Thesis (MEng) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: Distillation is one of the most widely used processes for the separation of fluids with different volatilities. Due to the popularity of this process it is often assumed that the hydrodynamic behaviour inside distillation columns is well-defined. However, this is not always the case and this study therefore endeavoured to provide additional insight into the topic through a systematic investigation into the hydrodynamics and the capacity limitations of a sieve tray distillation column. The objective of the study was to measure and evaluate the effects of the following variables on entrainment and weeping: - Fluid flow rate (gas and liquid). - Plate geometry (i.e. hole diameter and fractional hole area). - Liquid properties (i.e. surface tension, viscosity and density). - Gas properties (i.e. viscosity and density). The hydrodynamic effects were evaluated at zero mass transfer in a pilot-scale tray column, by passing pure liquids and gases in counter current configuration. The pilot column was rectangular in shape with internal dimensions of 175 mm by 635 mm. A chimney tray was used to capture the weeping liquid, while a de-entrainment tray was used in combination with a mist eliminator pad to capture the entrained liquid. The fractional hole areas for the sieve trays under investigation were 7%, 11% and 15% and the hole diameters were 3.2 mm (⅛ in.), 6.4 mm (¼ in.) and 12.7 mm (½ in.). The experimental liquids were ethylene glycol, butanol, water and silicone oil, while the gases were air and carbon dioxide (CO2). These experimental measurements produced over 10 000 data points for entrainment and over 7 000 data points of weeping. The results were repeatable and the entrainment values compared reasonably well with previous data produced by Nutter (1971) and Uys (2012). The differences between entrainment for the different liquids were more significant in the spray regime than in the froth regime, and butanol was entrained more readily than silicone oil, ethylene glycol and water. Fluids that caused a larger spray layer in the dispersion zone produced more entrainment. Entrainment increased with decreasing liquid density, decreasing liquid surface tension and decreasing liquid viscosity. The more unstable the dispersion layer, the higher the entrainment. The liquid density strongly influenced weeping, i.e. weeping increased with increasing liquid density. On the other hand, gases with higher densities – and thus with a higher mass flow rates at similar volumetric flow rates through the sieve tray – displayed less weeping and more entrainment than less dense gases, because of an increased upward drag force on the fluids. When considering tray geometry and when operating in the spray regime, the magnitude of entrainment increased with decreasing fractional hole area, while the dependency of entrainment on fractional hole area was more prominent at lower fractional hole areas. When operating in the froth regime – typically above 23 m3/(h.m) – the fractional hole area had a relatively small influence on the magnitude of entrainment, while the cross-flowing liquid rate dominated related effects. In the spray regime, i.e. typically below 23 m3/(h.m), the entrainment increased with increasing sieve tray hole diameter, while hole diameter had a relatively small influence on entrainment at higher liquid flow rates between 23 and 60 m3/(h.m). However, at even higher liquid flow rates in the froth regime, i.e. above 60 m3/(h.m), the effect of hole diameter on the entrainment became more prominent again, with increased entrainment for smaller hole diameters. The effect of hole diameter on weeping differed with changing fluid combinations and the 12.7 mm hole size caused notably less weeping than the 3.2 mm and 6.4 mm trays at higher liquid flow rates. It is believed that weeping occurred preferentially at so-called localised high pressure zones on the sieve tray. At high gas and liquid flow rates, the resultant extended dispersion layer allows minimal intimate contact between the plate and the liquid (minimising such localized high-pressure zones). In effect, the liquid ‘jumps’ over the entire flow path length in the test rig, thus resulting in low weeping rates at high gas and liquid rates. The effects of fractional hole area and hole diameter on entrainment and weeping can be correlated with combinations of well-known hydrodynamic dimensionless numbers, such as the Weber number (We), Froude number (Fr) and Reynolds number (Re). Within the limitations of this study, the flow-Froude number was shown to be the most useful dimensionless number, since it displayed a monotonic relationship