The dynamic behaviour of liquid-liquid agitated dispersions—I. The hydrodynamics

Ribeiro, Lígia Maria; Regueiras, P.F.R.; Guimarães, M.M.L.; Madureira, C.M.N.; Cruz-Pinto, J.J.C.

doi:10.1016/0098-1354(94)00054-r

Cited by 28 publications

(25 citation statements)

References 16 publications

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“…Therefore, these values are considered universal and will be kept unchanged throughout this investigation. However, the value of these constants were found to be several orders of magnitude larger than those obtained by previous authors who used the same model to simulate liquid-liquid dispersions using MATs [50,[54][55][56][57]. The discrepancy depicted in Table 5 is most probably due to the simplifying assumptions used by these authors in which they assumed a uniform local energy dissipation rate throughout the entire volume of the MAT.…”

Section: Matching Model Predictions With Experimental Datacontrasting

confidence: 71%

“…However, it is important to add that the model parameters used by Ribeiro et al [57] for example were derived for two different systems whose interfacial tensions ranged from 9 to 32 mN m −1 . Therefore, even though the interfacial characteristics of the system play an important role in determining the extent of the model parameters, the importance of an accurate representation of the energy dissipation rate while characterizing breakage and coalescence processes remains imperative.…”

Section: Matching Model Predictions With Experimental Datamentioning

confidence: 99%

“…8. Since the older sets are of a similar magnitude, those obtained by Ribeiro et al [57] were chosen for the purpose of this comparison. The large discrepancy between the two simulation results is clearly shown in Fig.…”

Section: Matching Model Predictions With Experimental Datamentioning

confidence: 99%

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Turbulently flowing liquid–liquid dispersions. Part I: Drop breakage and coalescence

Azizi¹,

Taweel²

2011

Chemical Engineering Journal

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Section: Matching Model Predictions With Experimental Datacontrasting

confidence: 71%

Section: Matching Model Predictions With Experimental Datamentioning

confidence: 99%

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Turbulently flowing liquid–liquid dispersions. Part I: Drop breakage and coalescence

Azizi¹,

Taweel²

2011

Chemical Engineering Journal

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“…Although experimental techniques are often difficult and tedious to implement, drop size has been the most widely studied aspect of liquid-liquid mixing in agitated vessels and an attractive research area, considering the relative success of the theory and modeling of drop behavior, even for complex phenomena such as coalescence-redispersion [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Non-invasive system and procedures for the characterization of liquid–liquid dispersions

Ribeiro¹

2004

Chemical Engineering Journal

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A novel dispersed phase imaging system for batch/continuous agitated vessels is described in detail, together with the relevant drop-size distribution and data treatment procedures. This system enabled the non-invasive study of toluene-in-water agitated liquid-liquid dispersions. Most of other similar studies are invasive of the system's structure and behavior, which raises questions about the quality of the generated data. Drop-size distributions have been collected and used for testing the representativeness and stability of the samples obtained, and positively assess the physical meaningfulness of the results through the effects of the main operating variables-mean residence time, agitation intensity and dispersed phase hold-up. Inter-drop coalescence clearly shows its effects even in very lean agitated dispersions, and thus cannot be neglected; its modeling, however, is still very much an open question as will be shown in another paper.

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“…Os métodos de diferença finita no domínio das partículas são usados com muita freqüência na literatura para a discretização, como nos ensina RIBEIRO et al (1995).…”

Section: Introductionunclassified

Estudo do problema inverso em balanço populacional aplicado a degradação de polímeros.

Uliana¹

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Uliana, MuriloEstudo do problema inverso em balanço populacional aplicado a degradação de polímeros / M. Uliana. SATHYAGAL et al. (1995) e a obtida no presente trabalho usando o algoritmo do problema inverso, para o casoestudo 1; (b) Distribuição de partículas filhas obtida no presente trabalho para o casoestudo 1. σ -desvio padrão φ -Função para minimização na equação (3.4.2.28) dentro da função objetivo. Palavras-chave: taxa de quebra, balanço populacional, problema inverso, polímeros, modelagem. xiv ABSTRACT.Computational algorithms are used to obtain quantitative information from experimental observations. The aim of the present work was the application of the methodology of inverse problem in population balance used to describe the evolution of the chain length distribution in different polymer degradation processes. The time evolution of the chain length distribution during the polymer breakage can be mathematically described by a population balance equation.In the so-called inverse problem, experimentally measured distributions are used to estimate the parameters of the population balance, such as the distribution of breakage rate along the chain and as function of the chain length. The inverse problem is known to be an ill-conditioned numerical problem. An algorithm previously developed in the literature for liquid droplet breakage in liquid emulsions, based on the concept of self-similarity of the distributions, was adapted and applied in the present work for the problem of polymer scission during polymer degradation. Nestes estudos têm se observado que, para um tempos longos (t→∞), a distribuição atinge o estado estacionário sem ocorrer mais mudanças. Para uma fragmentação binária, dois fragmentos por partículas, a restrição acima é simplificada. Sendo equivalente a uma taxaUma expressão para a taxa, em que as partículas de tamanho v são formadas devido à quebra, pode ser deduzida para um caso simples de quebra binária: A taxa de geração de partículas de tamanho v é igual à soma de todos os tamanhos maiores que v, visto que, partículas menores são formadas pela quebra, de partículas maiores: Com as equações (1.1.2) e (1.1.3), podemos escrever um balanço populacional de quebra em (1.1.5) ou, de outro modo, uma formulação para o caso da quebra dominante, como descrito por PATRUNO et al. (2009). Este balanço só será apresentado mais adiante, após outras considerações.Os métodos de diferença finita no domínio das partículas são usados com muita freqüência na literatura para a discretização, como nos ensina RIBEIRO et al. (1995).Recentemente para a solução do BP foi desenvolvido no trabalho de HAGESAETHER; JAKOBSEN; SVENDSEN (2002) Dessa forma, a função de quebra também será discretizada, e resultando em β(v i ,v j ). O sucesso no uso das equações fundamentais de balanço populacional para predizer quantitativamente a distribuição de partículas em um sistema em que a quebra é dominante requer duas funções chave: a taxa de quebra que corresponde a um valor para cada volume 5 de partícula, e a distribu...

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The dynamic behaviour of liquid-liquid agitated dispersions—I. The hydrodynamics

Cited by 28 publications

References 16 publications

Turbulently flowing liquid–liquid dispersions. Part I: Drop breakage and coalescence

Turbulently flowing liquid–liquid dispersions. Part I: Drop breakage and coalescence

Non-invasive system and procedures for the characterization of liquid–liquid dispersions

Estudo do problema inverso em balanço populacional aplicado a degradação de polímeros.

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