Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments

Han, Luchang; Gong, Shenggao; Ding, Yaowen; Fu, Jun; Gao, Ningning; Luo, He’an

doi:10.1002/aic.14830

Cited by 30 publications

(20 citation statements)

References 50 publications

(209 reference statements)

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“…For both these liquid-liquid systems, pure breakage (dispersed phase volume fraction, φ = 0.001) as well as breakage together with coalescence (φ = 0.05) were simulated. In the calculations, the constant, C, in Equation (16) defining the coalescence efficiency is assumed to be C = 0.5 for the first liquid-liquid system characterized by partially mobile interfaces and drainage and interaction times are calculated from Equations (17) and (19), respectively. For the system with a drop surface mobility decreased due to a high dispersed phase viscosity, Equations (20) and (18) are used to estimate the drainage and interaction times and the constant is equal to C = 0.1.…”

Section: Resultsmentioning

confidence: 99%

“…Figure 9a presents the final drop size distributions (being the result of dynamic equilibrium between breakage and coalescence) produced by different impellers at a higher dispersed phase volume fraction (ϕ = 0.05) for a pure liquid-liquid system (no surfactant) with a dispersed phase of low viscosity. Under such conditions, droplets have partially mobile interfaces and gentle collisions are favored (Equations (17) and (19)). Therefore, fast coalescence takes place in the bulk.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…low viscosity. Under such conditions, droplets have partially mobile interfaces and gentle collisions are favored (Equations (17) and (19)). Therefore, fast coalescence takes place in the bulk.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…There is a group of breakage models based on a concept of collisions between droplets and eddies [15][16][17]. In recent years, these models, which were also formulated for the inertial subrange, were extended by using a wide energy spectrum [18][19][20][21]. The important question that appears when a breakage model is formulated is whether the droplet is broken by eddies smaller than the droplet, eddies of a size comparable to the drop diameter, or eddies larger than the droplet.…”

Section: Introductionmentioning

confidence: 99%

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The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions

Podgórska

2019

Entropy

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The influence of the impeller type on drop size distribution (DSD) in turbulent liquid-liquid dispersion is considered in this paper. The effects of the application of two impellers, high power number, high shear impeller (six blade Rushton turbine, RT) and three blade low power number, and a high efficiency impeller (HE3) are compared. Large-scale and fine-scale inhomogeneity are taken into account. The flow field and the properties of the turbulence (energy dissipation rate and integral scale of turbulence) in the agitated vessel are determined using the k-ε model. The intermittency of turbulence is taken into account in droplet breakage and coalescence models by using multifractal formalism. The solution of the population balance equation for lean dispersions (when the only breakage takes place) with a dispersed phase of low viscosity (pure system or system containing surfactant), as well as high viscosity, show that at the same power input per unit mass HE3 impeller produces much smaller droplets. In the case of fast coalescence (low dispersed phase viscosity, no surfactant), the model predicts similar droplets generated by both impellers. In the case of a dispersed phase of high viscosity, when the mobility of the drop surface is reduced, HE3 produces slightly smaller droplets.

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Section: Resultsmentioning

confidence: 99%

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions

Podgórska

2019

Entropy

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“…This study assumes that the minimum effective size of turbulent structure is half of the Kolmogorov length scale, since below this limit the number density of vortices is negligible. Further, different limits have been exploited in the literature for the maximum effective size of turbulent structure, including, 3 d 0 , 5 d 0 , and 10 d 0 . In the present work, λ / d 0 ≤ 10 is employed as the upper limit of the vortex size. More details on the choice of integration bounds are provided in this section.…”

Section: Model Descriptionsmentioning

confidence: 99%

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

Karimi

Andersson

2019

AIChE Journal

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This work provides an in-depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov-sized droplets. K E Y W O R D S mathematical modeling, multiphase flow, process, simulation, turbulence 1 | INTRODUCTION The size distribution of fluid particles within a continuous medium is of vital importance for different industrial applications. In multiphase processes, knowledge of size distribution determines the rate of momentum, heat and mass transport. The mathematical framework commonly used to tackle this problem is population balance modeling, which requires closure terms for the breakup and coalescence of the dispersed fluid particles. 1,2 The present work concentrates on the breakup mechanisms of fluid particles in turbulent flows.The pioneering models for breakup were formulated by Rayleigh in the nineteenth century for jet flows, and considered dynamic stresses and surface tension. 3 Taylor, 4,5 on the other hand, has shown the relevance of viscous stresses for droplet distortions when the droplets are very small or when the continuous phase is highly viscous. Balancing the deforming and stabilizing stresses, Hinze has proposed a formulation for the maximum stable droplet diameter (d max ) for dispersion in turbulent flows. 6 The above advancements have paved the way for further developments in the field. Typically, the ratio between counteracting stresses acting on fluid particles represents a dimensionless number that indicates the probable breakup mechanism. For instance, when inertia is the principal cause of breakup, a critical Weber number is quantified, and the break up takes place above this number; examples can be found in Reference 7-9 . The other scenario is the definition of a critical Capillary number (i.e., the ratio of viscous stress over surface stresses) for viscous laminar flows. [10][11][12] Although the dimensionless numbers are a relevant means for interpreting the breakup process, relying on dimensionless numbers to explain the complicated physical phenomenon that occurs during the breakup in turbulent multiphase systems is too simplistic. 13,14 Thus, later breakup models are inclined toward the dynamics of bubble or drople...

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A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence

Solsvik

Jakobsen

2016

AIChE Journal

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The models for fluid particle breakage and coalescence due to turbulence are generally limited to the inertial subrange of isotropic turbulence and infinite Reynolds numbers. A rigorous procedure for extending the fluid particle breakage and coalescence closures to the entire spectrum of isotropic turbulence and for a wider range of Reynolds numbers can be established based on statistical turbulence theory. The modeling procedure consists of a three‐dimensional (3‐D) literature model energy spectrum for the dissipation, inertial, and energy containing subranges of isotropic turbulence, and an exact literature integral relation for determining the second‐order longitudinal structure function from the 3‐D energy spectrum. A review of the requisite statistical turbulence theory and the use of the model energy spectrum is provided, because the necessary details are not easily accessible in the chemical engineering literature and misconceptions are found in the publications of the previous modeling attempts. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1795–1820, 2016

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Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments

Cited by 30 publications

References 50 publications

The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions

The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence

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