with magnitude of entrainment for different combinations of fluid systems and tray configurations. Furthermore, both the construction number and fluid density ratio could be used in a sensible manner to correlate some of the effects of tray geometry on entrainment. / AFRIKAANSE OPSOMMING: Distillasie word wêreldwyd op groot en klein skaal toegepas as ʼn metode om chemiese komponente van mekaar te skei, gebasseer op hul verskil in vlugtigheid. Die hidrodinamiese gedrag van vloeistowwe en hul damp binne ʼn distillasiekolom beïnvloed die effektiwiteit van die skeidingsproses. Hierdie studie beoog dus om bykomende insig te verskaf tot die hidrodinamika en kapasiteitsbeperkings van ʼn plaat-distilleerkolom. Die doelwit van die studie was om die invloed van die volgende veranderlikes op die meesleuring en deurdripping van vloeistowwe te ondersoek: - Gas- en vloeistof vloeitempo. - Plaatgeometrie (i.e. gatdeursnit en fraksionele deurvloei-area). - Vloeistofeienskappe (i.e. oppervlakspanning, viskositeit en digtheid). - Gaseienskappe (i.e. viskositeit en digtheid). Die hidrodinamiese studie is uitgevoer in ʼn reghoekige plaatkolom met interne afmetings van 175 mm x 635 mm. Die vloeistof en gasfases is in kontak gebring op ʼn teenstroom basis, met geen massa-oordrag wat plaasvind nie. ʼn Skoorsteenplaat het die vloeistof opgevang wat deurdrip terwyl ʼn ekstra plaat aan die bokant van die kolom die meegesleurde vloeistof opgevang het. Hierdie ekstra plaat is gebruik tesame met ʼn mis-elimineerder om al die meegesleurde vloeistof op te vang. Plate met verskillende deurvloei-areas (7%, 11% en 15%) en gat deursnitte (3.2 mm, 6.4 mm en 12.7 mm) is gebruik in die ondersoek. Die vloeistowwe wat gebruik is, sluit in etileen glikol, butanol, water en silikon olie. Lug en koolstofdioksied is as gasse gebruik. Die eksperimentele data het goeie herhaalbaarheid getoon en is vergelykbaar met die gepubliseerde data van Nutter (1971) en Uys (2012). Meer as 10 000 data punte is gemeet vir vloeistofmeesleuring en meer as 7 000 vir deurdripping. Die verskil in hoeveelheid meesleuring tussen die vloeistowwe, soos ondersoek in hierdie studie, was mees beduidend in die spoei-regime. Butanol is die meeste meegesleur, gevolg deur silikon olie en dan etileen glikol. Water is die minste meegesleur is. Vloeistowwe wat ʼn groter sproeivolume in die dispersielaag bo die plaat gevorm het, is die meeste meegesleur. Meesleuring het toegeneem met ʼn afname in digtheid, oppervlakspanning en viskositeit van die vloeistof. ʼn Onstabiele dispersielaag bo die plaat het meer meesleuring tot gevolg gehad. Vloeistofdeurdripping is sterk beïnvloed deur vloeistofdigtheid, i.e. deurdripping het sterk toegeneem met digtheid. Gasse met ʼn hoër digtheid veroorsaak weer ʼn afname in deurdripping a.g.v. die hoër opwaartse sleurkragte wat ʼn gas met hoë digtheid op die vloeistof uitoefen. In die sproei-regime (tipies by vloeistofvloeitempos laer as 23 m3/(h.m) is gevind dat meesleuring toeneem met ʼn afname in fraksionele deurvloei-area. Meesleuring se afhanklikheid van fraksionele deurvloei-area was meer beduidend by laer fraksionele deurvloei-areas. In die skuim-regime (tipies by vloeistofvloeitempos hoër as 23 m3/(h.m)) was die afhanklikheid van meesleuring op fraksionele deurvloei-area relatief klein. In die sproei-regime is gevind dat meesleuring toeneem met ʼn toename in gat deursnit, terwyl dieselfde veranderlike ʼn minder beduidende invloed op meesleuring getoon het by hoër vloeistofvloeitempos (tussen 23 en 60 m3/(h.m)). By vloeitempos hoër as 60 m3/(h.m) het meesleuring weer begin toeneem met ʼn afname in gat deursnit. By hoë vloeistofvloeitempos het die plaat met 12.7 mm gat deursnit aansienlik minder deurdripping getoon as plate met 3.2 mm en 6.4 mm deursnitte. Daar word vermoed dat deurdripping hoofsaaklik plaasvind by lokale hoëdruk gebiede op die plaat. By hoër vloeistof- en gasvloeitempos beslaan die dispersielaag ʼn groter volume en is daar dus minder gebiede van digte vloeistofkontak met die plaat, wat ʼn afname in die lokale drukgebiede veroorsaak. Dit lei tot ʼn afname in deurdripping by hoër gas- en vloeistofvloeitempos. Die invloed van fraksionele deurvloei-area en gatdeursnit op meesleuring en deurdripping korreleer goed met kombinasies van welbekende hidrodinamiese dimensielose getalle, i.e. die Webergetal (We), die Froudegetal (Fr) en die Reynoldsgetal (Re). Die vloei-Froudegetal is mees bruikbaar om die invloed van vloeistof-en-gas kombinasies en kolomuitleg op meesleuring te korreleer. Die konstruksiegetal asook die digtheidsverhoudings tussen vloeistof en gas kan op ʼn sinvolle manier aangewend word om van die invloede van plaatgeometrie op meesleuring te beskryf.

