the two phase texture. An accelerated degradation rate was found for the blends relative to the neat polymers, and as a consequence, the values of the steady shear viscosity (η), magnitude of the complex viscosity |η*|, storage modulus (G') and steady state first normal stress difference (N₁) for samples melt blended in an extruder were lower than those of the neat polymers. Blends prepared by dry blending followed by mixing in a cone and plate device where the degradation occurring during extrusion was avoided were found to have a higher value of |η*| and G' and enhanced transient behavior relative to those of the neat polymers. Scaling of the transient stress indicated there was no intrinsic time constant for these blends at shear rates lower than the longest relaxation time of the neat polymers The theory developed by Doi and Ohta which describes the additional stresses arising as a consequence of interfacial tension in two phase systems was evaluated for its ability to model the rheology of the 2575 w/w PET/nylon 6,6 blend. The Doi-Ohta theory was found to be capable of qualitatively predicting the extra stresses arising as a result of the interfacial tension as observed in the steady state viscosity and steady state first normal stress difference and the transient stresses at the start up of steady shear flow. While the overshoot and undershoot of the stresses observed during stepwise changes of shear rate were not predicted, the scaling relation for the transient stresses predicted by the theory were found to hold for the blend using stepwise changes of shear rate at a constant step ratio. / Ph. D.

The performance characteristics of the particle beam interface (PB) coupled to supercritical fluid chromatography (SFC) and mass spectrometry (MS) were assessed with pure and methanol-modified CO₂. Factors which affect the nebulization and the subsequent desolvation of the droplets were assessed. The quantitative performance was evaluated yielding a limit of detection (LOD) of 40 ng (caffeine) for scan data which is some 3 to 25 times lower than previously reported studies. Operation of the SFC-PB-MS system was found to be highly dependent on the mobile phase characteristics (flow rate and composition). Between 0.1 to 0.64 mL/min liquid CO₂ flow, relatively stable operation of the system was determined; whereas beyond this range significant losses in sensitivity were observed. Mobile phase composition was shown to have a dramatic effect with 4% methanol-modified CO₂ yielding the most sensitive results; whereas, no detection was possible with pure CO₂. This lack of sensitivity with pure CO₂ and dependence of sensitivity on mobile phase composition, presented a problem in method development. The SFC-PB-MS system was therefore modified by employing a particle forming solvent (PFS). The purpose of the PFS was to aid in the formation of an aerosol. With the PFS solvent, mobile phase composition had no effect on sensitivity and detection of analytes eluted with pure CO₂ was achieved. The nature, composition, and flow rate of the PFS were found to be crucial to the optimum operation. Quantitative performance of the system was improved by a factor of 4 to 5 over the prior system. The analysis of pesticides, steroids, and polyaromatic hydrocarbons was achieved with the SFC-PB-MS system. The resulting EI spectra were artifact-free and gave good matches on comparing with on-line library spectra. Packed column SFC, however, is only able to handle directly non-polar to medium polar analytes. Thus for polar to highly polar analytes (peptides, proteins) liquid introduction (infusion, flow injection, chromatography) is the preferred method of sample delivery to the MS. Furthermore because of the polar nature and thermal lability of these compounds conventional ionization methods (EI, CI) are not suitable. Factors which have ramification on sample handling (flow rate, solution composition) were studied. The high sample flow rate capability was dependent on effective nebulization and desolvation. Thus, needle distance/angle and bath gas flow setting played a critical role in the performance of the ES-MS. The utility of the system was demonstrated by analysis of gramicidin s, myoglobin, and tryptic peptides of cytochrome c. / Ph. D.

