Motion of a bubble in a viscous liquid

Golovin, A. M.; Иванов, М. Ф.

doi:10.1007/bf00853987

Cited by 10 publications

(7 citation statements)

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“…The formulation in eq 90 is further corrected by Moore 217 by taking into account the boundary layer thickness at different surface regions of a bubble. Several numerical attempts in this direction can be seen in the literature. − It is known that C D decreases linearly with increase in Re. The most general formulation for C D can be given as i.e., for the case of passage of gas bubble into liquid, value of the term in bracket is negligible and correlation tends to C D = 16/ Re , whereas for the case of solid−liquid system, C D ≈ 24/ Re .…”

Section: Bubble Rise Velocity In Liquidmentioning

confidence: 99%

“…Several numerical attempts in this direction can be seen in the literature. [218][219][220][221][222][223][224][225][226] It is known that C D decreases linearly with increase in Re. The most general formulation for C D can be given as i.e., for the case of passage of gas bubble into liquid, value of the term in bracket is negligible and correlation tends to C D ) 16/Re, whereas for the case of solid-liquid system, C D ≈ 24/Re.…”

Section: Comparison Of Correlation For Bubble Rise Velocity In Pure A...mentioning

confidence: 99%

“…The different correlations for drag coefficient by several investigators (discussed here and also given in Table 5) when put together on the same plot could not clearly bring out their distinct features (due to several overlaps) and hence here we prefer to discuss the nature of different drag curves from the various correlations and their rage of validity. An empirical drag law (given in Table 5) was proposed by Mei and Klausner 225 is considered to yield accurate drag coefficient at almost all Re. In a recent attempt, Tomiyama et al, 236 have developed a generalized correlation with four coefficients and it gives an excellent match with the whole drag curve.…”

Section: Comparison Of Correlation For Bubble Rise Velocity In Pure A...mentioning

confidence: 99%

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Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review

Kulkarni

Joshi

2005

Ind. Eng. Chem. Res.

677

310

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The formation of gas bubbles and their subsequent rise due to buoyancy are very important fundamental phenomena that contribute significantly to the hydrodynamics in gas-liquid reactors. The rise of a bubble in dispersion can be associated with possible coalescence and dispersion followed by its disengagement from the system. The phenomenon of bubble formation decides the primitive bubble size in the system (which latter attains an equilibrium size), whereas the rise velocity decides the characteristic contact time between the phases which governs the interfacial transport phenomena as well as mixing. In view of their importance, we herein present a comprehensive review of bubble formation and bubble rise velocity in gas-liquid systems. The emphasis of this review is to illustrate the present status of the subjects under consideration and to highlight the possible future directions for further understanding of the subject. The bubble formation at a single submerged orifice and on multipoint sieve trays in Newtonian as well as non-Newtonian stagnant and flowing liquids is discussed in detail, which includes its mechanism as well as the effect of several system and operating parameters on the bubble size. The comparison of results has shown that the formulation of Gaddis and Vogelpohl 22 is the most suitable for the estimation of bubble size in stagnant liquids. The special cases, such as bubble formation in reduced gravity conditions and weeping and in flowing liquids, are discussed in detail. The section on the rise of a gas bubble in liquid covers the various parameters governing bubble rise and their effect on the rise velocity. A comprehensive comparison of the various formulations is made by validating the predictions with experimental data for Newtonian as well as non-Newtonian liquids, published over last several decades. The results highlight that for the estimation of rise velocity in (i) pure Newtonian liquids, (ii) contaminated Newtonian liquids, and (iii) non-Newtonian liquids, the formulation based on the wave theory by Mendelson,190 Nguyen's formulation, 155 and the formulation by Rodrigues, 153 (last two, based on the dimensional analysis), respectively are the most suitable. The motion of bubbles in non-Newtonian liquids and the reason behind the discontinuity in the velocity are also discussed in detail. The bubble rise is also analyzed in terms of the drag coefficient for different system parameters and bubble sizes.

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Section: Bubble Rise Velocity In Liquidmentioning

confidence: 99%

Section: Comparison Of Correlation For Bubble Rise Velocity In Pure A...mentioning

confidence: 99%

Section: Comparison Of Correlation For Bubble Rise Velocity In Pure A...mentioning

confidence: 99%

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Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review

Kulkarni

Joshi

2005

Ind. Eng. Chem. Res.