In this thesis we prove several different results about the number of primes represented by linear functions. The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q^{1/2}phi(q)) when log{x}/log{q}>8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem. Let k>1 and Pi(n) be the product of k linear functions of the form a_in+b_i for some integers a_i, b_i. Suppose that Pi(n) has no fixed prime divisors. Weighted sieves have shown that for infinitely many integers n, the number of prime factors of Pi(n) is at most r_k, for some integer r_k depending only on k. In Chapter 3 and Chapter 4 we introduce two new weighted sieves to improve the possible values of r_k when k>2. In Chapter 5 we demonstrate a limitation of the current weighted sieves which prevents us proving a bound better than r_k=(1+o(1))klog{k} for large k. Zhang has shown that there are infinitely many intervals of bounded length containing two primes, but the problem of bounded length intervals containing three primes appears out of reach. In Chapter 6 we show that there are infinitely many intervals of bounded length containing two primes and a number with at most 31 prime factors. Moreover, if numbers with up to 4 prime factors have `level of distribution' 0.99, there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and an almost-prime with at most 4 prime factors.

This experiment is composed of three parts: Gas sampling and analysis by Regenerative Thermal Oxidizer in the factory ¡Afabrication and screening of catalyst, and a discussion about efficiency of Catalytic Oxidation toluene by varied factors. Regarding gas sampling in the factory, we found that the transformation rate of VOCs by Regenerative Thermal Oxidizer(RTO) at operation temperature 982¢J into tolueneis 94.7%, into 2-butanone is 96.5%, into isopropyl alcohol is 95%. Among the three, toluene showed the lowest transformation rate. Regarding catalyst sampling and research, we found that metal catalyst by immersion method(immersion method) ( weight ratio of Cu:Co¡BCu¡GMn and Mn¡GCo is 1¡G1¡BPure Cu¡BPure Co and Pure Mn)and metal load(metal /molecular sieve) is 5%¡B10%. Among the twelve metal catalysts, we figured out 10% metal C-Co(1:1) is the best catalyst concerning transformation rate. Regarding the operation factors, the experiment showed¡G(1)the more the concentration of toluene¡Athe more the temporary inhibition¡Aand therefore, the transformation rate went down¡A(2)The more the speed of inhalation¡Athe time the air stayed still decreased, and a obvious decrease of transformation rate can be seen(3)the increase of oxygen concentration showed a positive effect toward transformation rate.(4)When at a higher reaction temperature, for the above mentioned three factors, the influence upon transformation rate became less. In addition, for the cost evaluation, the 10% metal Cu-Co(weight rate 1:1) catalyst we chose in our experiment is 92.79 Taiwanese Dollars for one batch of 120g and the catalyst per gram is 0.77 Taiwanese Dollars.

Nitrogen-selective Carbon Molecular Sieve (CMS) membranes were developed for nitrogen/methane separation. Effects of pyrolysis conditions including pyrolysis temperature protocol and pyrolysis atmosphere were studied for Matrimid® and 6FDA:BPDA-DAM precursors. It was revealed that high pyrolysis temperature is essential to achieve attractive nitrogen/methane selectivity due to the subtle size difference between the two gas penetrants. Detailed study on one of the best performing CMS membranes showed that diffusion selection, more specifically, the entropic factor responsible for diffusion selection provides a significant contribution to the high selectivity. The effect of precursor was studied by considering nine carefully selected polymers. The structures and properties of these polymer precursors were compared and correlated with the separation performance of resulting CMS membranes. The translation of intrinsic CMS transport properties into the hollow fiber morphology was also explored. Substructure collapse and asymmetry lost during pyrolysis were observed, which resulted in significant increases of separation layer thickness and decreases in permeance. Vinyltrimethoxy silane (VTMS)-treatment was applied to polymer hollow fiber before pyrolysis to overcome the problem of substructure collapse. The effects of VTMS-treatment on both the substructure and skin layer are discussed.

