Dissertations / Theses on the topic 'Mixing'

The thesis is dealing with mixing processes havingapplication to ground improvement by deep mixing. The mainobjectives of the thesis is to make a contribution to knowledgeof the basic mechanisms in mixing binding agents into soil andimprove the knowledge concerning factors that influence theuniformity of stabilised soil.

A great part of the work consists of a literature surveywith particular emphasis on literature on the processindustries. This review forms a basis for a profounddescription and discussion of the mixing process and factorsaffecting the process in connection with deep mixingmethods.

The thesis presents a method for a simple field test for thestudy of influential factors in the mixing process. A number offactors in the installation process of lime-cement columns havebeen studied in two field tests using statistical multifactorexperiment design. The effects of retrieval rate, number ofmixing blades, rotation speed, air pressure in the storagetank, and diameter of the binder outlet on the stabilisationeffect and the coefficient of variation determined byhand-operated penetrometer tests for excavated lime-cementcolumns, were studied.

The literature review, the description of the mixingprocess, and the results from the field tests provide a morebalanced picture of the mixing process and are expected to beuseful in connection to ground improvement projects and thedevelopment of mixing equipments.

The concept of sufficient mixture quality, i.e. theinteraction between the mixing process and the mechanicalsystem, is discussed in the last section. By means ofgeostatistical methods, the analysis considers thevolume-variability relationship with reference to strengthproperties. According to the analysis, the design values forstrength properties depends on the mechanical system, the scaleof scrutiny, the spatial correlation structure, and the conceptof safety, i.e. the concept of sufficient mixture quality isproblem specific.

Key words:Deep Mixing, Lime cement columns, Mixingmechanisms, Mixture quality, Field test, ANOVA, Variancereduction.

PEPT (positron emission particle tracking) is a technique for tracking a small radioactive tracer in Lagrangian co-ordinates. The technique was used to study the flow patterns of non-Newtonian CMC (Carboxy Methyl Cellulose) solutions inside a vessel agitated by an axial flow impeller. The 'non-intrusive' PEPT technique uses two position-sensitive detectors to track a radioactive particle in space and time. The particle is labelled with a positron emitting isotope. Once emitted from the nucleus a positron annihilates with an electron releasing energy in the form of two 511 keV back-to-back gamma-rays travelling in opposite directions, 180 degrees apart. The tracer particle is introduced into the stirred vessel which is mounted between the two detectors of the positron camera. Three axial flow impellers produced by Lightnin Mixers Ltd were used to carry out the experiments. Results showed that the discharge from the three impellers was radial when agitating non-Newtonian viscous solutions of CMC. Trajectory analysis was used to compare the performance of the impellers using the agitation index and the efficiency of circulation. A limited number of experiments was carried out to compare the effect of baffles on the circulation of the fluids in a mixing tank. The results showed that mixing of these non-Newtonian liquids in an unbaffled tank is better than in a baffled tank when using axial flow impellers. Other experiments were carried out to suspend solid particles in viscous fluids. Results showed that the minimum speed required to suspend large particles is lower than that required to suspend small particles. There are many correlations and models in the literature to determine the minimum speed required to suspend all the particles in a fluid; some of these correlations and models were compared with experimental results from this work. The correlation of Zweitering (1958) agreed with experimental data after modification. The Geisler et al. (1993) model agreed with the data provided that the power consumption is correctly substituted. The last part of this work concerned the flow of non-Newtonian viscous materials through industrial equipment. Yoghurt was chosen as the test fluid as one of the companies sponsoring this project was Eden Vale, a yoghurt manufacturer. A method was proposed using rheological measurements to simulate the flow through the dispensing pipeline and distributing nozzles; this method allows the designer to predict the final properties of yoghurt after passing through the paching head. Measurements were also carried out to determine the final gel structure of yoghurt in the delivery pots. This data of this thesis is useful in designing stirred tanks when non-Newtonian fluid is present, either for agitation or when suspending solids. Also, a method was provided to design yoghurt manufacturing line.

