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Computational fluid dynamics (CFD) is a widely used tool for investigating fluid flows in bioreactors. It has been used in the biopharmaceutical industry for years and has established itself as an important tool for process engineering characterisation. As a result, CFD simulations are increasingly being used to complement classical process engineering investigations in the laboratory with spatially and temporally resolved results, or even replace them when laboratory investigations are not possible. Parameters that can be determined include the specific power input, Kolmogorov length, hydrodynamic stress, mixing time, oxygen transfer rate, and for cultivations with microcarriers, the NS1 criterion. In the first part of this series, a literature review illustrates how these parameters can be determined using CFD and how they can be validated experimentally. In addition, an overview of the hardware and software typically used for bioreactor characterisation will also be provided, including process engineering parameter investigations from the literature. In the second part of this series, the authors’ research results will be used to show how the process engineering characterisation of mechanically driven bioreactors for the biopharmaceutical industry (stirred, orbitally shaken, and wave-mixed) can be determined and validated using CFD.

A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow, circulation flow rate, and mixing time during Ruhrstahl-Heraeus (RH) refining process. Also, a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up, and measurements were carried out to validate the mathematical model. The results show that, with a conventional gas blowing nozzle and the total gas flow rate of 40 L center dot min(-1), the mixing time predicted by the mathematical model agrees well with the measured values. The deviations between the model predictions and the measured values are in the range of about 1.3%-7.3% at the selected three monitoring locations, where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value. In addition, the circulation flow rate was 9 kg center dot s(-1). When the gas blowing nozzle was horizontally rotated by either 30 degrees or 45 degrees, the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle, due to the rotational flow formed in the up-snorkel. Furthermore, the mixing time at the monitoring point 1, 2, and 3 was shortened by around 21.3%, 28.2%, and 12.3%, respectively. With the nozzle angle of 30 degrees and 45 degrees, the averaged residence time of 128 bubbles in liquid was increased by around 33.3%., QC 20230301

folklore conjecture states that the Glauber dynamics on the set of k-colourings of a maximum degree D graph mixes rapidly as long as k>=D+2, namely in O(n log(n)) steps. This yields efficient almost uniform samplings and give FPRAS for counting the number of k-colourings of a graph. At criticality k=D+1, the chain isn't always ergodic due to the existence of frozen colourings. While this is a natural barrier for mixing, in this thesis we will explore other obstructions of local nature that might slow down mixing.

Dry powder inhaler (DPI) formulation is a major area of interest since they are employed by the healthcare system to treat relevant chronic diseases like asthma. Previous research has established that the manufacturing process and formulation composition are key for the active pharmaceutical ingredient to reach the lungs and achieve therapeutic effects. The aim of this study was to research the effect of lactose fines and magnesium stearate as well as mixing processes on the performance of adhesive mixtures for inhalation. The following research work was conducted by employing two mixers: Low shear (Turbula®) and high shear (Diosna®) for the manufacturing of the formulations. Three formulations were prepared varying the amount of excipients and mixing time, 27 batches were produced and filled into Novolizer® devices. Micronized budesonide was used as the active pharmaceutical ingredient. Quality control parameters like poured bulk density, drug content assay, and mixing homogeneity were executed. Formulation performance was analyzed by doing particle-size distribution analyses done mostly in an Andersen Cascade Impactor, although Next Generation Impactor was also used. Fine Particle Fraction (FPF) and Fine Particle Dose (FPD) were the central parameters to judge formulation performance. It was found that both lactose fines and magnesium stearate can improve formulation performance. In addition, high shear mixer formulations presented higher FPF values than low shear formulations. These findings suggest that lactose fines and magnesium stearate are key ingredients for an improved formulation performance and that high shear mixing is preferred to enhance FPF for DPIs., Dry powder inhaler (DPI) preparation is a key area of interest since they are used by the healthcare system to treat relevant persistent diseases like asthma. Earlier research has shown that the making process and composition of DPI are key for the medicinal ingredient to reach the lungs and have medicinal effects for dry powder inhalers. The objective of this study was to research the effect of the non-medicinal components in the DPI medicine and mixing processes on the ability of the composition to be used in dry powder inhalers and have medicinal value. The following research work was conducted by using two mixers: Low mixing force (Turbula®) and high mixing force (Diosna®) for the fabrication of the preparations. Three preparations were prepared varying the amount non-medicinal components and mixing time, 27 batches were produced. Small microparticles of budesonide were used as the medicinal ingredient. Quality control considerations like poured powder density, medicine content evaluation, and mixing consistency were done. Preparation performance was analyzed by using equipment that can filter the particles by their size and it is used to predict the preparation ability to reach the lungs. The chosen device was Novolizer®, 27 devices were filled with each preparation. They were connected to this equipment and the powder quantity in each filter was analyzed. It was found that adding small particles of lactose and a non-pharmaceutical ingredient that helps the preparation to have less agglomeration can improve the preparation performance. Also, the high mixing force mixer helped the preparations that were made in this mixer to have more probabilities to reach the lungs, than the ones prepared by the low mixing force mixer. In conclusion, these findings suggest adding small particles of lactose and other nonactive ingredients help the formulation to have less agglomeration thus improving performance. In addition, a high mixing force mixer is necessary to boost prep

We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded ( 2 + ¿ ) -moments on the in-degrees and of bounded out-degrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum in-degree. Under the further assumption that the order statistics of the in-degrees have a power-law behavior, we show that the extremal values of the stationary distribution also have a power-law behavior with the same index. In the same setting, we prove that these results extend to the PageRank scores of the random digraph, thus confirming a version of the so-called power-law hypothesis. Along the way we establish several facts about the model, including the mixing time cutoff and the characterization of the typical values of the stationary distribution, which were previously obtained under the assumption of bounded in-degrees., The third author was supported by the Spanish Agencia Estatal de Investigación under projects MTM2017-82166-P and PID2020-113082GB-I00 and by the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M)., Postprint (author's final draft)

Robin Kaiser, Masterarbeit University of Innsbruck 2022

We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying acondition that involves only triplets of cards, based on earlier work by Morris involving pairs of cards. Then we use it to obtain a bound on the mixing time of the lazy version of a shuffle introduced by Diaconis. The Diaconis shuffle is a variation on the 15-puzzle. There are n2 tiles arranged in an n × n torus. Each step, a random tile and direction (North, South, East, West) are selected, and the chosen tile’s row or column is cycled in the chosen direction. Diaconis conjectured that the mixing time is O(n3 log n). We prove a mixing time bound of O(n3 log3 n).

Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for mixing human players onto teams. We quantify numerically the effectiveness of this mixing scheme over the seven or eight steps performed in practice. We give a combinatorial proof of the nontrivial fact that the chain is indeed irreducible.

Mixing plays a key role in mass and heat transfer, as well as chemical reactions in various vessels involving agitation. Several studies have confirmed that the mixing time obtained from several monitor locations cannot reflect the mixing time for the whole bath because stirring situation in different locations is variable due to the change of operation schemes. It is proved that some zones with inefficient stirring cannot be monitored by applying a limited amount of probes in physical and mathematical models. This study provides a novel approach to quantify mixing time evaluation considering the tracer variation for the whole bath using a mathematical model. It was found that the mixing time obtained by considering the whole bath is more representative than that of the probe monitor method. Compared with the traditional probe method, about 50 to 70 pct longer mixing times were obtained for different operations by applying the volume track method. In addition, the volume integral of the concerned variable for the whole bath is more representative to determine the developed flow compared to the points monitoring method for a transient simulation., QC 20230613

Robin Kaiser, Masterarbeit University of Innsbruck 2022

Optimizing bioprocesses requires an in-depth understanding, from a bioengineering perspective, of the cultivation systems used. A bioengineering characterization is typically performed via experimental or numerical methods, which are particularly well-established for stirred bioreactors. For unstirred, non-rigid systems such as wave-mixed bioreactors, numerical methods prove to be problematic, as often only simplified geometries and motions can be assumed. In this work, a general approach for the numerical characterization of non-stirred cultivation systems is demonstrated using the CELL-tainer bioreactor with two degree of freedom motion as an example. In a first step, the motion is recorded via motion capturing, and a 3D model of the culture bag geometry is generated via 3D-scanning. Subsequently, the bioreactor is characterized with respect to mixing time, and oxygen transfer rate, as well as specific power input and temporal Kolmogorov length scale distribution. The results demonstrate that the CELL-tainer with two degrees of freedom outperforms classic wave-mixed bioreactors in terms of oxygen transport. In addition, it was shown that in the cell culture version of the CELL-tainer, the critical Kolmogorov length is not surpassed in any simulation.

