Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Business models enhancing the diffusion of mobile Internet in emerging markets

Tämän tutkimuksen päätavoitteena oli selvittää, millaiset liiketoimintamallit soveltuvat mobiilin internet-liiketoiminnan harjoittamiseen kehittyvillä markkinoilla. Tavoitteena oli myös selvittää tekijöitä, jotka vaikuttavat mobiilin internetin diffuusioon. Tutkimus tehtiin käyttäen sekä kvantitatiivista että kvalitatiivista tutkimusmenetelmää. Klusterianalyysin avulla 40 Euroopan maasta muodostettiin sisäisesti homogeenisiä maaklustereita. Näiden klustereiden avulla oli mahdollista suunnitella erityyppisille markkinoille soveltuvat liiketoimintamallit. Haastatteluissa selvitettiin asiantuntijoiden näkemyksiä tekijöistä, jotka vaikuttavat mobiilin internetin diffuusioon kehittyvillä markkinoilla. Tutkimuksessa saatiin selville, että tärkeimmät liiketoimintamallin elementit kehittyvillä markkinoilla ovat hinnoittelu, arvotarjooma ja arvoverkko. Puutteellisen kiinteän verkon todettiin olevan yksi tärkeimmistä mobiilin internetin diffuusiota edistävistä tekijöistä kehittyvillä markkinoilla.

Mass transfer and particleinteractions in granular systems and suspension flows

The purpose of this study was to investigate some important features of granular flows and suspension flows by computational simulation methods. Granular materials have been considered as an independent state ofmatter because of their complex behaviors. They sometimes behave like a solid, sometimes like a fluid, and sometimes can contain both phases in equilibrium. The computer simulation of dense shear granular flows of monodisperse, spherical particles shows that the collisional model of contacts yields the coexistence of solid and fluid phases while the frictional model represents a uniform flow of fluid phase. However, a comparison between the stress signals from the simulations and experiments revealed that the collisional model would result a proper match with the experimental evidences. Although the effect of gravity is found to beimportant in sedimentation of solid part, the stick-slip behavior associated with the collisional model looks more similar to that of experiments. The mathematical formulations based on the kinetic theory have been derived for the moderatesolid volume fractions with the assumption of the homogeneity of flow. In orderto make some simulations which can provide such an ideal flow, the simulation of unbounded granular shear flows was performed. Therefore, the homogeneous flow properties could be achieved in the moderate solid volume fractions. A new algorithm, namely the nonequilibrium approach was introduced to show the features of self-diffusion in the granular flows. Using this algorithm a one way flow can beextracted from the entire flow, which not only provides a straightforward calculation of self-diffusion coefficient but also can qualitatively determine the deviation of self-diffusion from the linear law at some regions nearby the wall inbounded flows. Anyhow, the average lateral self-diffusion coefficient, which was calculated by the aforementioned method, showed a desirable agreement with thepredictions of kinetic theory formulation. In the continuation of computer simulation of shear granular flows, some numerical and theoretical investigations were carried out on mass transfer and particle interactions in particulate flows. In this context, the boundary element method and its combination with the spectral method using the special capabilities of wavelets have been introduced as theefficient numerical methods to solve the governing equations of mass transfer in particulate flows. A theoretical formulation of fluid dispersivity in suspension flows revealed that the fluid dispersivity depends upon the fluid properties and particle parameters as well as the fluid-particle and particle-particle interactions.

Predicting diffusion of innovations with self-organisation and machine learning

The main subject of this master's thesis was predicting diffusion of innovations. The prediction was done in a special case: product has been available in some countries, and based on its diffusion in those countries the prediction is done for other countries. The prediction was based on finding similar countries with Self-Organizing Map~(SOM), using parameters of countries. Parameters included various economical and social key figures. SOM was optimised for different products using two different methods: (a) by adding diffusion information of products to the country parameters, and (b) by weighting the country parameters based on their importance for the diffusion of different products. A novel method using Differential Evolution (DE) was developed to solve the latter, highly non-linear optimisation problem. Results were fairly good. The prediction method seems to be on a solid theoretical foundation. The results based on country data were good. Instead, optimisation for different products did not generally offer clear benefit, but in some cases the improvement was clearly noticeable. The weights found for the parameters of the countries with the developed SOM optimisation method were interesting, and most of them could be explained by properties of the products.