In order to increase our understanding of magma mixing processes and their impact on the geochemical evolution of silicate melt we present in the following works, the first set of experiments performed using natural basaltic and rhyolitic melts. In particular, we investigate the interplay of physical dynamics and chemical exchanges between these two melts using time-series mixing experiments performed under controlled, chaotic, dynamical conditions. The variation of major and trace elements is studied in detail by electron microprobe (EMPA) and Laser Ablation ICP-MS (LA-ICP-MS) and the time-evolution of chemical exchanges during mixing is investigated. Using the concentration variance as a proxy to measure the rate of chemical element homogenization in time, a model to quantify chemical element mobility during chaotic mixing of natural silicate melts is proposed. The morphology of mixing patterns at different times is quantified by measuring their fractal dimension and an empirical relationship between mixing time and morphological complexity is derived. The complexity of mixing patterns is also compared to the degree of homogenization of chemical elements during mixing and empirical relationships are established between the fractal dimension and the variation of concentration variance of chemical elements in time. Finally we discuss the petrological and volcanological implications of this work.
Um unser Verständnis über die Prozesse bei der Vermischung von Magmen und dessen Auswirkungen auf die geochemische Entwicklung von Silikatschmelzen zu verbessern, werden in dieser Arbeit erstmalig eine Reihe von „Magma Mixing“ Experimenten vorgestellt, in der natürliche Basalte und Rhyolite verwendet werden. In dynamischen Zeitreihen-Mischungsexperimenten, die unter kontrollierten, chaotischen, dynamischen, Bedingungen abliefen, wurde vor allem das Zusammenspiel der physikalischen Prozessen durch das mechanische Vermengen zweier Schmelzen und der resultierenden chemischen Austauschreaktionen durch Diffusion an den Grenzflächen zwischen diesen beiden Schmelzen untersucht. Die Variation von Haupt- und Spurenelementen wurde mittels Elektronen-Mikrosonde (EMPA) und Laser Ablation ICP-MS (LA-ICP-MS) im Detail untersucht und zusätzlich konnte die zeitliche Entwicklung des chemischen Austauschs während des Mischungsvorgang dargestellt werden. Die Varianz der Konzentration einzelner Elemente über die Grenzflächen zwischen Basalt und Rhyolit hinweg wurde als Proxy verwendet, um die Homogenisierungsrate der chemischen Elemente bezogen auf die Zeit zu bestimmen. Dies wird als Modell vorgeschlagen, mit dem die Mobilität chemischer Elemente während chaotischem Mischens von natürlichen Silikatschmelzen quantifiziert werden kann. Im Weiteren wurde mit Hilfe von Fraktalanalyse die Morphologie der Mischungsmustern zu unterschiedlichen Zeiten quantifiziert und eine empirische Beziehung zwischen Mischzeit und morphologischer Komplexität abgeleitet. Die Komplexität der Mischungsmuster wurde zudem mit dem Grad der Homogenisierung der chemischen Elemente während des Mischens verglichen. Dadurch konnten empirische Beziehungen zwischen der fraktalen Dimension von Mischungsmorphologien und der zeitlichen Variation der Konzentration von chemischen Elementen abgeleitet werden. Im Laufe dieser Arbeit werden zudem die petrologischen und vulkanologischen Auswirkungen diskutiert.

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2000.
Includes bibliographical references (p. 51-53).
The hi-end tools available to today's sound designers give them almost limitless control over audio processing. Devices such as Yamaha's new digital mixers and Digidesign's Pro-Tools computerized editing workstations allow users in a small studio to accomplish tasks which would have required racks full of gear only seven years ago in a professional studio. However, the evolution of the interfaces used with these systems have not kept pace with the improvements in functionality. With all of their complexity, the new digital mixing consoles still look like the old analog mixers, with the addition of an LCD screen. This thesis will introduce a new type of concept called Multi-Modal Mixing that aims to enhance current systems and point to a new standard of audio control.
by Edward Vickers Hammond.
S.M.