In this paper, which is a culmination of our previous research efforts, we provide a general framework for studying mixing profiles of non-backtracking random walks on dynamic random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph tends to infinity. Subject to mild general conditions, we link two mixing times: one for a static version of the random graph, the other for a class of dynamic versions of the random graph in which the edges are randomly rewired but the degrees are preserved. With the help of coupling arguments we show that the link is provided by the probability that the random walk has not yet stepped along a previously rewired edge. To demonstrate the utility of our framework, we rederive our earlier results on mixing profiles for global edge rewiring under weaker assumptions, and extend these results to an entire class of rewiring dynamics parametrised by the range of the rewiring relative to the position of the random walk. Along the way we establish that all the graph dynamics in this class exhibit the trichotomy we found earlier, namely, no cut-off, one-sided cut-off or two-sided cut-off. For interpolations between global edge rewiring, the only Markovian graph dynamics considered here, and local edge rewiring (i.e., only those edges that are incident to the random walk can be rewired), we show that the trichotomy splits further into a hexachotomy, namely, three different mixing profiles with no cut-off, two with one-sided cutoff, and one with two-sided cut-off. Proofs are built on a new and flexible coupling scheme, in combination with sharp estimates on the degrees encountered by the random walk in the static and the dynamic version of the random graph. Some of these estimates require sharp control on possible short-cuts in the graph between the edges that are traversed by the random walk.

[EN] Drinking water storage tanks allow to store water in the supply systems and help managing water demand variations. However, the tanks’ configuration and operation modes can also affect the quality of the supplied water. This paper presents a characterization of water storage tanks in Portugal, focusing on the physical and operational characteristics that affect their performance regarding mixing and water renewal. For the first time, water mixing in Portuguese storage tanks was assessed by determining the volume of renewal fractions needed to ensure the mixing of water entering each filling cycle with the existing one. The results show that mixing is guaranteed in about 74% of the circular cells and that the level variation required for this in a filling cycle is, on average, of 51%., [PT] Os reservatórios de água para consumo humano permitem garantir reservas de água nos sistemas de abastecimento e gerir variações do consumo. Contudo, a sua configuração e os modos de operação podem ter implicações na qualidade da água distribuída. Este trabalho apresenta uma caracterização dos reservatórios de água em Portugal, incidindo nas características físicas e operacionais que condicionam o seu desempenho do ponto de vista da mistura e renovação da água. Foi pela primeira vez avaliada a mistura da água nos reservatórios portugueses, pela determinação das frações de volumes de renovação necessárias para garantir a mistura da água que entra em cada ciclo de enchimento com a já existente. Os resultados mostram que a mistura é garantida em cerca de 74% das células circulares e que a variação de nível necessária para tal num ciclo de enchimento é, em média, de 51%.

[ES] Cuando se mezclan fluidos pseudoplásticos no newtonianos en un tanque agitado, se pueden formar compartimentos o pseudocavernas alrededor del impulsor. En él, un volumen de forma toroidal de movimiento de fluido rápido aparece cerca del impulsor, con el resto del recipiente casi estancado, lo que impide una mezcla eficiente. En este trabajo, se estudia la formación de compartimentos en un grupo de soluciones poliméricas pseudoplásticas de reologías muy distintivas en tres tanques agitados de diferentes escalas y geométricamente similares mediante el uso de una turbina Rushton. Los tamaños de los compartimentos formados se evalúan mediante un método validado en el que se inyecta una solución coloreada del fluido examinado cerca del impulsor para luego ser fotografiada para su posterior procesamiento. Se estiman las características del fluido y las condiciones del proceso que propician la formación del compartimento y se encuentra una correlación basada en la cuantificación de la viscosidad del fluido y la escala mediante análisis dimensional. También se intenta correlacionar el desarrollo del compartimento con un nuevo conjunto de parámetros obtenidos del análisis dimensional. Sin embargo, el desarrollo del compartimento se describe mejor mediante el uso del número de elasticidad con una constante de proporcionalidad que se encuentra diferente para cada fluido en cada escala. También se propone una ecuación que cuantifique esta constante de proporcionalidad., [EN] When non-Newtonian pseudoplastic fluids are mixed in a stirred tank compartments or pseudocaverns can be formed around the impeller. In it, a toroidally shaped volume of fast fluid motion appears near the impeller, having the rest of the vessel nearly stagnant, preventing efficient mixing. In this work, compartment formation is studied in a group of pseudoplastic polymeric solutions of very distinctive rheologies in three different scaled and geometrically similar stirred tanks by using a Rushton turbine. The formed compartment sizes are evaluated by a validated method in which a coloured solution of the examined fluid is injected near the impeller to then be photographed for its later processing. The fluid characteristics and process conditions that propitiate compartment formation are estimated and a correlation based on the quantification of the fluid viscosity and the scale is found by using dimensional analysis. Compartment development is also tried to be correlated with a new set of parameters obtained from dimensional analysis. Compartment development is however best described by usage of the elasticity number with a proportionality constant that is found to be different for each fluid in each scale. An equation that quantifies this proportionality constant is also proposed.

[ES] Cuando se mezclan fluidos pseudoplásticos no newtonianos en un tanque agitado, se pueden formar compartimentos o pseudocavernas alrededor del impulsor. En él, un volumen de forma toroidal de movimiento de fluido rápido aparece cerca del impulsor, con el resto del recipiente casi estancado, lo que impide una mezcla eficiente. En este trabajo, se estudia la formación de compartimentos en un grupo de soluciones poliméricas pseudoplásticas de reologías muy distintivas en tres tanques agitados de diferentes escalas y geométricamente similares mediante el uso de una turbina Rushton. Los tamaños de los compartimentos formados se evalúan mediante un método validado en el que se inyecta una solución coloreada del fluido examinado cerca del impulsor para luego ser fotografiada para su posterior procesamiento. Se estiman las características del fluido y las condiciones del proceso que propician la formación del compartimento y se encuentra una correlación basada en la cuantificación de la viscosidad del fluido y la escala mediante análisis dimensional. También se intenta correlacionar el desarrollo del compartimento con un nuevo conjunto de parámetros obtenidos del análisis dimensional. Sin embargo, el desarrollo del compartimento se describe mejor mediante el uso del número de elasticidad con una constante de proporcionalidad que se encuentra diferente para cada fluido en cada escala. También se propone una ecuación que cuantifique esta constante de proporcionalidad., [EN] When non-Newtonian pseudoplastic fluids are mixed in a stirred tank compartments or pseudocaverns can be formed around the impeller. In it, a toroidally shaped volume of fast fluid motion appears near the impeller, having the rest of the vessel nearly stagnant, preventing efficient mixing. In this work, compartment formation is studied in a group of pseudoplastic polymeric solutions of very distinctive rheologies in three different scaled and geometrically similar stirred tanks by using a Rushton turbine. The formed compartment sizes are evaluated by a validated method in which a coloured solution of the examined fluid is injected near the impeller to then be photographed for its later processing. The fluid characteristics and process conditions that propitiate compartment formation are estimated and a correlation based on the quantification of the fluid viscosity and the scale is found by using dimensional analysis. Compartment development is also tried to be correlated with a new set of parameters obtained from dimensional analysis. Compartment development is however best described by usage of the elasticity number with a proportionality constant that is found to be different for each fluid in each scale. An equation that quantifies this proportionality constant is also proposed.