The purpose of this investigation was to test the existing methods of correlating pipe-line data on dilatant fluids in a laminar flow, to gather pertinent physical properties of dilatant fluids, and to propose a theory for the mechanism of dilatancy. In order that the correlation for flow of dilatant fluids in conduits could be tested it was necessary to build a flow apparatus from which pressure drops and flow rates could be measured, to develop viscometric equipment such that flow curves could be determined at shearing conditions similar to those in the flow tests, and to uae the data from the two sources to calculate the variables of interest: the friction factor, f, and the modified Reynolds number, R'_e. A flow apparatus suitable for the purpose outlined was constructed from 1-1/4 inch, Schedule 40 galvanized pipe with motive power provided by a Moyno pump, was provided with temperature control and calming sections, and was provided with a ten foot test section. Flow curves were determined independently with a specially constructed cone and plate viscometer. Provisions were made to determine pressure drop over the fittings: coupling, glove valve, and 90 degree elbow. Dilatant fluids consisting of corn starch suspended in the liquids water, ethylene glycol, and glycerine with values of flow behavior index, n from 1.15-2.50 flowing in laminar flow between R’_e of 12-410 were studied. Results of the investigation showed that the Metzner-Reed correlation method could be used in correlating dilatant, laminar flow. Equivalent resistances of fittings, expressed as equivalent diameters of pipe, were found not to match those found in the literature for Newtonian fluids, except that for the case of couplings the value was negligible for both fluid types. Rather, much lower values were found for the case of flow through a globe valve, and the value found for the 90 degree elbow was strongly dependent on the flow rate. A cone and plate viscometer was used to study the dependency of the Power Law parameters on temperature for a starch suspension in glycerine and ethylene glycol. The parameter n was found to be independent of temperature over the 80-130° F range of temperature studied. Conversely, K varied with temperature in a manner described by an Arrhenius equation and its rate of change with temperature roughly paralleled that of the glycerine. A theory of the basic mechanism responsible for the phenomenon of dilatancy was presented and discussed, and its relation to the Power Law Model established. / Ph. D.

Fluids are associated with a wide range of physical and chemical processes in the Earth, including transporting and concentrating important ore elements such as Cu, Au, Zn, and Pb. Significant amounts of fluid may be generated as a result of dehydration or decarbonation reactions, and the volatile content of a magma is directly linked to the explosivity of eruptions. In most cases, small amounts of the fluids involved in the formation or alteration of rocks are trapped within minerals in the form of fluid inclusions. These fluid inclusions may be studied to understand the composition and pressure and temperature of the original fluid involved in the geologic process of interest, however, an understanding of the composition of the fluid as well as how the fluid behaves under changing pressure and temperature conditions is essential to reconstruct the fluid evolution path based on data obtained from fluid inclusions. Several analytical techniques are involved in the study of fluids, including fluid inclusion microthermometry and Raman spectroscopy. Microthermometry is the heating/cooling of fluid inclusions to observe and record temperatures of phase changes which, in turn, are used to determine properties such as salinity (based on the freezing point depression of liquid), or density based on the temperature at which all phases within the fluid inclusion homogenize to a single phase. Raman spectroscopy is a non-destructive analytical technique that measures the vibrational frequency of molecules in a given material. The Raman spectral properties of fluids act as a "fingerprint" of the chemical species within the fluid and serve to identify both the presence of chemical species, such as H2O, N2, CO2, and CH4, and the density of the fluid. Microthermometric and Raman spectroscopic experiments involving synthetic fluid systems are necessary to elucidate the pressure-volume-temperature-composition (PVTX) and Raman spectral behavior of the fluid systems, which then aids in the study and characterization of natural fluids. In chapter 1, the partitioning of NaCl and KCl between coexisting immiscible fluid phases during boiling is experimentally determined at temperatures and pressures relevant to magmatic-hydrothermal systems using synthetic fluid inclusions. The partitioning behavior is then combined with literature data to calculate the Na/K ratio of the original silicate melt phase in a magma body before the exsolution of a fluid phase. In chapter 2, we explore the Raman spectral behavior of N2, CO2, and CH4 in pure, single-component systems from PT conditions corresponding to the liquid-vapor curve to elevated temperatures and pressures, and relate the changes in the spectral behavior to changes in the bonding environment of the molecules through intermolecular attraction and repulsion. In chapter 3, the observations and relationships determined for pure fluids and described in chapter 2 are used to explore the Raman spectral properties of N2, CO2, and CH4 in the N2-CO2-CH4 ternary system and the manner in which the spectral behavior of each component in the system varies with changing temperature, pressure, molar volume, and fugacity. / Doctor of Philosophy / Water and other fluids play an important role in the formation of mineral deposits that are the source of the many metals, such as copper, silver, gold, and others, that are needed by a modern technological society. In addition, water and other fluids affect the way rocks behave under stress and can promote earthquakes and influence the explosivity of volcanoes. When minerals in a rock form, often small amounts of the fluid will be trapped within the minerals in the form of fluid inclusions. These fluid inclusions contain samples of the fluid involved in the geologic process of interest and can be studied using a variety of methods to determine the chemistry and the temperature and pressure conditions of rock formation. Two of the many methods used to study fluid inclusions are microthermometry and Raman spectroscopy. Microthermometry involves heating and/or cooling the fluid inclusion while it is being observed on a microscope, and this method can be used to determine the salinity of water in the inclusion and the fluid density. The density of the fluid may then be used to determine the pressure or temperature at which the fluid was encapsulated into the rock, and by extension the temperature and pressure at which the rock formed. Raman spectroscopy is an analytical technique in which a rock or fluid is illuminated using a laser. The laser light interacts with the rock or fluid and gains or loses energy, and this change in energy serves as a "fingerprint" to identify the molecules in the rock or fluid. The Raman spectrum can also be used to determine fluid density because the signal generated when the laser interacts with the fluid depends on the density of the fluid. Experiments on fluids at carefully-controlled laboratory conditions are necessary to understand the behavior of fluids trapped in natural samples. In chapter 1, the preference of sodium and potassium to go into either a liquid or a gas phase during boiling at high pressures and temperatures is determined. In chapter 2, gases containing only nitrogen, carbon dioxide, or methane are studied using Raman spectroscopy and the changes in the Raman behavior of the gases with changing pressure and temperature are related to molecular interactions. In chapter 3, the results from chapter 2 are used to understand the Raman behavior of nitrogen, carbon dioxide, and methane in gas mixtures as pressure and temperature are changed and how this relates to the interactions of the molecules.

