Optical nephelometry is the measurement of the angular distribution of light scattered from a particle suspension. Experimental nephelometers confirm the predictions of optical models and their readings are inverted to determine properties of unknown suspensions. Single scattering models, which assume a single particle interaction prior to detection, are used to model tenuous suspensions in the nephelometer. Multiple scattering models can be used to obtain higher-order solutions, but lack generality. Any given method addresses some subset of possible problems, e.g. tenuous or dense suspensions, small or large particles. This thesis explores the feasibility of using empirical models to extrapolate the single scattering approach in a non-linear manner, improving the generality of a multiple-scattering description. Initially, single scattering (Mie) theory for spherical particles is presented and extended to polydispersions of particles and to spectral scattering. The principle of integrating the single scattering result over a finite scattering volume is examined as a precursor to modelling the actual nephelometer. A low-cost, PC controlled scanning nephelometer is developed with a 0.9° resolution and ±150° range and a small (-25ml) volume sample cell. The photodiode detector has a numerical aperture of 0.079, providing, for most angles, a scattering volume with length 10mm and cross-section determined by the HeNe laser source ('-1mrn 2). The optics of the air/glass/water interfaces and of single and first-order multiple scattering over the scattering volume are modelled. These models are found to predict the scattering footprints observed in tenuous suspensions of spherical latex particles. Experimental data are obtained from tenuous to relatively dense (5% by volume) suspensions of latex spheres over a size range of 54nm to 14tm. These data are compared with single and first-order multiple scattering and their form and dependencies are considered. They are used to train an empirical neural (multi-layer perceptron) model of the multiple scattering based on particle characteristics and on the scattering footprint of the individual particles. This non-linear extrapolation of the single scattering model is applied to the nephelometer, improving the generality over a purely theoretical multiple scattering approach. The trained neural model is used, initially, to investigate some of the empirical characteristics of the multiple scattering process.

Este trabalho estudou a aplicação de oito métodos clássicos de escalonamento de tanques condicionadores, testando sua validade para dois tanques de geometria semelhante, mas com diferentes volumes (V1=10 e V2=49 decímetros cúbicos). No interior dos tanques, operavam impulsores (diâmetro D1=0,078m x D2=0,132m) que exibiam três distintos desenhos (2 pás versus 4 pás inclinadas em 45 graus versus turbina de Rushton). Sua rotação (N1 no tanque menor x N2 no tanque maior) visava à suspensão de partículas grossas de apatita (diâmetro médio = 254 micrometros) em polpas com 40% de sólidos em massa. Para balizar o escalonamento, adotou-se como variável de controle a mínima rotação do impulsor (Njs) que é capaz de fazer com que nenhuma partícula repouse no fundo do tanque por mais do que 1 ou 2 segundos (Critério 1-s), além de perfis axiais de distribuição de sólidos e a extensão da Zona Turbulenta versus Zona Quiescente no interior dos tanques. A diferença entre o valor previsto de Njs para o tanque de 49 decímetros cúbicos (N2) pelos métodos de escalonamento versus o valor de Njs (N2) determinado experimentalmente foi expressa como erro percentual (E). Consideraram-se como adequados para a aplicação que constitui o objetivo desta dissertação todos os métodos que exibiram E menor que 10%. Para o impelidor de 2 pás inclinadas, a adequação do método baseado na constância da razão potência/volume (E=2%) e também do método empírico de Rautzen (E=6%), indica a expressão N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros variando entre 0,67 e 0,75 para a aplicação desejada. Considerando o impulsor de 4 pás inclinadas, a adequação do método da constância da razão potência/volume (E=4%); assim como dos métodos empíricos de Rautzen (E=0%) e Zwietering (5%), sugere o uso da expressão N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros variando entre 0,67 e 0,85. Para a turbina de Rushton, o único método que exibiu E menor que 10% foi o da constância da relação potência/volume (E=8%), cuja expressão é N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros igual a 0,67. Uma vez que a determinação do valor real de N2 foi baseada numa técnica experimental influenciada pelas limitações do observador, pode-se inferir que uma expressão geral de escalonamento do tipo N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros igual a 0,75 atende aos propósitos desta aplicação. Por outro lado, o uso da relação P/V provê um critério mais objetivo para se balizar o escalonamento, haja vista que ele se adequou a todos os três tipos de impelidores contemplados por este estudo. / This work has studied the application of eight classical methods appointed by literature to accomplish the scale-up of stirred tanks which aimed to suspend slurries of 40% of solids, containing coarse (mean diameter=254 micrometers) apatite particles. The validity of the methods was accomplished by using two tanks of similar geometry but different capacity (V1=10 e V2=49 cubic decimeter), together with impellers of different diameter (D1=0,078m versus D2=0,132m) and design (turbine of 2 or 4 blades inclined at 45 degrees and Rushton turbine). To assist the process of validation, the impeller speed (Njs) under which no particle rests on the bottom of the tank for more than 1-2 seconds (1-s Criterium) was used together with the axial profile of solids percent distribution plus the extension of the turbulent versus quiescent zones within the two tanks. For any of the eight scale-up methods, the difference between the predicted value of Njs (N2) for the 49 cubic decimeter tank and the actual value (experimental) of the same variable was determined and its magnitude was expressed in terms of the percent error (E). The methods that yielded E less than 10% were considered as suitable for the aimed application. Considering the 2-inclined blade impeller, low value of E yielded by the method based on the constancy of the ratio power/volume (E=2%) and also by the empiric method of Rautzen (E=6%) indicate that the expression N2=N1.