[ES] Cuando se mezclan fluidos pseudoplásticos no newtonianos en un tanque agitado, se pueden formar compartimentos o pseudocavernas alrededor del impulsor. En él, un volumen de forma toroidal de movimiento de fluido rápido aparece cerca del impulsor, con el resto del recipiente casi estancado, lo que impide una mezcla eficiente. En este trabajo, se estudia la formación de compartimentos en un grupo de soluciones poliméricas pseudoplásticas de reologías muy distintivas en tres tanques agitados de diferentes escalas y geométricamente similares mediante el uso de una turbina Rushton. Los tamaños de los compartimentos formados se evalúan mediante un método validado en el que se inyecta una solución coloreada del fluido examinado cerca del impulsor para luego ser fotografiada para su posterior procesamiento. Se estiman las características del fluido y las condiciones del proceso que propician la formación del compartimento y se encuentra una correlación basada en la cuantificación de la viscosidad del fluido y la escala mediante análisis dimensional. También se intenta correlacionar el desarrollo del compartimento con un nuevo conjunto de parámetros obtenidos del análisis dimensional. Sin embargo, el desarrollo del compartimento se describe mejor mediante el uso del número de elasticidad con una constante de proporcionalidad que se encuentra diferente para cada fluido en cada escala. También se propone una ecuación que cuantifique esta constante de proporcionalidad., [EN] When non-Newtonian pseudoplastic fluids are mixed in a stirred tank compartments or pseudocaverns can be formed around the impeller. In it, a toroidally shaped volume of fast fluid motion appears near the impeller, having the rest of the vessel nearly stagnant, preventing efficient mixing. In this work, compartment formation is studied in a group of pseudoplastic polymeric solutions of very distinctive rheologies in three different scaled and geometrically similar stirred tanks by using a Rushton turbine. The formed compartment sizes are evaluated by a validated method in which a coloured solution of the examined fluid is injected near the impeller to then be photographed for its later processing. The fluid characteristics and process conditions that propitiate compartment formation are estimated and a correlation based on the quantification of the fluid viscosity and the scale is found by using dimensional analysis. Compartment development is also tried to be correlated with a new set of parameters obtained from dimensional analysis. Compartment development is however best described by usage of the elasticity number with a proportionality constant that is found to be different for each fluid in each scale. An equation that quantifies this proportionality constant is also proposed.

[EN] Drinking water storage tanks allow to store water in the supply systems and help managing water demand variations. However, the tanks’ configuration and operation modes can also affect the quality of the supplied water. This paper presents a characterization of water storage tanks in Portugal, focusing on the physical and operational characteristics that affect their performance regarding mixing and water renewal. For the first time, water mixing in Portuguese storage tanks was assessed by determining the volume of renewal fractions needed to ensure the mixing of water entering each filling cycle with the existing one. The results show that mixing is guaranteed in about 74% of the circular cells and that the level variation required for this in a filling cycle is, on average, of 51%., [PT] Os reservatórios de água para consumo humano permitem garantir reservas de água nos sistemas de abastecimento e gerir variações do consumo. Contudo, a sua configuração e os modos de operação podem ter implicações na qualidade da água distribuída. Este trabalho apresenta uma caracterização dos reservatórios de água em Portugal, incidindo nas características físicas e operacionais que condicionam o seu desempenho do ponto de vista da mistura e renovação da água. Foi pela primeira vez avaliada a mistura da água nos reservatórios portugueses, pela determinação das frações de volumes de renovação necessárias para garantir a mistura da água que entra em cada ciclo de enchimento com a já existente. Os resultados mostram que a mistura é garantida em cerca de 74% das células circulares e que a variação de nível necessária para tal num ciclo de enchimento é, em média, de 51%.

[EN] Drinking water storage tanks allow to store water in the supply systems and help managing water demand variations. However, the tanks’ configuration and operation modes can also affect the quality of the supplied water. This paper presents a characterization of water storage tanks in Portugal, focusing on the physical and operational characteristics that affect their performance regarding mixing and water renewal. For the first time, water mixing in Portuguese storage tanks was assessed by determining the volume of renewal fractions needed to ensure the mixing of water entering each filling cycle with the existing one. The results show that mixing is guaranteed in about 74% of the circular cells and that the level variation required for this in a filling cycle is, on average, of 51%., [PT] Os reservatórios de água para consumo humano permitem garantir reservas de água nos sistemas de abastecimento e gerir variações do consumo. Contudo, a sua configuração e os modos de operação podem ter implicações na qualidade da água distribuída. Este trabalho apresenta uma caracterização dos reservatórios de água em Portugal, incidindo nas características físicas e operacionais que condicionam o seu desempenho do ponto de vista da mistura e renovação da água. Foi pela primeira vez avaliada a mistura da água nos reservatórios portugueses, pela determinação das frações de volumes de renovação necessárias para garantir a mistura da água que entra em cada ciclo de enchimento com a já existente. Os resultados mostram que a mistura é garantida em cerca de 74% das células circulares e que a variação de nível necessária para tal num ciclo de enchimento é, em média, de 51%.

[EN] Drinking water storage tanks allow to store water in the supply systems and help managing water demand variations. However, the tanks’ configuration and operation modes can also affect the quality of the supplied water. This paper presents a characterization of water storage tanks in Portugal, focusing on the physical and operational characteristics that affect their performance regarding mixing and water renewal. For the first time, water mixing in Portuguese storage tanks was assessed by determining the volume of renewal fractions needed to ensure the mixing of water entering each filling cycle with the existing one. The results show that mixing is guaranteed in about 74% of the circular cells and that the level variation required for this in a filling cycle is, on average, of 51%., [PT] Os reservatórios de água para consumo humano permitem garantir reservas de água nos sistemas de abastecimento e gerir variações do consumo. Contudo, a sua configuração e os modos de operação podem ter implicações na qualidade da água distribuída. Este trabalho apresenta uma caracterização dos reservatórios de água em Portugal, incidindo nas características físicas e operacionais que condicionam o seu desempenho do ponto de vista da mistura e renovação da água. Foi pela primeira vez avaliada a mistura da água nos reservatórios portugueses, pela determinação das frações de volumes de renovação necessárias para garantir a mistura da água que entra em cada ciclo de enchimento com a já existente. Os resultados mostram que a mistura é garantida em cerca de 74% das células circulares e que a variação de nível necessária para tal num ciclo de enchimento é, em média, de 51%.

[EN] Drinking water storage tanks allow to store water in the supply systems and help managing water demand variations. However, the tanks’ configuration and operation modes can also affect the quality of the supplied water. This paper presents a characterization of water storage tanks in Portugal, focusing on the physical and operational characteristics that affect their performance regarding mixing and water renewal. For the first time, water mixing in Portuguese storage tanks was assessed by determining the volume of renewal fractions needed to ensure the mixing of water entering each filling cycle with the existing one. The results show that mixing is guaranteed in about 74% of the circular cells and that the level variation required for this in a filling cycle is, on average, of 51%., [PT] Os reservatórios de água para consumo humano permitem garantir reservas de água nos sistemas de abastecimento e gerir variações do consumo. Contudo, a sua configuração e os modos de operação podem ter implicações na qualidade da água distribuída. Este trabalho apresenta uma caracterização dos reservatórios de água em Portugal, incidindo nas características físicas e operacionais que condicionam o seu desempenho do ponto de vista da mistura e renovação da água. Foi pela primeira vez avaliada a mistura da água nos reservatórios portugueses, pela determinação das frações de volumes de renovação necessárias para garantir a mistura da água que entra em cada ciclo de enchimento com a já existente. Os resultados mostram que a mistura é garantida em cerca de 74% das células circulares e que a variação de nível necessária para tal num ciclo de enchimento é, em média, de 51%.

A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all.

Small-scale physical models are commonly used to investigate gas-stirred processes in steelmaking practice. The argon oxygen decarburization (AOD) converter is among various processes widely used in the metallurgy field and utilizes side blowing of oxygen and inert gas for mixing in the bath. Herein, the effect of the converter inclination on mixing time and jet-penetration length with a side-blown physical model is investigated. Scaling with the modified Froude number is applied on data from a real industrial AOD converter to achieve a system with reasonable gas flow rates. During the experiments, water is used to simulate liquid steel and air is blown through side-mounted nozzles for stirring. A NaCl tracer is added and subsequent conductivity measurements are used to measure mixing time. Overall, the penetration length is shown to be independent of inclination angle. The mixing time is found to be influenced by the change of bath height to diameter ratio, change of geometry in the bath volume, gas flow rate, and the intensified wave motion at the interface caused by the inclination of the vessel. The mixing time increase with 14% when 14° angle is applied., QC 20220323