Methyl and ethyl chloride synthesis in microreactors

Methyl chloride is an important chemical intermediate with a variety of applications. It is produced today in large units and shipped to the endusers. Most of the derived products are harmless, as silicones, butyl rubber and methyl cellulose. However, methyl chloride is highly toxic and flammable. On-site production in the required quantities is desirable to reduce the risks involved in transportation and storage. Ethyl chloride is a smaller-scale chemical intermediate that is mainly used in the production of cellulose derivatives. Thus, the combination of onsite production of methyl and ethyl chloride is attractive for the cellulose processing industry, e.g. current and future biorefineries. Both alkyl chlorides can be produced by hydrochlorination of the corresponding alcohol, ethanol or methanol. Microreactors are attractive for the on-site production as the reactions are very fast and involve toxic chemicals. In microreactors, the diffusion limitations can be suppressed and the process safety can be improved. The modular setup of microreactors is flexible to adjust the production capacity as needed. Although methyl and ethyl chloride are important chemical intermediates, the literature available on potential catalysts and reaction kinetics is limited. Thus the thesis includes an extensive catalyst screening and characterization, along with kinetic studies and engineering the hydrochlorination process in microreactors. A range of zeolite and alumina based catalysts, neat and impregnated with ZnCl2, were screened for the methanol hydrochlorination. The influence of zinc loading, support, zinc precursor and pH was investigated. The catalysts were characterized with FTIR, TEM, XPS, nitrogen physisorption, XRD and EDX to identify the relationship between the catalyst characteristics and the activity and selectivity in the methyl chloride synthesis. The acidic properties of the catalyst were strongly influenced upon the ZnCl2 modification. In both cases, alumina and zeolite supports, zinc reacted to a certain amount with specific surface sites, which resulted in a decrease of strong and medium Brønsted and Lewis acid sites and the formation of zinc-based weak Lewis acid sites. The latter are highly active and selective in methanol hydrochlorination. Along with the molecular zinc sites, bulk zinc species are present on the support material. Zinc modified zeolite catalysts exhibited the highest activity also at low temperatures (ca 200 °C), however, showing deactivation with time-onstream. Zn/H-ZSM-5 zeolite catalysts had a higher stability than ZnCl2 modified H-Beta and they could be regenerated by burning the coke in air at 400 °C. Neat alumina and zinc modified alumina catalysts were active and selective at 300 °C and higher temperatures. However, zeolite catalysts can be suitable for methyl chloride synthesis at lower temperatures, i.e. 200 °C. Neat γ-alumina was found to be the most stable catalyst when coated in a microreactor channel and it was thus used as the catalyst for systematic kinetic studies in the microreactor. A binder-free and reproducible catalyst coating technique was developed. The uniformity, thickness and stability of the coatings were extensively characterized by SEM, confocal microscopy and EDX analysis. A stable coating could be obtained by thermally pretreating the microreactor platelets and ball milling the alumina to obtain a small particle size. Slurry aging and slow drying improved the coating uniformity. Methyl chloride synthesis from methanol and hydrochloric acid was performed in an alumina-coated microreactor. Conversions from 4% to 83% were achieved in the investigated temperature range of 280-340 °C. This demonstrated that the reaction is fast enough to be successfully performed in a microreactor system. The performance of the microreactor was compared with a tubular fixed bed reactor. The results obtained with both reactors were comparable, but the microreactor allows a rapid catalytic screening with low consumption of chemicals. As a complete conversion of methanol could not be reached in a single microreactor, a second microreactor was coupled in series. A maximum conversion of 97.6 % and a selectivity of 98.8 % were reached at 340°C, which is close to the calculated values at a thermodynamic equilibrium. A kinetic model based on kinetic experiments and thermodynamic calculations was developed. The model was based on a Langmuir Hinshelwood-type mechanism and a plug flow model for the microreactor. The influence of the reactant adsorption on the catalyst surface was investigated by performing transient experiments and comparing different kinetic models. The obtained activation energy for methyl chloride was ca. two fold higher than the previously published, indicating diffusion limitations in the previous studies. A detailed modeling of the diffusion in the porous catalyst layer revealed that severe diffusion limitations occur starting from catalyst coating thicknesses of 50 μm. At a catalyst coating thickness of ca 15 μm as in the microreactor, the conditions of intrinsic kinetics prevail. Ethanol hydrochlorination was performed successfully in the microreactor system. The reaction temperature was 240-340°C. An almost complete conversion of ethanol was achieved at 340°C. The product distribution was broader than for methanol hydrochlorination. Ethylene, diethyl ether and acetaldehyde were detected as by-products, ethylene being the most dominant by-product. A kinetic model including a thorough thermodynamic analysis was developed and the influence of adsorbed HCl on the reaction rate of ethanol dehydration reactions was demonstrated. The separation of methyl chloride using condensers was investigated. The proposed microreactor-condenser concept enables the production of methyl chloride with a high purity of 99%.