(D1/D2) with its exponent of the relation between diameters ranging between 0,67 and 0,75 is suitable for the desired application. Regarding the 4-inclined blade impeller, because the method based on the constancy of the ratio power/volume (E=4%) and also the empiric methods of Rautzen (E=0%) and Zwietering (E=5%) yielded the lowest values of E, the expression N2=N1.(D1/D2) with its exponent of the relation between diameters ranging between 0,67 and 0,85 is suitable for the aimed application. Moreover, for the Rusthon turbine, only the method based on the constancy of the ratio power/volume (E=8%) was adequate for the aimed application and, thus, the expression N2=N1.(D1/D2) with its exponent of the relation between the diameters equal to 0,67 is suitable for the purpose of this dissertation. Once the actual value of N2 is determined by visual observation, it is not possible to get very accurate results. This way, a generic scale-up expression is proposed: N2=N1.(D1/D2) with its exponent of the relation between the diameters equal to 0,75. On the other hand, the ratio P/V may provide a more objective criterium for scale-up, because the three sort of impellers used in this study yielded E less than 10% when the power/volume method was applied for the purpose of scale-up.

Este trabalho estudou a aplicação de oito métodos clássicos de escalonamento de tanques condicionadores, testando sua validade para dois tanques de geometria semelhante, mas com diferentes volumes (V1=10 e V2=49 decímetros cúbicos). No interior dos tanques, operavam impulsores (diâmetro D1=0,078m x D2=0,132m) que exibiam três distintos desenhos (2 pás versus 4 pás inclinadas em 45 graus versus turbina de Rushton). Sua rotação (N1 no tanque menor x N2 no tanque maior) visava à suspensão de partículas grossas de apatita (diâmetro médio = 254 micrometros) em polpas com 40% de sólidos em massa. Para balizar o escalonamento, adotou-se como variável de controle a mínima rotação do impulsor (Njs) que é capaz de fazer com que nenhuma partícula repouse no fundo do tanque por mais do que 1 ou 2 segundos (Critério 1-s), além de perfis axiais de distribuição de sólidos e a extensão da Zona Turbulenta versus Zona Quiescente no interior dos tanques. A diferença entre o valor previsto de Njs para o tanque de 49 decímetros cúbicos (N2) pelos métodos de escalonamento versus o valor de Njs (N2) determinado experimentalmente foi expressa como erro percentual (E). Consideraram-se como adequados para a aplicação que constitui o objetivo desta dissertação todos os métodos que exibiram E menor que 10%. Para o impelidor de 2 pás inclinadas, a adequação do método baseado na constância da razão potência/volume (E=2%) e também do método empírico de Rautzen (E=6%), indica a expressão N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros variando entre 0,67 e 0,75 para a aplicação desejada. Considerando o impulsor de 4 pás inclinadas, a adequação do método da constância da razão potência/volume (E=4%); assim como dos métodos empíricos de Rautzen (E=0%) e Zwietering (5%), sugere o uso da expressão N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros variando entre 0,67 e 0,85. Para a turbina de Rushton, o único método que exibiu E menor que 10% foi o da constância da relação potência/volume (E=8%), cuja expressão é N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros igual a 0,67. Uma vez que a determinação do valor real de N2 foi baseada numa técnica experimental influenciada pelas limitações do observador, pode-se inferir que uma expressão geral de escalonamento do tipo N2=N1.(D1/D2) com seu expoente da relação entre os diâmetros igual a 0,75 atende aos propósitos desta aplicação. Por outro lado, o uso da relação P/V provê um critério mais objetivo para se balizar o escalonamento, haja vista que ele se adequou a todos os três tipos de impelidores contemplados por este estudo. / This work has studied the application of eight classical methods appointed by literature to accomplish the scale-up of stirred tanks which aimed to suspend slurries of 40% of solids, containing coarse (mean diameter=254 micrometers) apatite particles. The validity of the methods was accomplished by using two tanks of similar geometry but different capacity (V1=10 e V2=49 cubic decimeter), together with impellers of different diameter (D1=0,078m versus D2=0,132m) and design (turbine of 2 or 4 blades inclined at 45 degrees and Rushton turbine). To assist the process of validation, the impeller speed (Njs) under which no particle rests on the bottom of the tank for more than 1-2 seconds (1-s Criterium) was used together with the axial profile of solids percent distribution plus the extension of the turbulent versus quiescent zones within the two tanks. For any of the eight scale-up methods, the difference between the predicted value of Njs (N2) for the 49 cubic decimeter tank and the actual value (experimental) of the same variable was determined and its magnitude was expressed in terms of the percent error (E). The methods that yielded E less than 10% were considered as suitable for the aimed application. Considering the 2-inclined blade impeller, low value of E yielded by the method based on the constancy of the ratio power/volume (E=2%) and also by the empiric method of Rautzen (E=6%) indicate that the expression N2=N1.