Seawater intrusion presents one of the most unique and ubiquitous groundwater problems in the field of hydrogeology. Its complex boundary conditions coupled with variable density flow results in non-uniform flow which lead to non-trivial mixing dynamics. The mixing of fresh and saline waters in the subsurface is known to play a key role in an array of geochemical reactions. Such reactions include the dissolution and precipitation of calcite which shape the coastal landscape over millennia, as well as reactions associated to anthropogenic contamination of coastal groundwater such as nitrogen reduction or iron oxide precipitation which can act to limit the fluxes of harmful pollutants to vulnerable near shore marine ecosystems. In addition to reactions, understanding the mixing mechanisms is crucial to predicting the movement of the saltwater wedge and the size of the salt-freshwater interface. This has direct implications on the management of fresh groundwater reserves and its risk to salinization. In this thesis we focus on understanding the influence variable density flow on mixing and the spatial distribution of enhanced geochemical activity along the saline-freshwater interface. First, we look to see the impact of heterogeneity on mixing and reaction for fast calcite dissolution. We find that heterogeneity permits reactions to occur over a greater area of the mixing zone due to enhanced mixing rates than would otherwise be permitted in homogeneous media. Furthermore, we observe unique patterns of enhanced localized reactivity that strongly deviate from the homogeneous case. Our study suggests that karst topology in coastal aquifers may be strongly linked to non-uniform flow induced by variable density flow and strongly linked to the type of heterogeneity present. Since initial stages of karst development are known to dictate the evolution of cave systems and conduits, we hypothesize that heterogeneity plays an integral role in its propagation. Second, we study mixing across the salt-freshwater interface and the influence of compression caused by the flow of freshwater towards the saltwater body. In the absence of transient effects and heterogeneity, we find that mixing interface grow via transverse dispersion until some critical distance at which point it begins to recompress due to accelerating flow resulting from a decrease in area between the confining unit and the interface. Using a modified Glover solution to define the mixing interface, we are able to capture the velocity change along the interface from which a stretching rate (acceleration) can be deduced. We find that the behaviour of interface compression can be well-approximated by assuming a local Bachelor scale, which defines the equilibrium between dispersive growth and compression due to accelerating flow. Finally, we establish a new method to study fast mixing-dependent reactions across the salt-freshwater interface. Our findings lead us to the use of luminol chemiluminescence, which allows for the direct visualization of reaction rates along the saline-freshwater interface. Unlike conservative studies of mixing in sand tank, we bypass the need for complex image analysis techniques required to resolve local concentration gradients needed to evaluate mixing metrics. Results from experiments performed under both steady state and transient conditions consistently confirm local reaction hotspots at both the interface toe and at the head of the interface, which we attribute to stagnation point flow and accelerating flow respectively. Evaluation of the interface during the transient advance and retreat were also able to capture unique reactive behaviours that capture a shift in mixing behaviour due to a change in the flow field across the mixing zone
La intrusión de agua de mar presenta uno de los problemas más singulares y omnipresentes de aguas subterráneas en el campo de la hidrogeología. Sus complejas condiciones de contorno junto con un flujo de densidad variable dan como resultado un flujo irregular y, consecuentemente, provocando una dinámica de mezcla no trivial. La mezcla de agua dulce y salada en el subsuelo juega un papel clave en una serie de reacciones geoquímicas, tal como la disolución y precipitación de la calcita, que ha dado forma al paisaje costero durante milenios. También controla reacciones asociadas a la contaminación antropogénica de las aguas subterráneas costeras, tal como la reducción de nitrógeno o la precipitación de óxido de hierro,que pueden actuar para limitar los flujos de elementos contaminantes. Dichos elementos son nocivos para las zonas vulnerables cercanas a la costa, como los ecosistemas marinos. Además de las reacciones, comprender los mecanismos de mezcla es crucial para predecir el movimiento de la cuña de agua salada y el tamaño de la interfaz que separa el agua salada de la dulce. Esto tiene implicaciones directas en la gestión de las reservas de agua dulce subterránea y su riesgo de salinización. En esta tesis nos enfocamos en comprender la influencia del flujo de densidad variable en el proceso de mezcla y la distribución espacial de la actividad geoquímica (mejorada) sobre la interfaz agua dulce y salada. Primero, buscamos ver el impacto de la heterogeneidad hidráulica en la mezcla y reacción para una rápida disolución de la calcita. Encontramos que tal heterogeneidad permite que se produzcan reacciones en un área mayor de la zona de mezcla debido a velocidades de mezcla mejoradas respecto de las que serían posibles en medios homogéneos. Además, observamos patrones únicos de reactividad localizada mejorada que se desvían fuertemente del caso homogéneo. Nuestro estudio sugiere que la topología kárstica en los acuíferos costeros puede estar fuertemente ligada a un flujo no uniforme inducido por un flujo de densidad variable y fuertemente vinculado al tipo de heterogeneidad presente. Dado que se sabe que las etapas iniciales del desarrollo kárstico dictan la evolución de los sistemas de cuevas y conductos, planteamos la hipótesis de que la heterogeneidad juega un papel integral en su propagación. En segundo lugar, estudiamos el proceso de mezcla que se da en la interfaz de agua dulce y salada y la influencia de la compresión causada por el flujo de agua dulce hacia el cuerpo de agua salada. En ausencia de efectos transitorios y heterogeneidad, encontramos que la interfaz de mezcla crece a través de la dispersión transversal hasta una distancia crítica en cuyo punto comienza a comprimirse, debido al flujo acelerado resultante de una disminución en el área entre la unidad confinante y la interfaz. Usando una solución Glover modificada para definir la interfaz de mezcla, podemos capturar el cambio de velocidad a lo largo de la interfaz de la cual se puede deducir una tasa de estiramiento (aceleración). Encontramos que el comportamiento de la compresión de la interfaz se puede aproximar bien asumiendo una escala de Bachelor local, que define el equilibrio entre el crecimiento dispersivo y la compresión debido al flujo acelerado. Finalmente, establecemos un nuevo método para estudiar reacciones rápidas dependientes de la mezcla a través de la interfaz sal-agua dulce. Nuestros hallazgos nos llevan al uso de quimioluminiscencia de luminol, que permite la visualización directa de la distribución espacial de la tasa de reacción a lo largo de la interfaz agua dulce-salada. A diferencia de la práctica más habitual en estudios de mezcla en tanques de arena, que típicamente utilizan trazadores no reactivos, evitamos aquí la necesidad de resolver gradientes de concentración para computar métricas de mezcla. Los resultados de los experimentos, realizados tanto en condiciones estacionarias como transitorias, confirman consistentemente la generación de puntos calientes de reacción local, tanto en la cuña como en la cabeza de la interfaz, que atribuimos al estancamiento y aceleración del flujo, respectivamente. La evaluación de la interfaz durante el avance y retroceso transitorio también pudo capturar comportamientos reactivos únicos que capturan un cambio en el comportamiento de mezcla debido a un cambio en el campo de flujo a través de la zona de mezcla.
Enginyeria del terreny