Fusion weld metal solidification:Continuum from weld interface to centerline

We present a brief résumé of the history of solidification research and key factors affecting the solidification of fusion welds. There is a general agreement of the basic solidification theory, albeit differing - even confusing - nomenclatures do exist, and Cases 2 and 3 (the Chalmers' basic boundary conditions for solidification, categorized by Savage as Cases) are variably emphasized. Model Frame, a tool helping to model the continuum of fusion weld solidification from start to end, is proposed. It incorporates the general solidification models, of which the pertinent ones are selected for the actual modeling. The basic models are the main solidification Cases 1…4. These discrete Cases are joined with Sub-Cases: models of Pfann, Flemings and others, bringing needed Sub-Case variables into the model. Model Frame depicts a grain growing from the weld interface to its centerline. Besides modeling, the Model Frame supports education and academic debate. The new mathematical modeling techniques will extend its use into multi-dimensional modeling, introducing new variables and increasing the modeling accuracy. We propose a model: melting/solidification-model (M/S-model) - predicting the solute profile at the start of the solidification of a fusion weld. This Case 3-based Sub-Case takes into account the melting stage, the solute back-diffusion in the solid, and the growth rate acceleration typical to fusion welds. We propose - based on works of Rutter & Chalmers, David & Vitek and our experimental results on copper - that NEGS-EGS-transition is not associated only with cellular-dendritic-transition. Solidification is studied experimentally on pure and doped copper with welding speed range from 0 to 200 cm/min, with one test at 3000 cm/min. Found were only planar and cellular structures, no dendrites - columnar or equiaxed. Cell sub structures: rows of cubic elements we call "cubelettes", "cell-bands" and "micro-cells", as well as an anomalous crack morphology "crack-eye", were detected, as well as microscopic hot crack nucleus we call "grain-lag cracks", caused by a grain slightly lagging behind its neighbors in arrival to the weld centerline. Varestraint test and R-test revealed a change of crack morphologies from centerline cracks to grainand cell boundary cracks with an increasing welding speed. High speed made the cracks invisible to bare eye and hardly detectable with light microscope, while electron microscope often revealed networks of fine micro-cracks.

Detection of Pathologic Changes Following Traumatic Brain Injury Using Magnetic Resonance Imaging

Background: Approximately two percent of Finns have sequels after traumatic brain injury (TBI), and many TBI patients are young or middle-aged. The high rate of unemployment after TBI has major economic consequences for society, and traumatic brain injury often has remarkable personal consequences, as well. Structural imaging is often needed to support the clinical TBI diagnosis. Accurate early diagnosis is essential for successful rehabilition and, thus, may also influence the patient’s outcome. Traumatic axonal injury and cortical contusions constitute the majority of traumatic brain lesions. Several studies have shown magnetic resonance imaging (MRI) to be superior to computed tomography (CT) in the detection of these lesions. However, traumatic brain injury often leads to persistent symptoms even in cases with few or no findings in conventional MRI. Aims and methods: The aim of this prospective study was to clarify the role of conventional MRI in the imaging of traumatic brain injury, and to investigate how to improve the radiologic diagnostics of TBI by using more modern diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) techniques. We estimated, in a longitudinal study, the visibility of the contusions and other intraparenchymal lesions in conventional MRI at one week and one year after TBI. We used DWI-based measurements to look for changes in the diffusivity of the normal-appearing brain in a case-control study. DTI-based tractography was used in a case-control study to evaluate changes in the volume, diffusivity, and anisotropy of the long association tracts in symptomatic TBI patients with no visible signs of intracranial or intraparenchymal abnormalities on routine MRI. We further studied the reproducibility of different tools to identify and measure white-matter tracts by using a DTI sequence suitable for clinical protocols. Results: Both the number and extent of visible traumatic lesions on conventional MRI diminished significantly with time. Slightly increased diffusion in the normal-appearing brain was a common finding at one week after TBI, but it was not significantly associated with the injury severity. Fractional anisotropy values, that represent the integrity of the white-matter tracts, were significantly diminished in several tracts in TBI patients compared to the control subjects. Compared to the cross-sectional ROI method, the tract-based analyses had better reproducibility to identify and measure white-matter tracts of interest by means of DTI tractography. Conclusions: As conventional MRI is still applied in clinical practice, it should be carried out soon after the injury, at least in symptomatic patients with negative CT scan. DWI-related brain diffusivity measurements may be used to improve the documenting of TBI. DTI tractography can be used to improve radiologic diagnostics in a symptomatic TBI sub-population with no findings on conventional MRI. Reproducibility of different tools to quantify fibre tracts vary considerably, which should be taken into consideration in the clinical DTI applications.