Batch high-shear mixers are used in a variety of different processing industries,such as the pharmaceutical, chemical and food industries. One company that utilize this type of mixers is Tetra Pak. High-shear mixers can be used for many different mixing scenarios, but only liquid-liquid mixing is discussed in the thesis. The batch high-shear mixer is constructed with a rotor-stator at the bottom of the tank. The rotor stator structure is a rotor which rotates inside the stationary stator. The fluid effected by the rotor is pushed through small holes on the stator and out into the tank region. The flow field generated inside the vessel is both complex and highly turbulent. With the technology of today it is highly interesting to use Computational Fluid Dynamics, CFD, simulations to determine these performances, from both an economically and time-dependant perspective. One property that is interesting is the time the mixing tank needs to achievea homogene mixture, i.e. the mixing time. However, simulations regarding rotor-stator mixers are in general very computational demanding. It is therefore of interest to improve the methodology to decrease the simulation time while still giving realistic results. This thesis evaluates Tetra Paks current methodology and also suggests possible improvements. The methodology can be divided into two parts, predicting the flow field inside the tank and predicting the mixing time.To decrease the simulation time, Tetra Pak uses a time-scale separationmethod in the current methodology. The separation utilizes that the flow around the rotor-stator converges to a stable state quicker than the rest of the vessel.The stabilized flow is then approximated by boundary conditions. Different boundary conditions have been tested. Of all methods, a transient boundary condition which imitates the motions of the rotor-stator was deemed generate the most realistic flow field. The second best option was a time-averaged boundary condition, simulated wit, Food processing is a cornerstone of today's society. Almost all products on the store shelves are created from some sort of processing line. In these lines, high-shear mixers are often used for combining the different ingredients. To understand how this machinery works and make the process more efficient, the flow field inside the mixer is analyzed. Preferably, Computational Fluid Dynamics (CFD) is used to simulate the flow instead of costly physical experiments. However, due to the complex geometry of this mixer these simulations are very time-consuming. The goal of this thesis is therefore to create a CFD-methodology which is both time effective and yields realistic results.

A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all.

A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

[Abstract] The effect of two different mixing protocols on the fresh-state behaviour of self-compacting mortars with and without recycled sand was compared. For this purpose, the mortar mixes were designed considering three solid volume fractions, while maintaining the water to cement ratio and superplasticiser dosage constant. The results conclude that the inclusion of recycled sand harmfully affects the rheological behaviour of the mortars and this effect can be mitigated using mixing protocols with longer mixing times and delayed admixture addition times. Finally, a rheograph was developed to explain the expectable changes in a conventional mix when recycled sand is incorporated, the solid volume fraction is varied and changes are applied to the mixing procedure.

We study bond percolation on the hypercube {0,1} m in the slightly subcritical regime where p = p c (1 − ε m ) and ε m = o(1) but ε m ≫ 2 −m/3 and study the clusters of largest volume and diameter. We establish that with high probability the largest component has cardinality Θ(ε m −2 log(ε m 3 2 m )), that the maximal diameter of all clusters is (1+o(1))ε m −1 log(ε m 3 2 m ), and that the maximal mixing time of all clusters is Θ(ε m −3 log 2 (ε m 3 2 m )). These results hold in different levels of generality, and in particular, some of the estimates hold for various classes of graphs such as high-dimensional tori, expanders of high degree and girth, products of complete graphs, and infinite lattices in high dimensions.

Understanding the local structure of a graph provides valuable insights about the underlying phenomena from which the graph has originated. Sampling and examining k-subgraphs is a widely used approach to understand the local structure of a graph. In this paper, we study the problem of sampling uniformly k-subgraphs from a given graph. We analyse a few different Markov chain Monte Carlo (MCMC) approaches, and obtain analytical results on their mixing times, which improve significantly the state of the art. In particular, we improve the bound on the mixing times of the standard MCMC approach, and the state-of-the-art MCMC sampling method PSRW, using the canonical-paths argument. In addition, we propose a novel sampling method, which we call recursive subgraph sampling RSS, and its optimized variant RSS+. The proposed methods, RSS and RSS+, are provably faster than the existing approaches. We conduct experiments and verify the uniformity of samples and the efficiency of RSS and RSS+., QC 20210426

I den här studien så var syftet att undersöka omrörningen och relaterade fenomen i den nyutvecklade IronArc processen. Processen använder sig av gasinjektion genom plasmageneratorer för att smälta och reducera en slagg bestående av järnoxid. Både penetrationsdjupet hos gasen och omrörningstiden undersöktes under olika förhållanden för att de är viktiga parametrar för processen. Undersökningen har gjorts både genom experiment och Computational Fluid Dynamics (CFD). Först utvecklades en nerskalad modell i akrylplast av IronArc pilot reaktorn i skala 1:3, där både penetrationsdjupet och omrörningstiden bestämdes för ett system med luft och vatten genom fysiska experiment. Sedan så skapades en matematisk modell för att beskriva penetrationen av luft injicerat i vatten. Den validerade modellen användes sedan för att beskriva penetrationsdjupet av den injicerade gasen i slaggen för pilotreaktorn. Vidare så utvecklades en ny metod för att bestämma omrörningstiden i pilotreaktorn med slagg som flytande medium. Slaggen undersöktes också både med hjälp av ljusoptiskt mikroskop (LOM) och även genom beräkningar i Thermo-Calc. Detta gjordes för att undersöka huruvida slaggen är i smält tillstånd då processen körs. Ytterligare en matematisk modell utvecklades sedan för att beskriva omrörningen i den nedskalade modellen av akrylplast med luft och vatten. Samma CFD modell användes för att beskriva omrörningen i pilotreaktorn, där modellen validerades mot de tidigare resultaten från de fysiska experimenten med slagg i pilotreaktorn. Slutligen så utfördes ytterligare försök i pilotreaktorn för att bestämma omrörningstiden, men med vatten istället för slagg. Det bör även nämnas att det enbart var luft som injicerades utan att gasen värmdes upp i plasmageneratorn, då vattnet skulle evaporerat om man värmt gasen. Den genomsnittliga omrörningstiden för den nerskalade modellen där luft injicerades i vatten bestämdes till 7,6 s och 10,2 sekunder för respektive homogeniseringsgrad på 95% oc, QC 20200609

I den här studien så var syftet att undersöka omrörningen och relaterade fenomen i den nyutvecklade IronArc processen. Processen använder sig av gasinjektion genom plasmageneratorer för att smälta och reducera en slagg bestående av järnoxid. Både penetrationsdjupet hos gasen och omrörningstiden undersöktes under olika förhållanden för att de är viktiga parametrar för processen. Undersökningen har gjorts både genom experiment och Computational Fluid Dynamics (CFD). Först utvecklades en nerskalad modell i akrylplast av IronArc pilot reaktorn i skala 1:3, där både penetrationsdjupet och omrörningstiden bestämdes för ett system med luft och vatten genom fysiska experiment. Sedan så skapades en matematisk modell för att beskriva penetrationen av luft injicerat i vatten. Den validerade modellen användes sedan för att beskriva penetrationsdjupet av den injicerade gasen i slaggen för pilotreaktorn. Vidare så utvecklades en ny metod för att bestämma omrörningstiden i pilotreaktorn med slagg som flytande medium. Slaggen undersöktes också både med hjälp av ljusoptiskt mikroskop (LOM) och även genom beräkningar i Thermo-Calc. Detta gjordes för att undersöka huruvida slaggen är i smält tillstånd då processen körs. Ytterligare en matematisk modell utvecklades sedan för att beskriva omrörningen i den nedskalade modellen av akrylplast med luft och vatten. Samma CFD modell användes för att beskriva omrörningen i pilotreaktorn, där modellen validerades mot de tidigare resultaten från de fysiska experimenten med slagg i pilotreaktorn. Slutligen så utfördes ytterligare försök i pilotreaktorn för att bestämma omrörningstiden, men med vatten istället för slagg. Det bör även nämnas att det enbart var luft som injicerades utan att gasen värmdes upp i plasmageneratorn, då vattnet skulle evaporerat om man värmt gasen. Den genomsnittliga omrörningstiden för den nerskalade modellen där luft injicerades i vatten bestämdes till 7,6 s och 10,2 sekunder för respektive homogeniseringsgrad på 95% oc, QC 20200609

The performance of a dual helical ribbon impeller in a gassed stirred tank reactor filled with a shear-thinning polymer has been investigated experimentally in this study. Sodium carboxymethyl cellulose with different concentrations were applied to change the viscosity and rheological behaviour of working fluid. Titration reaction between HCl and NaOH then took place inside the reactor under controlled pH, evaluating the influence of a dual helical ribbon impeller on the performance of a two-phase agitated reactor. The impact of impeller rotational speed, gas flow rate, viscosity, and clearance to the bottom on power uptake and mixing time are explored. The results thus reveal that the presence of bubbles reduces both required power uptake and mixing time to reach an endpoint reaction. Contrary to expectations, this study indicates that increasing the impeller's speed beyond a certain level, not only fails to further reduction in mixing time, whilst the power uptake increases exponentially. Furthermore, for the first time, this study suggest that power number is inversely proportional to the square root of Reynolds number when systems are equipped with a dual helical ribbon impeller. The response surface method and quadratic numerical models are applied to suggest models in order to calculate the mixing time and power consumption.