Initiation and maintenance of motion within a pulp suspension is necessary for effective mixing. This requires imposition of forces greater than the network strength and depends on suspension rheology once motion begins. As pulp suspensions display non-Newtonian and solid-like behaviour, studies were conducted using profiled rotors which imposed stress within the body of suspensions contained in cylindrical devices. A concentric cylinder device capable of high torques (85 N-m) and high rotational speeds (524 rad/s) was built to study pulp suspension dynamic behaviour. Most work used a profiled rotor 0.1 m in diameter with baffled housings 0.13 and 0.22 m in diamter. The yield stress of low consistency pulp suspensions were measured with a Haake RV12 Ro-tovisco concentric cylinder viscometer. Semi-bleached kraft pulp was used throughout the study. Some tests were made with stone groundwood and thermomechanical pulps. Yield stress measurements were made for nylon and Spectra-900 fibre suspensions. The yield stress of pulp suspensions, ty, have been measured and correlated with mass concentration (Cm) and volumetric concentration (Cv) over the range 0.4 ≤ Cm(%) ≤ 33. It was found that because of increasing gas content that correlations developed using the mass concentration were inaccurate above approximately 20% Cm. Correlations developed using the volumetric concentration were accurate over the full range tested. For a West-Coast semi-bleached kraft pulp, ty(Pa) = 1.40CV(%)²ֹ⁷². Once rotor motion was initiated, pulp suspensions exhibited two distinct regimes of behaviour. The first was a tangential-cavity regime in which predominantly tangential motion grew to fill the chamber as shear rate increased. When motion reached the outer housing wall a flow transition occurred, likely triggered by flow interaction with the housing baffles. The subsequent post-transition regime was characterized by radial and axial flow that effectively mixed the suspension on both the macroscale and fibre-scale. The flow transition appeared to be what earlier workers reported as the onset of "fluidization". During tangential-cavity flow, phase segregation occurred. Gas present in the suspension collected around the rotor and reduced momentum transfer from the rotor to the suspension. This caused the torque for the pulp suspension to fall below that for water at the same rotational speed, and the cessation of flow development in the chamber. If sufficient momentum transfer was attained to initiate post-transition flow, the chamber contents became effectively mixed. The torque could still fall below that of water depending on the effective density of the suspension in the rotor vicinity.
Applied Science, Faculty of
Chemical and Biological Engineering, Department of
Graduate

This thesis investigates some problems related to graph colouring, or. more precisely. graph re-colouring. Informally, the basic question addressed can be phrased as follows. Suppose one is given a graph G whose vertices can be properly k-coloured. for some k > 2. Is it possible to transform any k-colouring of G into any other by recolouring vertices of G one at a time, making sure a proper k-colouring of G is always maintained? If the answer is in the affirmative, G is said to be k-mixing. The related problem of deciding whether, given two k-colourings of G7 it is possible to transform one into the other by recolouring vertices one at a time, always maintaining a proper k-colouring of G, is also considered. These questions can be considered as having a hearing on certain mathematical and "real-world" problems. In particular, being able to recolour any colouring of a given graph to any other colouring is a necessary pre-requisite for the method of sampling colourings known as Glauber dynamics. The results presented in this thesis may also find application in the context of frequency reassignment: given that the problem of assigning radio frequencies in a wireless communications network is often modelled as a graph colouring problem. the task of re-assigning frequencies in such a network can be thought of as a graph recolouring problem. Throughout the thesis. the emphasis is 011 the algorithmic aspects and the computational complexity of the questions described above. In other words, how easily. in terms of computational resources used, can they be answered? Strong results are obtained for the k = 3 case of the first question, where a characterisation theorem for 3-mixing graphs is given. For the second question. a dichotomy theorem for the complexity of the problem is proved: the problem is solvable in polynomial time for k < 3 and PSPACE-complete for k > 4. In addition, the possible length of a shortest sequence of recolourings between two colourings is investigated, and an interesting connection between the tractability of the problem and its underlying structure is established. Some variants of the above problems are also explored.

Increases in reactive nitrogen from human actions have led to negative impacts on surface water (SW) and groundwater (GW) quality, and it is important to better understand denitrification processes in aquatic systems. The hyporheic zone has unique biogeochemical conditions, and is known to attenuate contaminants originating from SW and traveling through the hyporheic zone, together with necessary reactants. However, the ability of the hyporheic zone to attenuate contaminants from deeper upwelling GW plumes as they exit to SW is less understood. I used MODFLOW and SEAM3D to simulate hyporheic flow cells induced by riverbed dunes and upwelling GW together with mixing dependent denitrification of an upwelling nitrate (NO3-) plume. My basecase model scenario entailed dissolved organic carbon (DOC) and dissolved oxygen (DO) advecting from SW and DO and NO3- advecting from GW, which is typical of water in agricultural land uses. I conducted a sensitivity analysis to determine controls on mixing dependent denitrification. Mixing dependent denitrification increased with increasing hydraulic conductivity, decreasing lower bottom flux, as well as increasing DOC in SW and NO3- in GW. Non-mixing dependent denitrification also occurred when there was SW NO3-, and I found its magnitude was much greater than mixing dependent denitrification. Nevertheless, potential for hyporheic zones to attenuate upwelling NO3- plumes seems to be substantial, though highly variable depending on biogeochemical reaction rates as well as geomorphic, hydraulic and biogeochemical conditions. Stream and river restoration efforts may be able to increase both mixing and non-mixing dependent reactions by increasing hyporheic zone residence times.
Master of Science