Mobile Communications within the European Union: The Role of Location in the Evolution and Forecasting of the Diffusion Process

In the European Union, the importance of mobile communications was realized early on. The process of mobile communications becoming ubiquitous has taken time, as the innovation of mobile communications diffused into the society. The aim of this study is to find out how the evolution and spatial patterns of the diffusion of mobile communications within the European Union could be taken into account in forecasting the diffusion process. There is relatively lot of research of innovation diffusion on the individual (micro) andthe country (macro) level, if compared to the territorial level. Territorial orspatial diffusion refers either to the intra-country or inter-country diffusionof an innovation. In both settings, the dif- fusion of a technological innovation has gained scarce attention. This study adds knowledge of the diffusion between countries, focusing especially on the role of location in this process. The main findings of the study are the following: The penetration rates of the European Union member countries have become more even in the period of observation, from the year 1981 to 2000. The common digital GSM system seems to have hastened this process. As to the role of location in the diffusion process, neighboring countries have had similar diffusion processes. They can be grouped into three, the Nordic countries, the central and southern European countries, and the remote southern European countries. The neighborhood effect is also domi- nating in thegravity model which is used for modeling the adoption timing of the countries. The subsequent diffusion within a country, measured by the logistic model in Finland, is af- fected positively by its economic situation, and it seems to level off at some 92 %. Considering the launch of future mobile communications systemsusing a common standard should implicate an equal development between the countries. The launching time should be carefully selected as the diffusion is probably delayed in economic downturns. The location of a country, measured by distance, can be used in forecasting the adoption and diffusion. Fi- nally, the result of penetration rates becoming more even implies that in a relatively homoge- nous set of countries, such as the European Union member countries, the estimated final pene- tration of a single country can be used for approximating the penetration of the others. The estimated eventual penetration of Finland, some 92 %, should thus also be the eventual level for all the European Union countries and for the European Union as a whole.

Diffusion of Administrative Innovation: TQM Implementation and Effectiveness in a Global

The main objective of this dissertation is to create new knowledge on an administrative innovation, its adoption, diffusion and finally its effectiveness. In this dissertation the administrative innovation is approached through a widely utilized management philosophy, namely the total quality management (TQM) strategy. TQM operationalizes a self-assessment procedure, which is based on continual improvement principles and measuring the improvements. This dissertation also captures the theme of change management as it analyzes the adoption and diffusion of the administrative innovation. It identifies innovation characteristics as well as organisational and individual factors explaining the adoption and implementation. As a special feature, this study also explores the effectiveness of the innovation based on objective data. For studying the administrative innovation (TQM model), a multinational Case Company provides a versatile ground for a deep, longitudinal analysis. The Case Company started the adoption systematically in the mid 1980s in some of its units. As part of their strategic planning today, the procedure is in use throughout the entire global company. The empirical story begins from the innovation adoption decision that was made in the Case Company over 22 years ago. In order to be able to capture the right atmosphere and backgrounds leading to the adoption decision, key informants from that time were interviewed, since the main target was to clarify the dynamics of how an administrative innovation develops. In addition, archival material was collected and studied, available memos and data relating to the innovation, innovation adoption and later to the implementation contained altogether 20500 pages of documents. A survey was furthermore conducted at the end of 2006 focusing on questions related to the innovation, organization and leadership characteristics and the response rate totalled up to 54%. For measuring the effectiveness of the innovation implementation, the needed longitudinal objective performance data was collected. This data included the profit unit level experience of TQM, the development of the self assessment scores per profit unit and performance data per profit unit measured with profitability, productivity and customer satisfaction. The data covered the years 1995-2006. As a result, the prerequisites for the successful adoption of an administrative innovation were defined, such as the top management involvement, support of the change agents and effective tools for implementation and measurement. The factors with the greatest effect on the depth of the implementation were the timing of the adoption and formalization. The results also indicated that the TQM model does have an effect on the company performance measured with profitability, productivity and customer satisfaction. Consequently this thesis contributes to the present literature (i) by taking into its scope an administrative innovation and focusing on the whole innovation implementation process, from the adoption, through diffusion until its consequences, (ii) because the studied factors with an effect on the innovation adoption and diffusion are multifaceted and grouped into individual, organizational and environmental factors, and a strong emphasis is put on the role of the individual change agents and (iii) by measuring the depth and consistency of the administrative innovation. This deep analysis was possible due to the availability of longitudinal data with triangulation possibilities.