Both bird and fish locomotion are thought to be more efficient than the equivalent man-made vehicles driven by propellers/impellers and jet engines. Through studies that decompose the different kinematic and shape effects of these biological systems, we can understand what leads to their high cruising performance and efficiency. Two major studies were conducted. The first was on the effect of different kinematic parameters of large soaring birds on flight performance and the second was on the effect of caudal fin shape on the performance of thunniform swimmers. For the first study on flight performance, flapping, folding, and twist were the wing motions of interest. The second study on swimming performance observed how caudal fin sweep angle affects propulsion while isolating the effect of this shape difference from aspect ratio and area effects. Low order models were primarily used to conduct the bird flight study, though experimental methods were investigated as well. The thunniform swimming study was conducted through experimentation on a biomimetic system. The flight study found that, under the right circumstances, both wing twist and wing folding have a positive effect on flight performance. However, the impact of wing twist is much larger. To incorporate this wing twist into a robotic system, a new reduced order model that partially accounts for 3D effects was developed and validated. In the future, this model can be used in conjunction with a flight controller to control wing twist. The swimming study found that caudal fin sweep had a significant impact on performance, moderately swept fins showing the greatest improvement. Using an overly large sweep angle led to diminished performance when compared to the moderately swept fins, but still demonstrated improved performance over a non-swept fin. The increased performance of the moderately swept fins was due to how it affected LEV formation and stability. / Ph. D. / Bird flight and fish swimming are thought to be more efficient than drones and submersible vehicles respectively. By conducting studies on the motion of the wing and the shape of the tail fin, we can gain a better understanding of how to produce efficient vehicles that are inspired by fish/birds. Two major studies were conducted. The first study analyzed the wing motion of birds such as seagulls. The three most important wing motions were analyzed using fast computational simulations. Functional flapping aircraft that can be used in future studies were also constructed. The second study analyzed the tail fin shape of tuna, specifically how the swept shape affects propulsion performance. This study was conducted by operating a robotic tuna with interchangeable tails in a water tunnel. The computational studies on wing motion showed that controlling twist of the wing in addition to typical flapping motion could greatly improve performance of a flapping bird-like aerial vehicle. To incorporate this wing twist into a future system, a mathematical model that provided aerodynamic predictions was developed. This model can be used in conjunction with a controller to provide efficient real time control of the wing twist. The experimental swimming study found that fin sweep had a significant impact on performance. Using a moderately swept fin (25-35 degrees) increases thrust production without increased energy expenditure. Fins with greater sweep angles start to yield diminished performance benefits. Using an elliptical area distribution can also lead to increased performance.

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