A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Xing, Chutian; Wang, Tiefeng; Guo, Kunyu; Wang, Jinfu

doi:10.1002/aic.14709

Cited by 72 publications

(54 citation statements)

References 66 publications

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“…Many breakup models such as those of the works use the classical framework given in Equation , ie, they employ a total breakup rate Ω t ( v ′ ) and a separate continuous function for the daughter size distribution β ( v , v ′ ). Other breakup models, introduce kernels with an incorporated binary daughter size distribution, thereby providing the partial breakup rate Ω p ( v , v ′ ) directly. It is mirror symmetrical about v = v ′ /2 and defined by the product of the total breakup rate and the daughter size distribution

Ω_{p} false(v, v^{'} false) = Ω_{t} false(v^{'} false) β false(v, v^{'} false) .

The Luo breakup model is one of the most widely used partial breakup kernels.…”

Section: Previous Workmentioning

confidence: 99%

A discrete population balance equation for binary breakage

Liao

Oertel

Kriebitzsch

et al. 2018

Numerical Methods in Fluids

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Summary The numerical solution of the population balance equation is frequently achieved by means of discretization, ie, by the method of classes. An important concern of discrete formulations is the preservation of 2 chosen moments of the distribution, eg, numbers and mass, while remaining flexible on the grid and kernels applied. Existing formulations for breakage are either able to perserve only one moment or restricted by the choice of grid and kernels. Two types of kernel functions for the description of breakup rate exist, ie, total breakup model and partial breakup model. The first type states the total breakup rate of a mother particle and requires a daughter size distribution function. The other type gives the breakup rate between a mother and a daughter particle directly. Existing formulations are known to work well for the former type but inefficiently for the latter one due to the need of additional numerical integrations. The particular focus of the present work lies in developing an efficient formulation for this type of kernels. A discrete formulation of the breakup terms due to binary breakage is proposed, which allows a direct implementation of both types of breakup kernels and an efficient solution of the population balance equation, making it favorable for the coupling to computational fluid dynamics codes. The results for a pure breakage process obtained by using the new formulation and various kernels are compared with those by a reference formulation as well as analytical solutions. Good agreement is achieved in all test cases, and numerical efficiency of the new formulation for partial breakup models is evidenced.

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Ω_{p} false(v, v^{'} false) = Ω_{t} false(v^{'} false) β false(v, v^{'} false) .

The Luo breakup model is one of the most widely used partial breakup kernels.…”

Section: Previous Workmentioning

confidence: 99%

A discrete population balance equation for binary breakage

Liao

Oertel

Kriebitzsch

et al. 2018

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…For example, Xing et al 10 put forward a unified mathematical model describing the bubble active breakup in turbulent flows, which predicted well both the effect of pressure/gas density on the bubble breakup rate and the different daughter size distribution. For example, Xing et al 10 put forward a unified mathematical model describing the bubble active breakup in turbulent flows, which predicted well both the effect of pressure/gas density on the bubble breakup rate and the different daughter size distribution.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of bubble breakup in a four‐branched microchannel based on non‐Newtonian pseudoplastic fluid

Fan

et al. 2019

Asia-Pacific J Chem Eng

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Bubble breakup in a four-branched microchannel with carboxymethyl cellulose (CMC) solution was investigated by an improved coupled level set and volume of fluid (CLSVOF) method based on consideration of the rheological characteristic of the fluid. The validity of the numerical approach was satisfactorily verified by comparing with the experimental results. The regime and pattern of bubble breakup were evaluated by analyzing the evolution of bubble morphology. The effects of gas velocity, solution concentration, and subchannel width on daughter bubble length were examined, respectively. The results indicate that three split regimes at the branch comprising expansion, squeezing, and pinch-off stage and three flow patterns including long slug, short slug, and bubble flows can be observed. Daughter

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“…Bubble breakup in a turbulent flow is determined by the hydrodynamic conditions in the surrounding liquid and the characteristic of itself, and four categories of breakup mechanisms have been summarized: turbulence fluctuation, viscous shear stress, shearing‐off process, and interfacial instability . Study on bubble breakup mainly includes macroscopic dispersion analysis and single fluid particle analysis …”

Section: Introductionmentioning

confidence: 99%

“…Garstecki et al found that bubble breakup at the T‐junction microchannel consists of two forms: squeezing regime and dripping regime . Besides, the internal flow through the bubble neck in the breakup process was measured and analyzed, and a mathematical model was proposed based on the Young–Laplace and Bernoulli equations …”

Section: Introductionmentioning

confidence: 99%

Single bubble breakup in the flow field induced by a horizontal jet—The experimental research

Feng

Cao

Jiang

et al. 2018

Asia-Pacific J Chem Eng

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Bubble breakup in multiphase reactors has a direct and important impact on the mass transfer and reaction process. This paper experimentally investigated the single bubble behaviors of deformation and breakup under the affecting of a jet submerged in a water‐filled tank. The dispersed phase motion was captured by a high speed camera, while the continuous phase flow field was analyzed by Particle Image Velocimetry. By changing the downstream location of bubble generation, the liquid flow rate and the initial bubble size, the breakup processes were analyzed and discussed. The breakup point, break pattern, and distribution of daughter bubbles were summarized. The position where the bubble gets the maximum acceleration was defined as the shear position, and the forces on the bubble at the shear position had a significant impact on whether breakup will occur. The expected bubble number, which could reflect a combination of the breakup probability and daughter bubbles distribution, was defined and found to be directly proportional to the capillary number of bubbles at the shear position. The research result will contribute to promoting the understanding and control of multiphase flow, and providing a theoretical basis and technical support for the design and optimization of multiphase reactors.

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A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Cited by 72 publications

References 66 publications

A discrete population balance equation for binary breakage

A discrete population balance equation for binary breakage

Numerical investigation of bubble breakup in a four‐branched microchannel based on non‐Newtonian pseudoplastic fluid

Single bubble breakup in the flow field induced by a horizontal jet—The experimental research

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