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Master of Science / Grain Science and Industry / Cassandra K. Jones / A total of 7 experiments were conducted to evaluate the effects of particle size and thermal processing on swine growth performance or to develop improved analytical methods for particle size prediction. First, 5 experiments utilized 596 nursery pigs to assess how corn particle size and pelleting affected nursery pig growth performance and feed preference. The improvements from reducing particle size were mixed among experiments, potentially because pigs preferred to consume more coarsely ground corn in both mash (P < 0.05; 79.3 vs. 20.7%) and pelleted diets (P < 0.05; 58.2 vs. 31.8%) diets. Pelleting diets led to a reduction in feed disappearance, which tended to improve feed efficiency in nursery pigs (P < 0.05; 0.61 vs. 0.64 for pigs fed mash vs. pelleted diets in Exp. 1). Next, a total of 270 finishing pigs were utilized to determine the effects of long-term conditioning or extrusion of low energy feedstuffs on finishing pig nutrient digestibility, growth performance and carcass characteristics. Treatments included the same basal diet processed as: 1) non-processed mash, 2) pelleted with 45 s conditioner retention time, 3) pelleted with 90 s conditioner retention time, or 4) extruded. Thermal processing, regardless of type, improved daily gain and feed efficiency (P < 0.05), but did not affect feed intake (P > 0.10). Extruded diets tended to improve feed efficiency compared to pelleted diets (P < 0.10). However, pigs fed thermally-processed diets had greater jowl iodine value compared to those fed mash diets (P < 0.05). Finally, 420 samples were used to determine the impact of top sieve size, grain type, technician, and flow agent on the ability of a 3-sieve analytical method to accurately predict the mean particle size determined by a standardized 12-sieve method. The experiment was a 3 × 2 × 2 × 3 factorial with 3 technicians, 2 sieve sizes (U.S. No. 12 vs. 16 sieve as the top sieve), 2 flow agent levels (0 vs. 0.5 g), and 3 grain types (corn, sorghum, or wheat). Linear regression was used to develop individual equations to predict the mean particle size for each of the 3-sieve methods compared to the standard 12-sieve method recognized as ASAE S319.4, and the GLIMMIX procedure of SAS was used to evaluate the impact of main effects and interactions on predication accuracy. All interactions were removed from the model due to insignificance (P > 0.10). Technician, screen size and flow agent did not affect (P > 0.10) the accuracy of the prediction equations. Grain was the only main effect of significance (P < 0.05), where the prediction equation overestimated the particle size of wheat by approximately 15 µm and underestimated the particle size of corn by approximately 12 µm. While statistically significant, these variations were deemed to be sufficiently accurate for the 3-sieve method, and that separate equations for each grain type were not warranted to retain the simplicity of the method. In summary, technician, sieve size, grain type, and the use of flow agent did not greatly affect the accuracy of the 3-sieve particle size analytical method, so the original method was concluded to be accurate and the preferred method.