We consider a problem from the field of biological fluid mechanics which considers the flow associated with the motion of a flagellum on a sessile micro-organism. Motivation is taken from the movement of fluid around a species of choanoflagellate, \(Salpingoeca\) \(Amphoridium\). Choanoflagellates are a class of organism in the phylum Protozoa. Because the length scales and velocities are very low, the flow is one dominated by viscous forces and the environment is characterised by a low Reynolds number. The flow caused by the flagellum is initially modelled via a point force. These microorganisms operate in more than one location and the motion they create is modelled in a qualitative sense by using two stokeslets (appropriate to Stokes' flow) whose orientation and position is varied with time. The sessile micro-organism resides above a boundary which is modelled, most generally, as an interface between two fluids possessing different properties. Efficiency of feeding currents generated by the flagellum motion is studied. The resulting dynamics are investigated using chaotic measures, which examine the stretching and consequent mixing of elements within the fluid. Different point force locations lead to various eddy structures such that their superposition results in chaotic advection. The model is developed to examine the flow of particles around a three-dimensional realisation of a micro-organism which involves a flagellum and a cell body attached to a substrate. Green's functions are used to satisfy a number of boundary conditions simultaneously. Particle paths of a tracer introduced into the fully three-dimensional model are investigated. Comparisons with experimental data illustrate good agreement between theoretical and experimental results. Further extensions to the model are suggested.

This work investigates the laminar mixing performance of viscoelastic fluids in laboratory-scale batch stirred tanks agitated by “butterfly” impellers and in-line Kenics KM static mixers. Constant-viscosity viscoelastic (Boger) fluids were formulated to investigate viscous and elastic effects separately; multiphase viscoelastic suspensions were formulated from 40-50 volume% glass spheres in glycerol. Particle Image Velocimetry in stirred tanks agitated by high impeller-to-tank diameter ratio butterfly impellers (D/T=0.98) showed that secondary flows in Boger fluid increased solid body rotation and reduced local shear rates (≤16 s-1) compared to equivalent viscosity Newtonian fluids, though the effect was non-monotonic. Mixing times obtained from Planar Laser Induced Fluorescence (PLIF) increased by ≤23%. Positron Emission Particle Tracking in multiphase suspensions showed increased axial mixing due to more dominant secondary flows. In static mixers, Boger fluid striation patterns at the mixer outlet obtained from PLIF showed time dependence and flow instability due to reduced local shear rates. Energy consumption in all geometries displayed an increase of ≤200% with viscoelastic fluids. Using a generalised Reynolds number Reg enabled viscoelastic power draw prediction, previously only possible through empirical relationships. Overall, viscoelasticity generally increases energy consumption whilst reducing blending performance though the link between elasticity and mixing quality is highly non-linear.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 163-175).
Mesoscale eddies mix and transport tracers such as heat and potential vorticity laterally in the ocean. While this transport plays an important role in the climate system, especially in the Southern Ocean, we lack a, comprehensive understanding of what sets mixing rates. This thesis seeks to advance this understanding through three related studies. First, mixing rates are diagnosed from an eddy-resolving state estimate of the Southern Ocean, revealing a meridional cross-section of effective diffusivity shaped by the interplay between eddy propagation and mean flow. Effective diffusivity diagnostics are then applied to quantify surface mixing rates globally, using a, kinematic model with velocities derived from satellite observations; the diagnosed mixing rates show a rich spatial structure, with especially strong mixing in the tropics and western-boundary-current regions. Finally, an idealized numerical model of the Southern Ocean is analyzed, focusing on the response to changes in win( stress. The sensitivity of the meridional overturning circulation to the wind changes demonstrates the importance of properly capturing eddy mixing rates for large-scale climate problems.
by Ryan Abernathey.
Ph.D.

We find a set of conditions on a roof function to ensure topological mixing for suspension flows over a topological mixing base. In the measure theoretic case, such conditions have already been established for certain flows. Specifically, certain suspensions are topologically mixing if and only if the roof function is not cohomologous to a constant. We show that an analogous statement holds to establish topological mixing with the presence of dense periodic points. Much of the work required is to find properties specific to the equivalence class of functions cohomologous to a constant. In addition to these conditions, we show that the set of roof functions that induce a topologically mixing suspension is open and dense in the space of continuous roof functions.

Over the previous summer I studied mixing of a passive tracer by flow in a straight cylindrical pipe, under the supervision of prof. Bernoff. The mixing process can be thought of as the successive action of advection by the fluid flow and diffusion modeled by random walks. With this method we were able to distinguish three different regimes. For short times, diffusion is more relevant than advection and we observed a Gaussian longitudinal distribution of the concentration. In an intermediate regime, advection by the shear is dominant over longitudinal diffusion and we observed a distinctively asymmetric distribution which spread much faster than would be expected by the action of diffusion alone. Finally when the tracer had completely mixed across the pipe’s cross- section, we recovered the classical Taylor regime with a longitudinal Gaussian distribution. In each regime we have analytical prediction of tracer distribution, confirmed by numerical calculation. The object of this thesis is to extend our results to curved pipes; we will start by considering curved planar pipes and helical pipes. We will try to determine if mixing in these geometries displays the same three distinctive regimes of mixing. The pipe’s curvature introduces a secondary flow in the form of a transverse recirculation with a dipolar form, discovered by Dean (1928). We believe this transverse flow should enhance mixing, which explains why curved pipes are used in cooling systems and other situations where heat exchange is relevant. Our object is to first understand existing analytical approximations to the flow in a curved pipe due to Dean and others and then to study analytically and numerically the spread of a passive scalar in these flows.