Stirred tank bioreactors are still the predominant cultivation systems in large scale biopharmaceutical production. Today, several manufacturers provide both reusable and single-use systems, whereas the broad variety of designs and properties lead to deviations in biological performance. Although the methods for bioreactor characterization are well established, varying experimental conditions and procedures can result in significantly different outcomes. In order to guarantee a reliable comparison and evaluation of different single-use and reusable bioreactor types, standardized methods for their characterization are needed. Equally important is the biological capability of bioreactors, which must be accessed by standardized cultivation procedures of industrially relevant organisms (bacteria, yeasts as well as mammalian and animal cell cultures). In addition, the implementation of well-defined uniform procedures for biological and engineering characterization during the development phase can support a fast assessment of the suitability of a bioreactor system. Based on stirred bioreactors, we describe the aspects of the engineering characterization in order to discuss further the biological characterization as a valuable complement. Finally, a case study is presented.

The performance of a dual helical ribbon impeller in a gassed stirred tank reactor filled with a shear-thinning polymer has been investigated experimentally in this study. Sodium carboxymethyl cellulose with different concentrations were applied to change the viscosity and rheological behaviour of working fluid. Titration reaction between HCl and NaOH then took place inside the reactor under controlled pH, evaluating the influence of a dual helical ribbon impeller on the performance of a two-phase agitated reactor. The impact of impeller rotational speed, gas flow rate, viscosity, and clearance to the bottom on power uptake and mixing time are explored. The results thus reveal that the presence of bubbles reduces both required power uptake and mixing time to reach an endpoint reaction. Contrary to expectations, this study indicates that increasing the impeller's speed beyond a certain level, not only fails to further reduction in mixing time, whilst the power uptake increases exponentially. Furthermore, for the first time, this study suggest that power number is inversely proportional to the square root of Reynolds number when systems are equipped with a dual helical ribbon impeller. The response surface method and quadratic numerical models are applied to suggest models in order to calculate the mixing time and power consumption.

Rheological properties are of significant importance in successful placement and performance of self-compacting concrete (SCC). In this work, the rheological properties of SCC, combined with a powder-viscosity modifying admixture, were investigated based on a series of experimental studies. The modified Bingham model was applied to determine the rheological parameters and shear thickening behavior of SCC. The effects of mixing procedures, including charging sequence, mixing time and mixing speed, were analyzed. The results show that the shear thickening of SCC is reduced by first mixing the aggregate and water and then adding other raw materials. The direct contact between aggregate and water leads to a large amount of free water to be adsorbed by the aggregate system, resulting in an increase of the yield stress. In order to ensure an excellent fluidity and a low shear thickening behavior of SCC, the mixing time should be controlled at 4-5 min and the mixing speed at 30-45 r/min., Materials and Environment

The performance of a dual helical ribbon impeller in a gassed stirred tank reactor filled with a shear-thinning polymer has been investigated experimentally in this study. Sodium carboxymethyl cellulose with different concentrations were applied to change the viscosity and rheological behaviour of working fluid. Titration reaction between HCl and NaOH then took place inside the reactor under controlled pH, evaluating the influence of a dual helical ribbon impeller on the performance of a two-phase agitated reactor. The impact of impeller rotational speed, gas flow rate, viscosity, and clearance to the bottom on power uptake and mixing time are explored. The results thus reveal that the presence of bubbles reduces both required power uptake and mixing time to reach an endpoint reaction. Contrary to expectations, this study indicates that increasing the impeller's speed beyond a certain level, not only fails to further reduction in mixing time, whilst the power uptake increases exponentially. Furthermore, for the first time, this study suggest that power number is inversely proportional to the square root of Reynolds number when systems are equipped with a dual helical ribbon impeller. The response surface method and quadratic numerical models are applied to suggest models in order to calculate the mixing time and power consumption.

The performance of a dual helical ribbon impeller in a gassed stirred tank reactor filled with a shear-thinning polymer has been investigated experimentally in this study. Sodium carboxymethyl cellulose with different concentrations were applied to change the viscosity and rheological behaviour of working fluid. Titration reaction between HCl and NaOH then took place inside the reactor under controlled pH, evaluating the influence of a dual helical ribbon impeller on the performance of a two-phase agitated reactor. The impact of impeller rotational speed, gas flow rate, viscosity, and clearance to the bottom on power uptake and mixing time are explored. The results thus reveal that the presence of bubbles reduces both required power uptake and mixing time to reach an endpoint reaction. Contrary to expectations, this study indicates that increasing the impeller's speed beyond a certain level, not only fails to further reduction in mixing time, whilst the power uptake increases exponentially. Furthermore, for the first time, this study suggest that power number is inversely proportional to the square root of Reynolds number when systems are equipped with a dual helical ribbon impeller. The response surface method and quadratic numerical models are applied to suggest models in order to calculate the mixing time and power consumption.

Stirred tank bioreactors are still the predominant cultivation systems in large scale biopharmaceutical production. Today, several manufacturers provide both reusable and single-use systems, whereas the broad variety of designs and properties lead to deviations in biological performance. Although the methods for bioreactor characterization are well established, varying experimental conditions and procedures can result in significantly different outcomes. In order to guarantee a reliable comparison and evaluation of different single-use and reusable bioreactor types, standardized methods for their characterization are needed. Equally important is the biological capability of bioreactors, which must be accessed by standardized cultivation procedures of industrially relevant organisms (bacteria, yeasts as well as mammalian and animal cell cultures). In addition, the implementation of well-defined uniform procedures for biological and engineering characterization during the development phase can support a fast assessment of the suitability of a bioreactor system. Based on stirred bioreactors, we describe the aspects of the engineering characterization in order to discuss further the biological characterization as a valuable complement. Finally, a case study is presented.

Rheological properties are of significant importance in successful placement and performance of self-compacting concrete (SCC). In this work, the rheological properties of SCC, combined with a powder-viscosity modifying admixture, were investigated based on a series of experimental studies. The modified Bingham model was applied to determine the rheological parameters and shear thickening behavior of SCC. The effects of mixing procedures, including charging sequence, mixing time and mixing speed, were analyzed. The results show that the shear thickening of SCC is reduced by first mixing the aggregate and water and then adding other raw materials. The direct contact between aggregate and water leads to a large amount of free water to be adsorbed by the aggregate system, resulting in an increase of the yield stress. In order to ensure an excellent fluidity and a low shear thickening behavior of SCC, the mixing time should be controlled at 4-5 min and the mixing speed at 30-45 r/min., Materials and Environment

I den här studien så var syftet att undersöka omrörningen och relaterade fenomen i den nyutvecklade IronArc processen. Processen använder sig av gasinjektion genom plasmageneratorer för att smälta och reducera en slagg bestående av järnoxid. Både penetrationsdjupet hos gasen och omrörningstiden undersöktes under olika förhållanden för att de är viktiga parametrar för processen. Undersökningen har gjorts både genom experiment och Computational Fluid Dynamics (CFD). Först utvecklades en nerskalad modell i akrylplast av IronArc pilot reaktorn i skala 1:3, där både penetrationsdjupet och omrörningstiden bestämdes för ett system med luft och vatten genom fysiska experiment. Sedan så skapades en matematisk modell för att beskriva penetrationen av luft injicerat i vatten. Den validerade modellen användes sedan för att beskriva penetrationsdjupet av den injicerade gasen i slaggen för pilotreaktorn. Vidare så utvecklades en ny metod för att bestämma omrörningstiden i pilotreaktorn med slagg som flytande medium. Slaggen undersöktes också både med hjälp av ljusoptiskt mikroskop (LOM) och även genom beräkningar i Thermo-Calc. Detta gjordes för att undersöka huruvida slaggen är i smält tillstånd då processen körs. Ytterligare en matematisk modell utvecklades sedan för att beskriva omrörningen i den nedskalade modellen av akrylplast med luft och vatten. Samma CFD modell användes för att beskriva omrörningen i pilotreaktorn, där modellen validerades mot de tidigare resultaten från de fysiska experimenten med slagg i pilotreaktorn. Slutligen så utfördes ytterligare försök i pilotreaktorn för att bestämma omrörningstiden, men med vatten istället för slagg. Det bör även nämnas att det enbart var luft som injicerades utan att gasen värmdes upp i plasmageneratorn, då vattnet skulle evaporerat om man värmt gasen. Den genomsnittliga omrörningstiden för den nerskalade modellen där luft injicerades i vatten bestämdes till 7,6 s och 10,2 sekunder för respektive homogeniseringsgrad på 95% oc, QC 20200609