677

310

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“…La expresión ha sido probada para . En este régimen de flujo, no pueden utilizarse la corrección de Oseen (Golovin y Ivanov, 1973) ). Por lo tanto, debido a la inexistencia de expresiones analíticas en el régimen de flujo estudiado, la expresión obtenida en este trabajo puede ser usada como una aproximación inicial.…”

Section: Conclusionesunclassified

Modelo Hidrodinámico para la Velocidad de un Par de Burbujas Ascendiendo en Línea

2007

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ResumenSe presenta un análisis hidrodinámico de la interacción de dos burbujas esféricas del mismo tamaño alineadas en la dirección de un flujo uniforme, laminar, newtoniano e incompresible. La burbuja puntera se considera aislada y la burbuja acarreada (segunda burbuja) está sujeta a la acción de cuatro fuerzas: flotación, arrastre cuasiestacionario, impulso del fluido y masa agregada. Aplicando un balance de fuerzas sobre cada burbuja se obtuvo una nueva expresión para la velocidad de ascenso de la burbuja acarreada. La expresión se comparó con mediciones experimentales, realizadas por otros autores citados en la literatura, para números de Reynolds de 3.06, 21.5 y 35.4 y se obtuvo un error relativo promedio entre 1.2% y 2.1%. Se discuten dos alternativas para aproximar la reducción del arrastre sobre la burbuja acarreada. Se encontró que el arrastre cuasiestacionario no puede incorporar el efecto total de la estela sobre la burbuja acarreada.Palabras clave: modelo hidrodinámico, velocidad de burbujas, efecto de la estela, arrastre Hydrodynamic Model for the Velocity of a Bubble Pair Rising In-line AbstractA hydrodynamic analysis on the interaction of two equal-size spherical bubbles aligned on the direction of a uniform, laminar, newtonian and incompressible flow, is presented. The leading bubble is considered as an isolated bubble and the trailing bubble (second bubble) is subjected to four forces: buoyancy, quasisteady drag, fluid impulse and added mass. By applying a force balance on each bubble, an expression for the rising velocity of the trailing bubble was obtained. Comparison of this expression with existing experimental data for 3.06, 21.5 and 35.4 Reynolds number was performed, obtaining a relative average error between 1.2% and 2.1%. Two possible approaches on the trailing bubble drag reduction effect are discussed. It was found that a quasisteady drag is, by itself, unable to incorporate the whole wake effect on the trailing bubble.

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“…Batchelor, 1967;Clift y col., 1987). La solución correspondiente para una burbuja que cumple con la restricción de esfuerzo tangencial nulo sobre la superficie de la burbuja fue obtenida por Golovin y Ivanov (1973).…”

Section: Soluciones Analíticas Para El Flujo Detrás De Una Partícula ...unclassified

Interacción hidrodinámica de un cuerpo esférico con la estela laminar de otro en un fluido newtoniano con flujo uniforme

Muñoz

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Agradezco a Dios por permitirme la vida y darme salud, a mi amada esposa (Alma) por brindarme todo su apoyo en los momentos difíciles y a mis adorados hijos (Naomi, Jorge y Alma) por inspirarme a seguir adelante y por su comprensión. Agradezco también a mi querida madre y a mis hermanos quienes siempre me han brindado todo su apoyo y cariño.Agradezco al Consejo Nacional de Ciencia y Tecnología (CONACyT) quien financió mis estudios de doctorado (No. becario: 171336) y a la Universidad Autónoma Metropolitana-Iztapalapa.Especial agradecimiento a mi asesor y gran amigo el Dr. Alberto Soria López y a la Dra.Elizabeth Salinas Barrios por sus enseñanzas y toda la confianza que depositaron en mí, a mis sinodales, a mis compañeros del posgrado y a todo el personal de esta universidad.

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Motion of a bubble in a viscous liquid

Cited by 10 publications

References 1 publication

Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review

Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review

Modelo Hidrodinámico para la Velocidad de un Par de Burbujas Ascendiendo en Línea

Interacción hidrodinámica de un cuerpo esférico con la estela laminar de otro en un fluido newtoniano con flujo uniforme

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