(D1/D2) with its exponent of the relation between diameters ranging between 0,67 and 0,75 is suitable for the desired application. Regarding the 4-inclined blade impeller, because the method based on the constancy of the ratio power/volume (E=4%) and also the empiric methods of Rautzen (E=0%) and Zwietering (E=5%) yielded the lowest values of E, the expression N2=N1.(D1/D2) with its exponent of the relation between diameters ranging between 0,67 and 0,85 is suitable for the aimed application. Moreover, for the Rusthon turbine, only the method based on the constancy of the ratio power/volume (E=8%) was adequate for the aimed application and, thus, the expression N2=N1.(D1/D2) with its exponent of the relation between the diameters equal to 0,67 is suitable for the purpose of this dissertation. Once the actual value of N2 is determined by visual observation, it is not possible to get very accurate results. This way, a generic scale-up expression is proposed: N2=N1.(D1/D2) with its exponent of the relation between the diameters equal to 0,75. On the other hand, the ratio P/V may provide a more objective criterium for scale-up, because the three sort of impellers used in this study yielded E less than 10% when the power/volume method was applied for the purpose of scale-up.

Particle breakage can be significant in stirred vessels such as crystallizers. During crystallization, particle breakage can occur due to particle contact with other particles, the impeller, the suspension fluid, and/or the vessel. Such breakage produces fines and can cause filter plugging downstream. Although research has been conducted with respect to particle breakage, a comprehensive study is still needed to quantify the breakage occurring in stirred vessels. The overall goal of this research is to model the particle breakage occurring in a stirred vessel by analyzing the particle size and shape distributions that result from breakage. Breakage experiments are based on collision influences that affect the two dominant collisions types, crystal-to-crystal and crystal-to-impeller collisions. Results showed that the quantity of fines produced are affected by the solids concentration or magma density and suspension fluid utilized. Additionally, aqueous saturated solutions produced particle size distributions that differ from those obtained using a nonsolvent. Similar particle size distributions for two different materials (NaCl and KCl) are achieved in the same nonsolvent (acetonitrile) by adjusting the agitation rate using the Zwietering correlation to account for property differences; moreover, the same agitation rate adjustment produced similar distributions for KCl in acetone and acetonitrile which were both nonsolvents. However, modifications to the Zwietering correlation, such as changing the significance of the initial particle size, are proposed before this method of adjustment is deemed accurate. Number-based population modeling of particle breakage is achieved within 1-5% error for NaCl at each agitation rate investigated. Breakage modeling using a discretized population balance equation with Austin's equation for attrition and the power law form of the product function for fragmentation is a viable approach; however, more work is needed to increase the accuracy of this model.

In this thesis, a new technique for using quartz crystal microbalance (QCM) in magnetic field was explored. This technique would take advantage of the sensitive nature of QCM to vibration changes. The idea is to perturb the QCM vibrations with magnetic materials on it by applying magnetic field. A new instrument called magnetic QCM (MQCM) was constructed to explore this technique. The thesis contains three bodies of work. The first body describes the development of the MQCM instrument and the demonstration of the technique. The resonance frequency of a QCM with conducting polymer (polyaniline) suspension in poly(ethylene glycol) was observed to increase with increasing applied DC magnetic field. The change in population of free spins through doping with HCl vapor is reflected in increased frequency-field curve magnitude. The second body of work describes the study of QCM proximity phenomenon discovered during the MQCM instrument development process. When an object approaches a vibrating QCM, the resonant frequency changes. This proximity effect is seen at the distance of 10 mm in air and becomes more pronounced as the distance decreases. This effect depends on the value of quality factor, conductivity of the object, and electrical connection of the object to the QCM electrodes. A simple modified Butterworth van-Dyke model is used to describe this effect. It must be recognized that this effect may lead to experimental artifacts in a variety of analytical QCM applications. The third body of work describes an improved version of MQCM. The complex geometry such as particle suspension were simplified to alternating stack of ferromagnetic and diamagnetic layers. When magnetic field was applied, changes in the QCM admittance magnitude and phase curves were observed. A mass-equivalent stack of continuous consecutive layers of nickel and gold was also exposed to magnetic field but no changes were observed. Butterworth-van-Dyke model attributed the effect to internal shear friction loss among other losses is modulated by the magnetic field. Quantum effect was considered. However, after examining SEM surface images, the source of acoustic response to magnetic field is more likely from interfacial stresses.