I den här studien så var syftet att undersöka omrörningen och relaterade fenomen i den nyutvecklade IronArc processen. Processen använder sig av gasinjektion genom plasmageneratorer för att smälta och reducera en slagg bestående av järnoxid. Både penetrationsdjupet hos gasen och omrörningstiden undersöktes under olika förhållanden för att de är viktiga parametrar för processen. Undersökningen har gjorts både genom experiment och Computational Fluid Dynamics (CFD). Först utvecklades en nerskalad modell i akrylplast av IronArc pilot reaktorn i skala 1:3, där både penetrationsdjupet och omrörningstiden bestämdes för ett system med luft och vatten genom fysiska experiment. Sedan så skapades en matematisk modell för att beskriva penetrationen av luft injicerat i vatten. Den validerade modellen användes sedan för att beskriva penetrationsdjupet av den injicerade gasen i slaggen för pilotreaktorn. Vidare så utvecklades en ny metod för att bestämma omrörningstiden i pilotreaktorn med slagg som flytande medium. Slaggen undersöktes också både med hjälp av ljusoptiskt mikroskop (LOM) och även genom beräkningar i Thermo-Calc. Detta gjordes för att undersöka huruvida slaggen är i smält tillstånd då processen körs. Ytterligare en matematisk modell utvecklades sedan för att beskriva omrörningen i den nedskalade modellen av akrylplast med luft och vatten. Samma CFD modell användes för att beskriva omrörningen i pilotreaktorn, där modellen validerades mot de tidigare resultaten från de fysiska experimenten med slagg i pilotreaktorn. Slutligen så utfördes ytterligare försök i pilotreaktorn för att bestämma omrörningstiden, men med vatten istället för slagg. Det bör även nämnas att det enbart var luft som injicerades utan att gasen värmdes upp i plasmageneratorn, då vattnet skulle evaporerat om man värmt gasen. Den genomsnittliga omrörningstiden för den nerskalade modellen där luft injicerades i vatten bestämdes till 7,6 s och 10,2 sekunder för respektive homogeniseringsgrad på 95% oc, QC 20200609

I den här studien så var syftet att undersöka omrörningen och relaterade fenomen i den nyutvecklade IronArc processen. Processen använder sig av gasinjektion genom plasmageneratorer för att smälta och reducera en slagg bestående av järnoxid. Både penetrationsdjupet hos gasen och omrörningstiden undersöktes under olika förhållanden för att de är viktiga parametrar för processen. Undersökningen har gjorts både genom experiment och Computational Fluid Dynamics (CFD). Först utvecklades en nerskalad modell i akrylplast av IronArc pilot reaktorn i skala 1:3, där både penetrationsdjupet och omrörningstiden bestämdes för ett system med luft och vatten genom fysiska experiment. Sedan så skapades en matematisk modell för att beskriva penetrationen av luft injicerat i vatten. Den validerade modellen användes sedan för att beskriva penetrationsdjupet av den injicerade gasen i slaggen för pilotreaktorn. Vidare så utvecklades en ny metod för att bestämma omrörningstiden i pilotreaktorn med slagg som flytande medium. Slaggen undersöktes också både med hjälp av ljusoptiskt mikroskop (LOM) och även genom beräkningar i Thermo-Calc. Detta gjordes för att undersöka huruvida slaggen är i smält tillstånd då processen körs. Ytterligare en matematisk modell utvecklades sedan för att beskriva omrörningen i den nedskalade modellen av akrylplast med luft och vatten. Samma CFD modell användes för att beskriva omrörningen i pilotreaktorn, där modellen validerades mot de tidigare resultaten från de fysiska experimenten med slagg i pilotreaktorn. Slutligen så utfördes ytterligare försök i pilotreaktorn för att bestämma omrörningstiden, men med vatten istället för slagg. Det bör även nämnas att det enbart var luft som injicerades utan att gasen värmdes upp i plasmageneratorn, då vattnet skulle evaporerat om man värmt gasen. Den genomsnittliga omrörningstiden för den nerskalade modellen där luft injicerades i vatten bestämdes till 7,6 s och 10,2 sekunder för respektive homogeniseringsgrad på 95% oc, QC 20200609

IronArc is a newly developed technology and an emerging future process for pig iron production. The long-term goal with this technology is to reduce the CO2 emissions and energy consumption compared to existing technologies. The production rate of this process is dependent on the stirring, which was investigated in the pilot plant process by measuring the mixing time in the slag bath. Moreover, slag investigations were done both based on light optical microscope studies as well as by Thermo-Calc calculations in order to determine the phases of the slag during operation. This was done because the viscosity (which is another important parameter) is dependent on the liquid and solid fractions of the slag. The overall results show that it was possible to determine the mixing time by means of the addition of a tracer (MnO2 powder) to the slag. The mixing time for the trials showed that the slag was homogenized after seconds. For two of the trials, homogenization had already been reached in the second sample after tracer addition, which means <= 8 s. The phase analysis from the slag indicated that the slag is in a liquid state during the operation of the process., QC 20190325

Drum mixers ensure a high level of uniformity when mixing the components of feed additives. However, the issues on theoretical and experimental substantiation of the structural and kinematic parameters of drum mixers have not been scientifically explored in detail. The aim of this study is to improve the efficiency of producing feed mixtures by ensuring the optimal angular rotation velocity of a drum mixer.To determine the radial speed of a particle’s motion along a drum blade, we solved a homogeneous differential equation. The numerical value for angular velocity was determined by a computer simulation method. We experimentally studied the uniformity of redistribution of feed components in a mixture of fodder using the designed experimental drum mixer. The mixer included a chamber, a rectangular frame, a supporting frame, and a drive. The mixing chamber included a loading/unloading window with a closed lid. Radial blades were installed inside the chamber along its entire length and evenly along the perimeter.Experiments were conducted using a drum mixer with a drum radius of 0.17 m, which included radial blades with a width of 25 mm, with a chamber’s fill factor of 0.5. It was established that the drum mixer ensures the maximum scattering of a material’s particles on the surface of the working segment at the drum’s angular rotation velocity of 9.69 rad/s.The results of experimental research have established that at rotation frequency of the laboratory plant’s drum of 9.42 rad/s the uniformity of mixture is 92.5‒93 %, which meets acting zootechnical requirements for all types of mixed fodder. In this case, a maximum deviation of the theoretical and experimental data was about 9 %. The results obtained suggest the possibility of determining a numerical value for the angular velocity of drum mixers by using the proposed method of computer simulation., Барабанные смесители могут обеспечить высокий уровень равномерности смешивания компонентов кормовых добавок. Однако вопросы теоретического и экспериментального обоснования конструкционных и кинематических параметров барабанных смесителей недостаточно научно исследовано. Целью работы является повышение эффективности производства кормовых смесей путем обеспечения оптимальной угловой скорости вращения барабанного смесителя.Для определения радиальной скорости движения частицы по лопатке барабана было использовано решение однородного дифференциального уравнения. Определение числового значения угловой скорости было реализовано методом компьютерного моделирования. Проведение экспериментальных исследований равномерности перераспределения кормовых компонентов в смеси комбикорма осуществлялось с помощью разработанного экспериментального барабанного смесителя. Смеситель состоял из камеры, прямоугольной рамки, опорной рамы и привода. Камера смешивания имела погрузочно-разгрузочное окно закрыто крышкой. Внутри камеры по всей ее длине и равномерно по периметру были установленной радиальные лопатки.Опыты проводились с использованием барабанного смесителя с радиусом барабана 0,17 м, который имел радиальные лопатки шириной 25 мм и при коэффициенте заполнения камеры 0,5. Установлено, что барабанный смеситель обеспечивает максимальное рассеивание частиц материала по поверхности рабочего сегмента при угловой скорости вращения барабана 9,69 рад/с.В результате экспериментальных исследований установлено, что при частоте вращения барабана лабораторной установки 9,42 рад/с. равномерность смеси составляет 92,5–93 %, что соответствует существующим зоотехническим требованиям всех видов комбикормов. При этом максимальное отклонение теоретических и экспериментальных данных составило возле 9 %. Полученные результаты позволяют утверждать о возможности определения числового значения угловой скорости барабанных смесителей предложенным методом компьютерного моделирования, Барабанні змішувачі можуть забезпечити заданий рівень рівномірності змішування, в тому числі компонентів кормових добавок. Однак питання теоретичного та експериментального обґрунтування конструкційно-кінематичних параметрів барабанних змішувачів недостатньо науково досліджене. Метою роботи є підвищення ефективності виробництва кормових сумішей шляхом забезпечення оптимальної кутової швидкості обертання барабанного змішувача.Для визначення радіальної швидкості руху частки по лопатці барабана був використаний розв’язок однорідного диференційного рівняння. Визначення числового значення кутової швидкості реалізовано методом комп’ютерного моделювання. Проведення експериментальних досліджень рівномірності перерозподілу кормових компонентів у суміші комбікорму здійснювалося за допомогою розробленого експериментального барабанного змішувача. Змішувач складався з камери, прямокутної рамки, опорної рами та приводу. Камера змішування мала завантажувально-розвантажувальне вікно закрите кришкою. Всередині камери по всій її довжині і рівномірно по периметру були встановленої радіальні лопатки.Досліди проводилися із використанням барабанного змішувача із радіусом барабана 0,17 м, який мав радіальні лопатки шириною 25 мм та при коефіцієнті заповнення камери 0,5. Встановлено, що барабанний змішувач забезпечує максимальне розсіювання часточок матеріалу по поверхні робочого сегменту при кутовій швидкості обертання барабану 9,69 рад/с.У результаті експериментальних досліджень встановлено, що при частоті обертання барабана лабораторної установки 9,42 рад/с рівномірність сумішки становить 92,5–93 %, що відповідає існуючим зоотехнічним вимогам для всіх видів комбікормів. При цьому максимальне відхилення теоретичних та експериментальних даних становило біля 9 %. Отримані результати дають змогу стверджувати про можливість визначення числового значення кутової швидкості барабанних змішувачів запропонованим методом комп’ютерного моделювання

