Past studies (primarily on steady state problems) that have compared the penalty and the velocity-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of one method over the other is dictated by which of the two is more efficient. In this work, we show that the penalty finite element method yields inaccurate solutions at large times on a class of transient problems, while the velocity-pressure formulation yields solutions that are in good agreement with the analytical solution. Numerical studies are conducted on various problems to compare these two formulations on the basis of rates of convergence, total number of equations to be solved and accuracy of results. We found that both formulations give almost the same rates of convergence in all problems, however the penalty formulation involves lesser number of equations than the velocity-pressure formulation due to implicit treatment of pressure field, and hence is more efficient. In some of the problems we have also compared a finite volume method with the penalty and velocity-pressure formulations on the basis of accuracy and computational cost.

In vitro mechanotransduction studies, uncovering the basic science of the response of cells to mechanical forces, are essential for progress in tissue engineering and its clinical application. Many varying investigations have described a multitude of cell responses, however as the precise nature and magnitude of the stresses applied are infrequently reported and rarely validated, the experiments are often not comparable, limiting research progress. This thesis provides physical and biological validation of a widely available fluid stimulation device, a see-saw rocker, as an In vitro model for cyclic fluid shear stress mechanotransduction. This allows linkage between precisely characterised stimuli and cell monolayer response in a convenient six-well plate format. Computational fluid dynamic models of one well were analysed extensively to generate convergent, stable and consistent predictions of the cyclic fluid velocity vectors at a rocking frequency of 0.5 Hz, accounting for the free surface. Validation was provided by comparison with flow velocities measured experimentally using particle image velocimetry. Qualitative flow behaviour was matched and quantitative analysis showed good agreement at representative locations and time points. A maximum shear stress of 0.22Pa was estimated near the well edge, and time-average shear stress ranged between 0.029 and 0.068Pa, within the envelope of previous musculoskeletal In vitro fluid flow investigations. The CFD model was extended to explore changes in culture medium viscosity, rocking frequency and the robustness to position on the rocking platform. Shear stress magnitude was shown to increase almost linearly with an increase in the viscosity of culture medium. Compared with 0.5 Hz, models at 0.083 and 1:167 Hz, the operational limits of the see-saw rocker, indicated a change in shear stress patterns at the cell layer, and a reduction and increase in mean shear stress respectively. At the platform edge at 0.5 Hz, a 1.67-fold increase in time-average shear stress was identified. Extensive biological validations using human tenocytes underlined the versatility of the simple In vitro device. The application of fluid-induced shear stress at 0.5 Hz under varying regimes up to 0.714Pa caused a significant increase in secreted collagen (p < 0.05) compared to static controls. Tenocytes stimulated at a shear stress magnitude of 1.023Pa secreted significantly less collagen compared to static controls. The potential for a local maximum in the relationship between collagen secretion rate and shear stress was identified, indicating a change from anabolic to catabolic behaviour. Collagen biochemical assay results were echoed with antibody stains for proteins, where a co-localisation of connexin-32 with collagen type-I was also identified. A custom algorithm showed that four hours of fluid-induced shear stress of 0:033Pa intermittently applied to tenocytes encouraged alignment and elongation over an eight day period in comparison to static controls. Primary cilia were identified in human tenocyte cultures and bovine flexor tendon tissue; however primary cilium abrogation In vitro using chloral hydrate proved detrimental to cell viability. Collaborative investigations identified that ERK signalling and c-Fos transcription factor expression peaked after the application of 0.012Pa at 0.083 Hz for 20 minutes and anabolic collagen gene expression relative quantities increased after 48 hours of rocking at 0.083 Hz. In conclusion, validated shear stresses within a six-well plate, induced by cyclic flow from a see-saw rocker, provides an exceptional model for the In vitro study of dynamic fluid shear stress mechanobiology. Biological investigations have been linked to precise applied shear stress, creating a foundation for understanding the complex relationship between tenocytes and fluid-induced shear stress In vitro. Using this model, research is repeatable, comparable and accurately attributed to shear stress, accelerating the scientific advancement of musculoskeletal mechanobiology.

Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / A full scale, three dimensional, transient, mathematical model was developed to simulate fluid flow and mixing in gas stirred ladles. The volume of fluid (VOF) and discrete phase (DPM) models were used in combination to account for multiphase aspects, and a slightly modified version of the standard - model was employed for turbulence modelling. The model was validated to compare well against published physical modelling results. Model results were interpreted from the fundamental grounds of kinetic energy transport within the ladle. This approach led to the specification of three key measures of mixing efficiency: The rate and efficiency of kinetic energy transfer from the buoyant gas to the bulk steel as well as the total kinetic energy holding capacity of the ladle. These measures describe the quantity of mixing in any specific ladle setup, whereas the traditional measure of mixing time reflects mixing quality, i.e. the degree of kinetic energy distribution through the entire ladle. The model was implemented in designed experiments to assess various operating and design variables pertaining to mixing quantity and quality. Considerable time was invested in finding the correct balance between numerical accuracy and computational time so that the model could be used to generate the required data within the given time frame. Experiments on the operating variables drew an important distinction between factors influencing the shape and the strength of gas induced flow patterns. Flow pattern strengthening variables, such as gas purge rate, significantly affected the quantity of mixing, but had a limited effect on mixing quality. Variables such as mass loading that influence the shape of the flow patterns had much larger potential to influence both the quantity and quality of mixing. Minimization of turbulence losses in the region of the plume eye was identified as the primary outcome of ladle design. It was shown that a taller vessel allowed more distance over which the plume could disperse, thereby reducing velocity gradients and subsequent turbulence generation at the free surface. Multiple tuyere systems yielded similar improvements by dividing the gas flow into several weakened plumes. Surface wave formation was investigated as an added mixing mechanism and demonstrated to be impractical for application in full scale gas stirred ladles. The conditions for resonance between the surface wave and the bubble plume were met only in vessels with a very low aspect ratio. Performance improvements offered by swirl in these ladles could easily be replicated in more practical ways. This study demonstrated the potential of mathematical modelling as a tool for in-depth investigation into fluid flow and mixing in the hostile environment of a full scale gas stirred ladle. Scaled-down cold models are the only alternative and can offer no more than a reasonably reliable predictive framework. The ease of flow data extraction from the numerical model also proved invaluable in facilitating a fundamental understanding of the effects of various important independent variables on ladle hydrodynamics. At this stage of development, however, the model is recommended for use on a comparative basis only. Two important developments are required for complete quantitative agreement: The inclusion of turbulence modulation by the bubbles and the increased turbulence kinetic energy dissipation rate in the vicinity of the free surface. A general strategy was developed to account for these effects and it compared favourably with published cold model results. Further research is required to generalize this approach for application in full scale gas stirred ladles.

Thesis (MScEng (Process Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Mass transfer efficiency in distillation, absorption and stripping depends on both thermodynamic efficiency and hydrodynamic behaviour. Thermodynamic efficiency is dependent on the system kinetics while hydrodynamics is the study of fluid flow behaviour. The focus of this thesis is the hydrodynamic behaviour in tray columns, which affects entrainment. In order to isolate hydrodynamic behaviour from the thermodynamic behaviour that occurs inside sieve tray columns, investigations are conducted under conditions of zero mass transfer. When the gas velocity is sufficiently high to transport liquid droplets to the tray above, entrainment occurs. The onset of entrainment is one of the operating limits that determines the design of the column and thus impacts on the capital cost. By improving the understanding of the parameters that affect entrainment, the design of the tray and column can be improved which will ultimately increase the operability and capacity while reducing capital costs. Existing correlations predicting entrainment in sieve tray columns are based on data generated mainly from an air/water system. Previous publications recommend that more testing should be performed over larger ranges of gas and liquid physical properties. An experimental setup was therefore designed and constructed to test the influence of the following parameters on entrainment: 1. gas and liquid physical properties 2. gas and liquid flow rates 3. tray spacing The experimental setup can also measure weeping rates for a continuation of this project. The hydrodynamic performance of a sieve tray was tested with air and water over a wide range of gas and liquid flow rates and at different downcomer escape areas. It was found that the downcomer escape area should be sized so that the liquid escaping the downcomer always exceeds a velocity of approximately 0.23 m/s in order to create a sufficient liquid seal in the downcomer. For liquid velocities between 0.23 and 0.6 m/s the area of escape did not have an effect on the percentage of liquid entrained. It was also established that entrainment increases with increasing gas velocity. The rate at which entrainment increases as the gas velocity increase depends on the liquid flow rate. As soon as the liquid flow rate exceeded 74 m3/(h.m) a significant increase in entrainment was noted and the gas velocity had to be reduced to maintain a constant entrainment rate. This is because the increased liquid load requires a longer flow path length for the froth to fully develop. The undeveloped froth, caused by the short (455 mm) flow path, then creates a non-uniform froth that is pushed up against the column wall above the downcomer. Consequently, the froth layer is closer to the tray above resulting in most of the droplets ejected from the froth reaching the tray above and increasing entrainment. By reducing the gas velocity, the froth height and ejecting droplet velocity is reduced, resulting in a decrease in entrainment. The results from the experiments followed similar trends to most of the entrainment prediction correlations found in literature, except for the change noted in liquid flow rates above 74 m3/(h.m). There was, however, a significant difference between the experimental results and the correlations developed by Hunt et al. (1955) and Kister and Haas (1988). Although the gas velocities used during the air/water experiments were beyond the suggested range of application developed by Bennett et al. (1995) their air/water correlation followed the results very well. The entrainment prediction correlation developed by Bennett et al. (1995) for non-air/water systems was compared with the experimental air/water results to test for system uniformity. A significant difference was noted between their non-air/water prediction correlation and the air/water results, which motivates the need for a general entrainment prediction correlation over a wider range of gas and liquid physical properties. Based on the shortcomings found in the literature and the observations made during the experiments it is suggested that the influence of liquid flow path length should be investigated so that the effect on entrainment can be quantified. No single correlation was found in the literature, which accurately predicts entrainment for a large range of liquid loads (17 – 112 m3/(h.m)), high superficial gas velocities (3 – 4.6 m/s) and different gas and liquid physical properties. It is therefore recommended that more work be done, as an extension of this project, to investigate the influence of gas and liquid physical properties on entrainment (under zero mass transfer conditions) for a large range of liquid (5 – 74 m3/(h.m)) and gas (2 – 4.6 m/s) flow rates. In order to understand the effect of droplet drag on entrainment, tray spacing should be varied and increased to the extent where droplet ejection velocity is no longer the mechanism for entrainment and droplet drag is responsible for droplet transport to the tray above. Since it is difficult and in most cases impossible to measure exact gas and liquid loads in commercial columns, another method is required to measure or determine entrainment. Since liquid hold-up was found to be directly related to the entrainment rate (Hunt et al. (1955), Payne and Prince (1977) and Van Sinderen et al. (2003) to name but a few), it is suggested that a correlation should be developed between the dynamic pressure drop (liquid hold-up) and entrainment. This will contribute significantly to commercial column operation from a hydrodynamic point of view.

One approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations. / text

No description available.

Nanofiltration (NF) can be used in water and wastewater treatment as well as water recycling applications, removing micropollutants such as hormones. Due to their potential health risk it is vital to understand their removal mechanisms by NF membranes aiming at improving and developing more effective and efficient treatment processes. Although NF should be effective and efficient in removing small molecular sized compounds such as hormones, the occurrence of adsorption onto polymeric membranes results in performances difficult to predict and with reduced effectiveness and efficiency. This study aims firstly at defining, understanding and quantifying the relevant filtration operation parameters and, secondly, in identifying the physical mechanisms of momentum and mass transfer controlling the adsorption and transport of hormones onto polymeric NF membranes in cross-flow mode. The hormones estrone (E1) and 17-b-estradiol (E2) were chosen as they have very high endocrine disrupting potency. The NF membranes used and tested were the NF 270, NF 90, BW30, TFC-SR2 and TFC-SR3 since they have a wide span of pore sizes. The first step is to experimentally acquire the knowledge of how fluid flow hydrodynamics and mass transfer close to the membrane affect hormone adsorption. The focus will be particularly on the effect of operating pressure, circulating Reynolds numbers (based on channel height, Reh) and hormone feed concentration. These hydrodynamic parameters play an important role in concentration polarisation development at the membrane surface. A Reh increase from 400 to 1400 for the NF 270 membrane caused the total mass adsorbed of E1 and E2 to decrease from 1.5 to 1.3 ng.cm-2 and 0.7 to 0.5 ng.cm-2, respectively. In contrast, a pressure increase from 5 to 15 bar yielded an increase in the adsorbed mass of E1 and E2 from 1.0 to 1.8 ng.cm-2 and 0.5 to 0.7 ng.cm-2, respectively. Moreover, increasing hormone feed concentration caused an increase in the mass adsorbed for both hormones. These observations led to the conclusion that adsorption is governed by the initial concentration at the membrane surface which, in turn, depends on the hormone feed concentration, operating Reh and pressure. Membrane retention, however, depends on the initial polarisation modulus, defined as the ratio between the initial concentration at the membrane surface and the initial feed concentration. The same trends were obtained for the TFC-SR2 membrane. However, this membrane has a much lower permeability compared to the NF 270 one (7.2 vs 17 L.h-1.m-2.bar-1, respectively) and concentration polarisation is less severe. The experimental variations in mass adsorbed and retention as a function of the operating filtration parameters (Reh and pressure) were therefore lower. Based on these experimental results, a sorption model was developed. This model predicts well both feed and permeate transient concentrations for both hormones and membranes (NF 270 and TFC-SR2) in the common range of operating pressures and Reh of spiral-wound membrane modules. The model was further applied for E2 in the presence of background electrolyte, yielding good predictions. These findings are an important advancement in determining which membrane would be more suitable to effectively remove hormones with a substantial reduction of experimental work. The above-mentioned developed model does not give insight into the phenomena occurring inside the membrane since it focuses on the feed conditions. However, membrane characteristics, such as material and pore radius were found to have an impact in adsorption and retention of hormones. It was found experimentally that polyamide, from which the active layer of the NF membranes is made, adsorbs three times more mass of hormone than any other polymers constituting the membranes. Since this active layer is the membrane selective barrier of the membrane that is in contact with the largest hormone concentration (due to concentration polarization in the feed solution) it is concluded that the active layer adsorbs most of the hormones. Further experimental work carried out in this thesis showed that increasing the pore radius from 0.32 nm to 0.52 nm increased the E2 mass adsorbed from 0.17 ng.cm-2 to 1.1 ng.cm-2 and decreased the retention from 88% to 34%. These results show that the wider the pore, the larger the quantity of hormone that penetrates (i.e. partitions) inside the membrane and, therefore, the more the membrane adsorbs the hormone. For membranes of similar pore radius, the membrane with larger internal surface area was found to adsorb more. All the previous results led to the establishment of a new model for the hormone transport inside the membrane pore taking convection, diffusion and adsorption into account. Since the differential equation describing the transport with adsorption inside the pore has no analytical solution, a numerical model based on the finite-difference approach was applied. With such a model, its validation against experiments and parametric studies it was possible to understand the transport mechanisms of adsorbing hormones through NF membranes. The results show that for low pressures the hormone transport is diffusion dominated. In contrast, for higher pressures (above 11 bar) the transport is convection dominated, showing that a purely diffusion transport model does not describe well the actual transport phenomena of hormones in NF membranes. Furthermore, it was found that two similar molecules can behave very differently in terms of adsorption on the membrane. E1, which adsorbs 20% more than E2 in static mode, being slightly smaller than E2, partitions more inside the membrane pore and adsorbs double under filtration conditions. This study contributes to illuminating the adsorption mechanisms of hormones onto NF membranes by understanding what parameters control adsorption such as hydrodynamics, materials, structure, etc. This not only identifies a potential problem in large scale applications, but it also provides an understanding of the mechanisms involved in the removal of these hormones and a tool that can be used to design future membranes for the improvement of micropollutant removal.