Diffusion of Smart Meters in Central East Europe

The present study deals with innovation diffusion as the central component of innovation process and takes smart meters as a concrete example from the electric power industry. Smart meters are seen as key enablers of the industry-wide shift towards smart grids and are recognized by the European Union as means of reaching its environmental and energy goals. However, the spread of smart meters through the market, especially in Central East Europe (CEE), is not corresponding to the expectations and identified benefits. The current work synthesizes available data for the under-researched geographical region of CEE and clarifies the process of smart meter diffusion and drivers behind it. In addition to innovation theories the methods applied are rate of adoption and thematic analysis. The results prove the large gap between optimal and actual diffusion as well as the lagging position of CEE in comparison to the EU’s market leaders. The smart metering market is driven from bottom-up and the majority of CEE countries have already carried out or started the initial activities. Therefore, in coming years more intensive smart meters deployment will be seen.

Immobilization of Burkholderia cepacia Lipase: Kinetic Resolution in Organic Solvents, Ionic Liquids and in Their Mixtures

Immobilization of Burkholderia cepacia Lipase: Kinetic Resolution in Organic Solvents, Ionic Liquids and in Their Mixtures Biocatalysis opens the door to green and sustainable processes in synthetic chemistry allowing the preparation of single enantiomers, since the enzymes are chiral and accordingly able to catalyze chemical reactions under mild conditions. Immobilization of enzymes enhances process robustness, often stabilizes and activates the enzyme, and enables reuse of the same enzyme preparation in multiple cycles. Although hundreds of variations of immobilization methods exist, there is no universal method to yield the highly active, selective and stable enzyme catalysts. Therefore, new methods need to be developed to obtain suitable catalysts for different substrates and reaction environments. Lipases are the most widely used enzymes in synthetic organic chemistry. The literature part together with the experimental part of this thesis discusses of the effects of immobilization methods mostly used to enhance lipase activity, stability and enantioselectivity. Moreover, the use of lipases in the kinetic resolution of secondary alcohols in organic solvents and in ionic liquids is discussed. The experimental work consists of the studies of immobilization of Burkholderia cepacia lipase (lipase PS) using three different methods: encapsulation in sol-gels, cross-linked enzyme aggregates (CLEAs) and supported ionic liquids enzyme catalysts (SILEs). In addition, adsorption of lipase PS on celite was studied to compare the results obtained with sol-gels, CLEAs and SILEs. The effects of immobilization on enzyme activity, enantioselectivity and hydrolysis side reactions were studied in kinetic resolution of three secondary alcohols in organic solvents, in ionic liquids (ILs), and in their mixtures. Lipase PS sol-gels were shown to be active and stable catalysts in organic solvents and solvent:IL mixtures. CLEAs and SILEs were highly active and enantioselective in organic solvents. Sol-gels and SILEs were reusable in several cycles. Hydrolysis side reaction was suppressed in the presence of sol-gels and CLEAs.

Modelling of ultrasound assisted mixing in Newtonian and non-Newtonian liquids

The purpose of this work is to obtain a better understanding of behaviour of possible ultrasound appliance on fluid media mixing. The research is done in the regard to Newtonian and non-Newtonian fluids. The process of ultrasound appliance on liquids is modelled in COMSOL Multiphysics software. The influence of ultrasound using is introduced as waveform equation. Turbulence modelling is fulfilled by the k-ε model in Newtonian fluid. The modeling of ultrasound assisted mixing in non-Newtonian fluids is based on the power law. To verify modelling results two practical methods are used: Particle Image Velocimetry and measurements of mixing time. Particle Image Velocimetry allows capturing of velocity flow field continuously and presents detailed depiction of liquid dynamics. The second way of verification is the comparison of mixing time of homogeneity. Experimentally achievement of mixing time is done by conductivity measurements. In modelling part mixing time is achieved by special module of COMSOL Multiphysics – the transport of diluted species. Both practical and modelling parts show similar radial mechanism of fluid flow under ultrasound appliance – from the horn tip fluid moves to the bottom and along the walls goes back. Velocity profiles are similar in modelling and experimental part in the case of Newtonian fluid. In the case of non-Newtonian fluid velocity profiles do not agree. The development track of ultrasound-assisted mixing modelling is presented in the thesis.