In a scrap based stainless steel plant the dominant process for carbon reduction is the Argon oxygen decarburisation process (AOD). The process goes through three steps: decarburisation, reduction and desulphurisation where the main challenge is to oxidise carbon to CO without oxidising the expensive chromium. The general practical approach is to inject a mixture of oxygen and an inert gas, like argon or nitrogen, through tuyeres at the converter side starting with a high amount of oxygen gas which followingly is reduced as the inert gas is increased during the decarburisation steps. This allows for a decrease in partial pressure for the CO bubbles which is thermodynamically favourable for carbon oxidation. Recent studies have shown that an aged AOD converter with a worn lining can decarburise the melt faster than a fresh vessel due to favourable thermodynamic conditions occurring since the bath height is lower in the aged converter. The studies show 8-10% savings of oxygen gas which have led to an interest to study the matter. One of two approaches are taken in the present work with the focus to develop a numerical model that simulates a downscaled AOD converter with applied inclinations that is to be validated through physical modelling. A 75-ton industrial converter was downscaled for water-air experiments where three inclination angles namely 0, 5.5 and 14° were studied with focus on mixing time and penetration length. The physical model was replicated for computational fluid dynamics (CFD) modelling using the Euler-Euler approach in ANSYS Fluent. The models show rather good similarities when comparing gas penetration length, flow structure and mixing time however needs some complementary work and final adjustments before upscaling as well as coupling with thermodynamic modelling can be done., Den dominerande processen för kolfärskning vid skrot baserad rostfri ståltillverkning är AOD- processen (Argon Oxygen Decarburisation). Processen går igenom tre steg, kolfärskning, reducering av krom och svavelrening där de största utmaningarna ligger i att oxidera kol utan att oxidera krom. I praktiken gör detta genom att injicera en blandning av argon och syrgas från sidan av AOD-konvertern för att sänka partial trycket av den kolmonoxid som bildas när kol oxideras. Syftet är att göra det mer termodynamiskt fördelaktigt att oxidera kol i systemet. Den injicerade blandgasen har olika förhållanden under kolfärskning med en hög andel syrgas i början som sedan sänks genom processen tills bara argon injiceras. Tidigare studier har visat att kolfärskningen är en funktion av konverterns ålder där ju äldre en konverter är desto snabbare går kolfärskning. Enligt studierna har det visats att 8-10% mindre syrgas eller användning av reducerings medel kan uppnås i en gammal konverter vilket har väckt ett intresse för vidare studier. I detta arbete har en av två metoder prövats för att undersöka om man kan applicera det som sker i en gammal konverter till en ny. En numerisk modell av en nerskalad AOD-konverter har utvecklats och validerats mot en vattenmodell då konvertern vinklas. En 75-tons konverter nerskalades till en vattenmodell där vinklarna 0, 5.5 och 14° studerades med fokus på blandningstid och penetrations djup. Vattenmodellen gjordes om till en numerisk modell som använde Euler-Euler metoden i ANSYS Fluent. Modellerna visade likheter gällande penetrationsdjup, flödes struktur och blandnings tid men kräver en del justeringar innan en uppskalning samt koppling till termodynamisk modellering kan ske.

When a stirring and mixing system is not correctly designed and controlled, undesirable mixtures are obtained, which can lead to product losses and increased process costs. Therefore, the objective of this study is to evaluate a system of agitation and mixing that can generate experimental data for the aid of researchers and designers of industrial impellers. This system was evaluated using four different configurations of impellers (Rushton-Rushton; Rushton-Smith; Smith-Rushton and Smith-Smith) based on two fundamental performance parameters of the stirring system: mixing time and energy consumption. The mixing time was determined by temperature pulse method and the calculation of the power consumption was obtained from the literature equations. The performance parameters were evaluated in three different rotation frequencies: 300, 500 and 700 rpm. The configuration (4) showed a reduction in the mixing time of 36% (300 rpm), 63% (500 rpm) and 79% (700 rpm) when compared to the standard configuration (1). From the obtained results, it was possible to conclude that the configuration (4), obtained the lowest mixing time and lower power consumption of all the configurations evaluated. In addition, it can be determined that the stirring frequency of 500 rpm was the most adequate for this study., Agitação e mistura são operações unitárias essenciais na maioria dos processos industriais e têm por objetivo a obtenção de matérias primas ou produtos uniformes. Quando um sistema de agitação e mistura não está corretamente projetado e controlado obtém-se misturas indesejáveis, o que pode acarretar em perdas de produto e aumento no custo do processo. Portanto, o objetivo deste estudo é avaliar um sistema de agitação e mistura que possa gerar dados experimentais para o auxílio de pesquisadores e projetistas de impelidores industriais. Este sistema foi avaliado utilizando quatro diferentes configurações de impelidores (Rushton-Rushton; Rushton-Smith; Smith-Rushton e Smith-Smith) com base em dois parâmetros de desempenho fundamentais do sistema de agitação: tempo de mistura e consumo de energia. O tempo de mistura foi determinado pelo método de pulso de temperatura e o cálculo do consumo de potência foi obtido através de equações da literatura. Avaliou-se os parâmetros de desempenho em três diferentes frequências de rotação: 300, 500 e 700 rpm. A configuração (4) apresentou uma redução no tempo de mistura de 36% (300 rpm), 63% (500 rpm) e 79% (700 rpm) quando comparada com a configuração padrão (1). A partir dos resultados obtidos, foi possível concluir que a configuração (4), obteve os menores tempo de mistura e menor consumo de energia de todas as configurações avaliadas. Além disso, pode-se determinar que a frequência de agitação de 500 rpm foi a mais adequada para este estudo., Agitación y mezcla son operaciones unitarias esenciales en la mayoría de los procesos industriales y tienen como objetivo la obtención de materias primas o productos uniformes. Cuando un sistema de agitación y mezcla no está correctamente proyectado y controlado se obtiene mezclas indeseables, lo que puede acarrear en pérdidas de producto y aumento en el costo del proceso. Por lo tanto, el objetivo de este estudio es evaluar un sistema de agitación y mezcla que pueda generar datos experimentales para el auxilio de investigadores y proyectistas de impulsores industriales. Este sistema se ha evaluado utilizando cuatro diferentes configuraciones de impulsores (Rushton-Rushton, Rushton-Smith, Smith-Rushton y Smith-Smith) basados en dos parámetros de rendimiento fundamentales del sistema de agitación: tiempo de mezcla y consumo de energía. El tiempo de mezcla fue determinado por el método de pulso de temperatura y el cálculo del consumo de potencia fue obtenido a través de ecuaciones de la literatura. Se evaluaron los parámetros de rendimiento en tres diferentes frecuencias de rotación: 300, 500 y 700 rpm. La configuración (4) disminuyó el tiempo de 36% de mezcla (300 rpm), 63% (500 rpm) y 79% (700 rpm) en comparación con el valor predeterminado (1). A partir de los resultados obtenidos, fue posible concluir que la configuración (4), obtuvo los menores tiempo de mezcla y menor consumo de energía de todas las configuraciones evaluadas. Además, se puede determinar que la frecuencia de agitación de 500 rpm fue la más adecuada para este estudio.