For more than half a century turbulent mixing layers have been the subject of intense experimental and numerical investigation. With the discovery of primary, spanwise aligned and secondary, streamwise oriented vortices the interest in low and high Reynolds number mixing layers has been invigorated. The immense increase of computational capabilities in recent years has lead to an ever growing number of numerical simulations of mixing layers. However, numerical simulations have had great difficulties in reproductions the structure dynamics and entrainment mechanisms observed in the experiments. In this study Large Eddy Simulations of the low and high Reynolds number spatially developing, three-dimensional mixing layer are performed. At the heart of the presented studies lies the focus on the inlet conditions of the simulations. The effects of spatial and temporal correlation of the inlet conditions are studied for the low and high Reynolds number planemixing layer. It is shown that physically correlated inlet fluctuations lead to the development of the spatially stationary, streamwise oriented vortices observed in experiments. The effects of the presence of the streamwise vortices on the momentumand passive scalar fields are investigated in detail. In the latter parts of this work, the effects of varying the inlet fluctuation levels are reported. By altering the inlet fluctuation magnitudes the number and strength of the spatially stationary streamwise vortices can be controlled. The implications of this on the dynamics of the primary, spanwise aligned vortices are discussed. A change in the number and strength of the spatially stationary streamwise vortices is shown to be critical for the shape of the obtained probability density functions. If spatially stationary streamwise vortices are present, the obtained probability density functions are of the non-marching type. A lack of spatially stationary streamwise vortices produces marching probability density functions.

In this research study, non-linear spectral mixing models have been developed and employed to achieve unmixing the proportions of components accurately and retrieving the physical parameters of the mixture. The first focus is on a comparative study of linear and non-linear spectral mixing models. A carefully-controlled experiment was conducted in the laboratory. The aim is to test both models to unmix ternary powdered-chalk mixtures by using the directional reflectance data. The results demonstrated the superiority of the non-linear model over the linear model. However, there was at least one case when the linear model produced more accurate results than the non-linear model. As a consequence, a hypothesis was made that the directional reflectance data obtained from certain measurement geometries may not contain useful information for deriving surface parameters. In order to investigate this, an error analysis was employed to observe the sensitivity to error of a physical parameter, which is needed in the non-linear unmixing, when estimated from directional reflectance data at certain measurement geometries. This theoretical investigation was tested against reflectance data of mineral mixtures obtained from a laboratory experiment. The results showed that the unmixing could be improved when the angular measurements were carefully chosen. Information contained in each surface measurement can be useful or damaging depending on the measurement geometry and the brightness of the surface itself. The next focus is on the utilisation of non-linear spectral mixing model to retrieve the biophysical properties of vegetation canopies by means of a canopy reflectance modelling. A two-layer model of the bidirectional reflectance of homogeneous vegetation canopies was proposed in this study. The anisotropic scatterings of both the vegetation canopy and the background were taken into account. This new model was validated against simulated and field-measurement data. The results showed that this model can be used to model the bidirectional reflectance and to retrieve the optical properties of canopy elements (leaves) and background of a homogeneous canopy. Finally, a simple non-linear spectral mixing model was developed. The second order interaction between vegetation and soil was taken into account. Results from the experiments showed that the vegetation cover and leaf area index of moderate density canopies can be retrieved by using this model.

An investigation has been made based on the measurements of the concentration profiles found from dynamic experiments to study axial and transverse mixing on sieve trays operating under froth, mixed and spray regimes. Two methods of tracer injection were employed, the line and point source tracer injection, and the experiments were carried out over a wide range of gas and liquid flow rates. Air and water were used as system fluids. Two different configurations of columns were used in the dispersion work in order to study the effect of the experimental configuration upon dispersion characteristics. The experimental results were analysed as appropriate for each configuration, the first by a one-dimensional axial plug flow model and the second by a two-dimensional axial and transverse plug flow model. An automatic method of optimization was employed to estimate the values of the longitudinal and transverse dispersion coefficients, and interstitial liquid velocities for each experiment. The variation in the liquid velocities were found to be quite considerable in the mixing studies. In the determination of the clear liquid height a new method was used to calculate the height of clear liquid in terms of the first moment of the dynamic response curve. The data were compared with those measured from manometric method.

Approved for public release, distribution unlimited
This thesis uses bivariate and multivariate analysis to estimate the factors that influence the effectiveness of U. S. Navy Medical Service Corps (MSC), Health Care Administrator (HCA) Inservice Procurement (IPP) and Direct Procurement (DP) Officer accession programs. Using data from the Navy Officer Master File, Navy Officer Loss File, and Navy Personnel Research and Development Center's Officer Fitness Report File, comparisons of the officers accessed though the DP and IPP are presented. Ordinary least square models estimate the influence of procurement source, education, and personnel demographics on separation behavior and fitness report performance. Proportional hazard models estimate the years of commissioned service MSC HCA officers are expected to serve before retiring or being voluntarily released from active duty. Logit models evaluate the probability of being promoted and the probability of having above average fitness report performance values as a function of procurement source, education level college quality, and personal demographics. The findings reveal that MSC HCAs with ten or more years of commissioned service tend to leave within a few years of becoming eligible to retire. Differences in educational levels and early fitness report performance between officers accessed through IPP and DP were noted. Based upon research results, it is recommended that a benefit-cost analysis be done to determine the optimal MSC HCA accession policy.