Title: Generating polynomials for number field sieve Author: Anežka Pejlová Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: The topic of this thesis is mainly focused on Kleinjung algorithm for generating polynomials within the General Number Field Sieve, which is the most efficient factorization algorithm nowadays. Commonly used consecu- tions are explained with respect to the fact whether they can be rigorously proven or they are based only on heuristic assumptions. Another contribution of this thesis is the attached implementation of Kleinjung algorithm develo- ped as a part of the Number Field Sieve project led by the Department of Algebra. The appropriateness of some heuristics used in the theory beyond the Kleinjung algorithm is supported by empirical data obtained from this implementation. Keywords: Number field sieve, Kleinjung algorithm

Indiana University-Purdue University Indianapolis (IUPUI) / Extrusion-based 3D printing is one of the emerging additive manufacturing technologies used for printing a range of materials from metal to ceramics. In this process, the required material is extruded from the extruder in the form of a slurry. Zeolite and MOFs are mainly used for CO2 adsorption in the form of pellets and beads due to their good adsorptive property. Researchers are developing monoliths of Zeolite and MOFs and fabricate them using traditional extrusion and implement them in the gas adsorption applications as an option for beads and pellets by developing a monolithic structure. Previous research on Zeolite 13X and 5A have shown good structural and physical properties in monolith form. In this study, we developed slurry of two molecular sieve Zeolite 3A and 4A monoliths powders, mixing it with bentonite clay, methyl cellulose, and PVA as a binder. The slurry preparation was carried out at room temperature. Once the 3D printed samples are dried at room temperature, a sintering process was performed to increase mechanical strength. To be used in real-time applications, the 3D printed Zeolite sample need to have sufficient mechanical strength. The BET surface area test showed good results for Zeolite 13X compared to available literature. The surface area calculated for 3D printed Zeolite 13X was 767m2/g and available literature showed 498 m2/g for 3D printed Zeolite 13X. The microhardness values of 3D printed Zeolite samples were measured using a Vicker hardness tester. The hardness value of the 3D - printed Zeolite samples increased from 8.3 ± 2 to 12.5 ± 3 HV0.05 for Zeolite 13X, 3.3 ± 1 to 7.3 ± 1 HV0.05 for Zeolite 3A, 4.3 ± 2 to 7.5 ± 2 HV0.05 for Zeolite 4A, 7.4 ± 1 to 14.0 ± 0.5 HV0.05 for Zeolite 5A respectively. The SEM, EDS and XRD analysis was performed for 3D printed samples before and after sintering to evaluate their structural properties. The SEM analysis reveals that all 3D printed Zeolite samples retained their microstructure after slurry preparation and also after the sintering process. The porous nature of 3D printed Zeolite walls was retained after the sintering process. The EDS analysis showed that the composition of 3D printed Zeolite samples remained somewhat similar with minor variation for before and after sintering. The framework structure of Zeolite Type X for Zeolite 13X and Zeolite Type A for Zeolite 3A, 4A, 5A were in good shape after sintering as standard peak intensity points were retained. Zn-MOF74 was synthesized using solvothermal synthesis which is a well-established synthesis process used for the synthesis of MOFs. We also developed slurry for Zn-MOF-74 using bentonite clay and PVA as binders and printed small parts using hand printing.

Indiana University-Purdue University Indianapolis (IUPUI) / Observational data are frequently used for causal inference of treatment effects on prespecified outcomes. Several widely used causal inference methods have adopted the method of inverse propensity score weighting (IPW) to alleviate the in uence of confounding. However, the IPW-type methods, including the doubly robust methods, are prone to large variation in the estimation of causal e ects due to possible extreme weights. In this research, we developed an ordinary least-squares (OLS)-based causal inference method, which does not involve the inverse weighting of the individual propensity scores. We first considered the scenario of homogeneous treatment effect. We proposed a two-stage estimation procedure, which leads to a model-free estimator of average treatment effect (ATE). At the first stage, two summary scores, the propensity and mean scores, are estimated nonparametrically using regression splines. The targeted ATE is obtained as a plug-in estimator that has a closed form expression. Our simulation studies showed that this model-free estimator of ATE is consistent, asymptotically normal and has superior operational characteristics in comparison to the widely used IPW-type methods. We then extended our method to the scenario of heterogeneous treatment effects, by adding in an additional stage of modeling the covariate-specific treatment effect function nonparametrically while maintaining the model-free feature, and the simplicity of OLS-based estimation. The estimated covariate-specific function serves as an intermediate step in the estimation of ATE and thus can be utilized to study the treatment effect heterogeneity. We discussed ways of using advanced machine learning techniques in the proposed method to accommodate high dimensional covariates. We applied the proposed method to a case study evaluating the effect of early combination of biologic & non-biologic disease-modifying antirheumatic drugs (DMARDs) compared to step-up treatment plan in children with newly onset of juvenile idiopathic arthritis disease (JIA). The proposed method gives strong evidence of significant effect of early combination at 0:05 level. On average early aggressive use of biologic DMARDs leads to around 1:2 to 1:7 more reduction in clinical juvenile disease activity score at 6-month than the step-up plan for treating JIA.