In a scrap based stainless steel plant the dominant process for carbon reduction is the Argon oxygen decarburisation process (AOD). The process goes through three steps: decarburisation, reduction and desulphurisation where the main challenge is to oxidise carbon to CO without oxidising the expensive chromium. The general practical approach is to inject a mixture of oxygen and an inert gas, like argon or nitrogen, through tuyeres at the converter side starting with a high amount of oxygen gas which followingly is reduced as the inert gas is increased during the decarburisation steps. This allows for a decrease in partial pressure for the CO bubbles which is thermodynamically favourable for carbon oxidation. Recent studies have shown that an aged AOD converter with a worn lining can decarburise the melt faster than a fresh vessel due to favourable thermodynamic conditions occurring since the bath height is lower in the aged converter. The studies show 8-10% savings of oxygen gas which have led to an interest to study the matter. One of two approaches are taken in the present work with the focus to develop a numerical model that simulates a downscaled AOD converter with applied inclinations that is to be validated through physical modelling. A 75-ton industrial converter was downscaled for water-air experiments where three inclination angles namely 0, 5.5 and 14° were studied with focus on mixing time and penetration length. The physical model was replicated for computational fluid dynamics (CFD) modelling using the Euler-Euler approach in ANSYS Fluent. The models show rather good similarities when comparing gas penetration length, flow structure and mixing time however needs some complementary work and final adjustments before upscaling as well as coupling with thermodynamic modelling can be done., Den dominerande processen för kolfärskning vid skrot baserad rostfri ståltillverkning är AOD- processen (Argon Oxygen Decarburisation). Processen går igenom tre steg, kolfärskning, reducering av krom och svavelrening där de största utmaningarna ligger i att oxidera kol utan att oxidera krom. I praktiken gör detta genom att injicera en blandning av argon och syrgas från sidan av AOD-konvertern för att sänka partial trycket av den kolmonoxid som bildas när kol oxideras. Syftet är att göra det mer termodynamiskt fördelaktigt att oxidera kol i systemet. Den injicerade blandgasen har olika förhållanden under kolfärskning med en hög andel syrgas i början som sedan sänks genom processen tills bara argon injiceras. Tidigare studier har visat att kolfärskningen är en funktion av konverterns ålder där ju äldre en konverter är desto snabbare går kolfärskning. Enligt studierna har det visats att 8-10% mindre syrgas eller användning av reducerings medel kan uppnås i en gammal konverter vilket har väckt ett intresse för vidare studier. I detta arbete har en av två metoder prövats för att undersöka om man kan applicera det som sker i en gammal konverter till en ny. En numerisk modell av en nerskalad AOD-konverter har utvecklats och validerats mot en vattenmodell då konvertern vinklas. En 75-tons konverter nerskalades till en vattenmodell där vinklarna 0, 5.5 och 14° studerades med fokus på blandningstid och penetrations djup. Vattenmodellen gjordes om till en numerisk modell som använde Euler-Euler metoden i ANSYS Fluent. Modellerna visade likheter gällande penetrationsdjup, flödes struktur och blandnings tid men kräver en del justeringar innan en uppskalning samt koppling till termodynamisk modellering kan ske.

Health Canada recommends an approximately 30% reduction of sodium levels in bread products, which brings a great challenge for bakery industry due to dough handling difficulties and product quality issues induced by sodium reduction. In order to address this challenge, the effects of wheat cultivar, water content and mixing time on the response of dough’s rheological properties and gas phase to salt (NaCl) reduction were investigated to develop processing strategies for improving the breadmaking performance of reduced salt content doughs. The rheological properties of doughs with a wide range of formulations were examined using the mixograph, dynamic oscillatory rheometry and creep-recovery tests. Outcomes from these rheological studies indicated that doughs with a better tolerance to salt reduction were prepared at higher water contents, and/or optimal mixing time. The gas phase parameters, i.e., the gas volume fraction and the volumetric bubble size distribution, of doughs were examined using synchrotron X-ray microtomography. In terms of the time evolution of the bubble size distribution in unyeasted doughs, increased water content, reduced salt content, and/or increased mixing time were seen to promote disproportionation in the dough. Dough gas phase studies also confirmed a cultivar-dependent response of dough to salt reduction and suggested that the optimal-mixing condition developed the doughs to be more tolerant to salt reduction compared to under- and over-mixing conditions. In conclusion, formulation and mixing conditions play an important role in determining dough’s response to salt reduction. The type of wheat flour (associated with the cultivar’s tolerance to salt reduction), water content and optimal mixing time need to be considered when improving the breadmaking performance of reduced-salt doughs.

In secondary metallurgy, argon gas stirring and alloying of elements are very important in determining the quality of steel. Argon gas is injected through the nozzle located at the bottom of the ladle into the molten steel bath; this gas breaks up into gas bubbles, rising upwards and breaking the slag layer at high gas flow rates, creating an open-eye. Alloy elements are added to the molten steel through the open-eye to attain the desired steel composition. In this work, experiments were conducted to investigate the effect of argon gas flow rate on the open-eye size and mixing time. An Eulerian volume of fluid (VOF) approach was employed to simulate the argon/steel/slag interface in the ladle, while a species transport model was used to calculate the mixing time of the nickel alloy. The simulation results showed that the time-averaged value of the open-eye area changed from 0.66 to 2.36 m2 when the flow rate of argon was varied from 100 to 500 NL/min. The mixing time (95% criterion) of tracer addition into the metal bath decreased from 139 s to 96 s, when the argon flow rate was increased from 100 to 500 NL/min. The model validation was verified by comparing with measured experimental results

The random-cluster (FK) model is a key tool for the study of phase transitions and for the design of efficient Markov chain Monte Carlo (MCMC) sampling algorithms for the Ising/Potts model. It is well-known that in the high-temperature region beta1 and p != p_c(q) the mixing time of the FK-dynamics is polynomial in n for every realizable boundary condition. Previously, for boundary conditions that do not carry long-range information (namely wired and free), Blanca and Sinclair (2017) had proved that the FK-dynamics in the same setting mixes in optimal O(n^2 log n) time. To illustrate the difficulties introduced by general boundary conditions, we also construct a class of non-realizable boundary conditions that induce slow (stretched-exponential) convergence at high temperatures.

Cheeger's inequality shows that any undirected graph G with minimum normalized Laplacian eigenvalue lambda_G has a cut with conductance at most O(sqrt{lambda_G}). Qualitatively, Cheeger's inequality says that if the mixing time of a graph is high, there is a cut that certifies this. However, this relationship is not tight, as some graphs (like cycles) do not have cuts with conductance o(sqrt{lambda_G}). To better approximate the mixing time of a graph, we consider a more general object. Specifically, instead of bounding the mixing time with cuts, we bound it with cuts in graphs obtained by Schur complementing out vertices from the graph G. Combinatorially, these Schur complements describe random walks in G restricted to a subset of its vertices. As a result, all Schur complement cuts have conductance at least Omega(lambda_G). We show that unlike with cuts, this inequality is tight up to a constant factor. Specifically, there is a Schur complement cut with conductance at most O(lambda_G).