A general model of music mixing is developed, which enables a mix to be evaluated as a set of acoustic signals. A second model describes the mixing process as an optimisation problem, in which the errors are evaluated by comparing sound features of a mix with those of a reference mix, and the parameters are the controls on the mixing console. Initial focus is placed on live mixing, where the practical issues of: live acoustic sources, multiple listeners, and acoustic feedback, increase the technical burden on the mixing engineer. Using the two models, a system is demonstrated that takes as input reference mixes, and automatically sets the controls on the mixing console to recreate their objective, acoustic sound features for all listeners, taking into account the practical issues outlined above. This reduces the complexity of mixing live music to that of recorded music, and unifies future mixing research. Sound features evaluated from audio signals are shown to be unsuitable for describing a mix, because they do not incorporate the effects of listening conditions, or masking interactions between sounds. Psychophysical test methods are employed to develop a new perceptual sound feature, termed the loudness balance, which is the first loudness feature to be validated for musical sounds. A novel, perceptual mixing system is designed, which allows users to directly control the loudness balance of the sounds they are mixing, for both live and recorded music, and which can be extended to incorporate other perceptual features. The perceptual mixer is also employed as an analytical tool, to allow direct measurement of mixing best practice, to provide fully-automatic mixing functionality, and is shown to be an improvement over current heuristic models. Based on the conclusions of the work, a framework for future automatic mixing is provided, centred on perceptual sound features that are validated using psychophysical methods.

Mesophilic anaerobic digestion is one of the most used and successful technologies to treat the sludges resulting from wastewater treatment. However, traditional approaches to digester design are firmly rooted in empiricism and rule of thumb rather than science. Mixing is an energy-intensive operation, and therefore the need to lower the wastewater process carbon footprint requires searching how to lower the input mixing energy without compromising–and indeed enhancing–biogas production. In particular, the literature on gas mixing is still particularly poor. For the first time, an Euler-Lagrangian CFD model was developed for gas mixing in anaerobic digestion. The model was validated against laboratory experiments with PIV and PEPT techniques. Full-scale simulations reproducing a real digester were performed with the validated model, and different scenarios were reproduced. Shear rate distribution was used as a parameter to assess the most appropriate value of input mixing power. The simulations also low-viscosity flow patterns for the first time. This phenomenon is intrinsically linked to the non-Newtonian nature of sludge, and leads to short-circuited mixing. Switching biogas injection between two different nozzle series was found to be an effective strategy to mitigate the issue of the low-viscosity flow patterns. Final recommendations on input mixing power and switching time were given to improve mixing efficiency in the full-scale design taken into consideration. A journal paper published in Water Research and a conference paper presented at the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing (Civil-Comp) were produced. Two other papers are currently in preparation.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1998.
Includes bibliographical references (p. 124-134).
by Adam Harrison Sobel.
Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.
Includes bibliographical references (leaf 64).
This thesis describes the processes of viscous dissipation in two generic situations for mixing flows. The objective is to illustrate, with simple examples, details of the entropy generation processes that are captured in an overall manner by a control volume analysis. The two situations are parallel mixing flows in a duct and the evolution of a wake in a centrifugal compressor. Results are given for the evolution of the velocity profile and for the dissipation function and stagnation pressure fields.
by François T. Le Floch-Yin.
S.M.

The work contained within this thesis is concerned with a theoretical investigatiop of both laminar and thermally driven types of cavity flow, together with an analysis of their associated mixing processes which find applications to Industrial mixing and also to the environment. The mixing efficiency has been viewed from two perspectives namely the tracking of a selection of fluid particles, and also the simulation of the dispersive mixing of a coloured fluid element as carried along by the flow. This thesis also incorporates features of both Newtonian and a wide range of non-Newtonian fluids.

Thesis (Ph.D.) - University of Glasgow, 2007.
Ph.D. thesis submitted to the Faculty of Physical Sciences, Department of Geographical and Earth Sciences, University of Glasgow, 2007. Includes bibliographical references. Print version also available.

