Population balances combined with Computational Fluid Dynamics: A modeling approach for dispersive mixing in a high pressure homogenizer

Dubbelboer, Arend; Janssen, Jo; Hoogland, Hans; Mudaliar, Ashvin; Maindarkar, Shashank N.; Zondervan, Edwin; Meuldijk, J.

doi:10.1016/j.ces.2014.06.047

Cited by 18 publications

(20 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…i j i j T 3 (12) For the inertial subrange, particles are bigger than the smallest eddy and the aggregation rate is expressed using Abrahamson's model 55…”

Section: Numerical Simulationmentioning

confidence: 99%

“…With the development of computer technology and computational fluid dynamics (CFD), numerical simulation has become an effective means of fluid mechanics. The CFD approach coupled population balance model (PBM) was employed to comprehensively investigate local droplet breakage and coalescence performance in the liquid–liquid two-phase mixing process. − Jaworski et al used the quadrature method of moments to solve the transport equations for the moments of the droplet size distribution (DSD) and studied turbulent droplet breakage in the KSM. A PBM utilizing the phenomenological model was developed and used to assess its ability to accurately simulate the liquid–liquid contacting performance achieved in screen-type static mixers where nearly isotropic turbulent plug flow conditions prevail .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

CFD–PBM Numerical Study on Liquid–Liquid Dispersion in the Q-Type Static Mixer

Meng

Wang

et al. 2021

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Numerical simulations of silicone oil−water twophase turbulent dispersion mixing in Q-type static mixers (QSM) are performed using computational fluid dynamics (CFD) coupled with a population balance model in the range of Re = 8000− 24 000. The numerical prediction of Sauter mean diameter (d 32 ) in the Kenics static mixer had a good agreement with experimental results. The centerlines of droplet size distributions gradually shift to the left, and the flat profiles with lower peak values become much thinner with higher peak values with increasing axial length. The dimensionless d 32 decreases with increasing element number and Re and stabilizes below 0.03 at the axial length z/l > 10. A correlation among d 32 , We, and residence time is obtained to predict the equilibrium characteristics of droplet groups. The average shear rate in the QSM with right−left staggered segments (RL-90-QSM) is 1.15−2.41 times that with right−right staggered segments, which indicates that RL-90-QSM has excellent droplet breakage performance.

show abstract

“…i j i j T 3 (12) For the inertial subrange, particles are bigger than the smallest eddy and the aggregation rate is expressed using Abrahamson's model 55…”

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

CFD–PBM Numerical Study on Liquid–Liquid Dispersion in the Q-Type Static Mixer

Meng

Wang

et al. 2021

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

show abstract

“…These models were recently applied to systems with non-uniform spatial energy and turbulence dissipation, such as high pressure homogenizers [24,9,25,26]. In this context, multi-scale modeling has also been considered in such non-uniform systems, by coupling computational fluid dynamic (CFD) simulations with the PBE model in order to investigate local droplet breakage and coalescence [27,28,29,30]. However, in static mixers, only few such studies can be reported.…”

Section: Fundamental Population Balance Equation-based Models Have Extensively Been Investigated In Recent Yearsmentioning

confidence: 99%

A population balance model for the prediction of breakage of emulsion droplets in SMX+ static mixers

Lebaz

Sheibat‐Othman

2019

Chemical Engineering Journal

View full text Add to dashboard Cite

This work deals with the numerical and experimental investigation of droplets breakage in SMX+ static mixers. While steady-state empirical correlations are commonly used for the prediction of the mean droplets size (e.g. Sauter mean diameter) during emulsification in static mixers, in the present study, a population balance equation (PBE) -based model is developed for the prediction of the dynamic evolution of the droplet size distribution (DSD). The system silicon oil-in-water stabilized by Polysorbate 20 (Tween20 R ) is considered under dilute conditions (< 5%vol.). Due to the physico-chemical properties of the system and the operating conditions, the droplets breakage process is dominant, while coalescence and Ostwald ripening are negligible. The breakage kernel proposed by Alopaeus et al. [1] is employed and its parameters are identified and validated for the present system under different operating conditions. The effects of the number of SMX+ elements, viscosity and fraction of the dispersed phase, the DSD at the inlet of the mixers as well as the volume-average energy dissipation rate within the SMX+ elements on the evolution of the DSD are investigated. The model was found to be able of predicting the DSD over a wide range of operating conditions.

show abstract

“…The population balance equation (PBE) provides an effective approach for modeling the DSDs due to droplet coalescence and breakage and has been applied to modeling emulsification in HPHs in some studies. ,− Among these, Soon et al, Raikar et al., ,, Vankova et al., Tcholakova et al, and Becker et al only considered droplet breakage based on the assumption of negligible droplet coalescence for low dispersed holdup and high emulsifier concentration. Maindarkar et al and Dubbelboer et al further took account of droplet coalescence. Håkansson et al ,, and Maindarkar et al , included droplet coalescence and breakage as well as emulsifier adsorption in their models to highlight the effects of emulsifier type and concentration.…”

Section: Introductionmentioning

confidence: 99%

“…The parameter is therefore critical and used in PBE as an input parameter for DSD prediction. In many studies, it was generally assumed that all energy was dissipated through turbulence, and then the magnitude of turbulence dissipation rate can be determined through empirical correlations and operating conditions. ,− , Other researchers estimated the mean effective turbulent dissipation rate from computational fluid dynamics (CFD). , Even if such mean value is more accurate than that obtained from empirical correlations, this method is not capable of well estimating the droplet coalescence and breakage rates, since these rates are nonlinearly dependent on the turbulent dissipation rate which is spatially nonuniform. In other words, the space-averaged coalescence or breakage rates are not equivalent to the rates calculated with the mean turbulent dissipation rate.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Droplet Size Distribution for High Pressure Homogenizers with Heterogeneous Turbulent Dissipation Rate

Guan

Yang

Nigam

2020

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Droplet size distribution (DSD) of an emulsion is one of the important properties that affect product quality, stability, appearance, and rheology. Reliable prediction of DSDs in high-pressure homogenizers under various emulsion formulation and processing conditions is still challenging. A zero-dimensional population balance equation (PBE) model was developed to take account of the heterogeneous turbulent dissipation rate through its volume fraction distribution rather than the mean value as the coupling parameter between CFD and PBE. Furthermore, the effect of emulsifier on coalescence was also incorporated through the surface coverage of emulsifier. The model can give satisfactory DSDs under different oil fractions, homogenization pressures, and emulsifier concentrations for the oil-in-water emulsions. Moreover, the predictions were more sensitive to the breakage kernel parameters than to the coalescence ones or the number of daughter droplets. This approach is beneficial to the fast computational product design with less computational cost and reasonable prediction.

show abstract

Population balances combined with Computational Fluid Dynamics: A modeling approach for dispersive mixing in a high pressure homogenizer

Cited by 18 publications

References 49 publications

CFD–PBM Numerical Study on Liquid–Liquid Dispersion in the Q-Type Static Mixer

CFD–PBM Numerical Study on Liquid–Liquid Dispersion in the Q-Type Static Mixer

A population balance model for the prediction of breakage of emulsion droplets in SMX+ static mixers

Prediction of Droplet Size Distribution for High Pressure Homogenizers with Heterogeneous Turbulent Dissipation Rate

Contact Info

Product

Resources

About