The dynamic properties of several rectangular and V-shaped microcantilevers were investigated. Particular attention was paid to the higher flexural eigenmodes of oscillation. The potential of the higher flexural modes was demonstrated through the use of cantilevers as standalone sensors for adsorbed mass. The mass adsorbed on the surface of a cantilever was in the form of a homogeneous water layer measured as a function of relative humidity. The minimum detectable water layer thicknesses were 13.7 Å, 3.2 Å, 1.1 Å, and 0.7 Å for the first four modes of a rectangular cantilever, clearly demonstrating enhanced accuracy for the higher eigenmodes of oscillation. These thicknesses correspond to minimum detectable masses of 33.5 pg, 7.8 pg, 2.7 pg and 1.7 pg for the first four modes. For quantitative applications the spring constants of each cantilever must be determined. Many methods exist but only a small number can calibrate the higher flexural eigenmodes. A method was developed to simultaneously calibrate all flexural modes of microcantilever sensors. The method was demonstrated for the first four eigenmodes of several rectangular and V-shaped cantilevers with nominal fundamental spring constants in the range of 0.03 to 1.75 N/m. The spring constants were determined with accuracies of 5-10 %. Spring constants of the fundamental mode were generally in agreement with those determined using the Sader method. The method is compatible with existing AFM systems. It relies on a flow of gas from a microchannel and as such poses no risk of damage to the cantilever beam, its tip, or any coating. A related method was developed for the torsional modes of oscillation. Preliminary results are shown for the fundamental mode of a rectangular cantilever. The method can be easily extended to the higher torsional modes, V-shaped cantilevers, and potentially, the flapping modes of the legs of V-shaped microcantilevers.

No description available.

English abstract Hydrothermal systems related to highly evolved granitic magmas host diverse mineralization styles and provide an important source of economic metals. This master thesis concentrates on description and interpretation of geological structure, petrographic and textural variability, alteration zoning and calculation of time-integrated fluid fluxes recorded in highly evolved granites and tin-mineralized greisens of the Horní Blatná massif in the Western Krušné hory pluton. The massif is a composite intrusion, which consists of a large number of intrusive units emplaced during two stages. The first stage is represented by sparsely porphyritic fine-grained low-lithian annite granites that can be correlated with marginal granites (G2) of the Fichtelgebirge (Smrčiny) batholith or with intermediate granites (Walfischkopf type) of the Western Krušné hory (Erzgebirge) pluton. Intrusive batches of the second stage progressively evolve from medium- to coarse-grained serial high-lithian annite and zinnwaldite granites with topaz and rare tourmaline towards aphyric fine-grained zinnwaldite (or trilithionite) granites. This suite corresponds to the EIB2 and EIB3 facies of the younger intrusive complex in the Western Krušné hory (Erzgebirge) pluton and it can be compared to the G3 Waldstein and G4 units in...