It is generally accepted that a linear stability theory, together with a slowly diverging base flow, can describe many of the characteristics of coherent structures in free shears flow. In this dissertation we model these two-dimensional instability waves as they travel in a slightly inhomogeneous steady and viscous unstable base flow. These unstable and inviscid wave packets are analysed using linear stability theory. The analysis is performed by separating the physical flow in two parts. In the first part, the instability waves are evolving in a parallel mixing layer and their solution serves of initial conditions for the second part of the flow. The parallel flow analysis leads to the receptivity of the flow to both pulse-type and periodic excitations. This part of the study is done by solving the initial-value problem completely and studying its long-time behaviour, which is a wave packet. We then repeat the same analysis with some modifications and arrive at the receptivity of the flow for sinusoidal excitations. We find that a shear layer is very receptive to high-frequency disturbances that are generated near the center line of the layer. The second part of the solution is concerned with the evolution of the wave packets on longer space-time scales which are associated with non-parallel effects arising from the spreading of the mixing layer. The solution in this part of the physical flow is handled by extending Whitham's kinematic wave theory, and the ray equations for instability waves are derived for physical and propagation spaces using a WKB J expansion. Our high-frequency ansatz also leads us to the derivation of a very simple complex amplitude equation. While the rays obtained represent characteristics in the complex plane along which the complex frequency of our disturbances is conserved (steady base flow), the amplitude equation expresses the conservation of the volume integrals of a complex wave action density subject to a certain flux and a source term. The amplitude equation was rendered easily tractable due to a transformation of our dependent variables and their practical projections on the cross and propagation spaces. Different methods, (steepest descent, ray-tracing, and fully numerical solution) are used to solve the ray equations, and comparisons are made among them. The results presented are obtained for the piecewise linear profile of Rayleigh and the general tanh profile. The very good agreement among all the methods of solution reveals the validity of the method of characteristics in the complex plane, (ie complex rays). Finally we perform some calculations for spatially varying shear layers and and study their implications in the development of spatial instability modes. We discover that when starting with a convectively unstable base velocity profile it is possilble to interrupt the development of spatial instability modes by allowing the base velocity profile to vary slowly and become absolutely unstable. However the reverse is not true. That is to say that in a base flow that is initially absolutely unstable, one does not observe spatial modes, even after the base flow is permitted to assume slowly a convectively unstable profile.

Suspension polymerisation is one of the major processes used to produce polymers. In this process, monomer is suspended as liquid droplets in a continuous water phase by mean of strong agitation and the presence of a suspending agent. As the suspension polymerisation proceeds, the viscosity of a monomer–polymer droplet increases with conversion. Hence, the physical behaviour of the droplet changes during the process. When new dispersible material is added to the existing suspension drops, the new material and existing drops can remain segregated for significant amounts of time. This will affect the properties of polymer products. The aim of this project was to study the behaviour of drop mixing when new material is added to the existing suspension polymerisation. This study concentrated on the effect of the dispersed phase viscosity on the drop mixing, but agitation intensity and surface stabilities were also important.

Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 34).
Torrefaction is a process by which low energy density biomass is converted to a higher energy density biofuel, called char. Small-scale torrefaction systems are a promising technology for developing countries where large amounts of biomass go underutilized due to inaccessibility and transportation costs. A by-product of torrefaction is volatile gas, thus, a system may be built to harness this otherwise wasted energy and use it to power the treatment of biomass. An efficient fuel-mixer and combustor system which recycles this volatile gas is central to the overall torrefaction system efficiency. In order to analyze the mixing efficiency in a swirl-type mixer such as the design proposed for the small-scale torrefaction system, a project was designed to visualize mixing in an annular mixer. A to-scale cold-mixing system was constructed from two cylinders, three pump systems, as well as an imaging system using a retrofitted green laser. The final model is a tested and proven system for flow imaging of two cold flows within a to-scale fuel-mixer.
by Kathryn K. Wopat.
S.B.

Rapid mixing is crucial for the efficient and environment-friendly operation of many industrial and propulsion devices involving jet flows. In this dissertation, two methodologies, self-excited nozzles and radially lobed nozzles, are studied and presented in order to enhance mixing in the near field of coflowing, subsonic, turbulent, free jet flows. The characteristics of the concentration field and the mixing performance are examined, mainly in quantitative manner. Two new parameters, mixing index and mixing efficiency index, are defined for free jets, allowing quantitative analysis of the mixing performance and efficiency. The flow fields are studied with hot wire anemometry, and with CFD simulation for some of the radially lobed nozzles. Due to the large vectoring angle of the jet flows from these nozzles, a new definition for the entrainment ratio is also adopted in order to take the large radial velocity component into consideration. Self-excited nozzles, rectangular and square shaped, are examined at Reynolds numbers of 17,000 and 31,000. The self-excited square jet has fastest mixing and highest mixing efficiency, with 400% higher mixing index at 4 diameters downstream than the unexcited square jet. The mixing is improved as the excitation frequency or coflow velocity increases. The study of flow field shows the presence of one pair of periodic, coherent array of large-scale, streamwise, counter-rotating inviscid vortices shedding from each of the two flaps which dominate the mean flow and the mixing process. The coflow is primarily entrained into the jet in the minor plane while the jet fluid vectors in the major plane. Significant increase in turbulent kinetic energy immediately downstream the nozzle exit improves small-scale mixing. Radially lobed nozzles, a cross-shaped and a clover-shaped with four lobes each, are analyzed in comparison to a conical nozzle. In addition, a few modified radially lobe nozzles, including a 6-lobe nozzle and an 8-lobe nozzle, two type of fully penetrating nozzles, and a cross-shaped nozzle with centerbody, are examined in order to achieve better mixing than the cross-shaped nozzle. At 4 diameters downstream, the mixing index of the cross-shaped nozzle is 650% higher than that of the conical nozzle. The cross-shaped nozzle with centerbody, the 6- lobe and 8-lobe nozzles have slower mixing and lower efficiency than the cross-shaped nozzle,but the fully-penetrating nozzles are generally better than the cross-shaped nozzle, especially at low coflow velocities and in the far field. The flow field study shows that parallel lobe walls and deep penetration of the coflow are importance factors responsible for the observed mixing enhancement.
Ph. D.