Abstract
The mass transfer and mixing performance in the static mixers with three twisted leaves (TKSM) were investigated by the computational fluid dynamics coupled population balance model. A high-precision and efficient gas-liquid two phase model were evaluated by considering several drag models based on experimental bubble size distributions. The bubble size prediction matched well with experimental data and the mean relative error of Sauter mean diameter (d 32) between the prediction and experiment values is 4.93 %. The drag correction factor considering hindering effect of small bubbles can improve the accuracy of cumulative probability distribution (CPD) prediction by 10.06 %. Bubble breakup capacity is quantized via gas-liquid interfacial area, and an empirical correlation between Eo and bubble aspect ratio (γ) have been proposed to predict morphological characteristics of bubble swarms. The effect of liquid Re on the mass transfer rate is much more significant than that of gas volume fraction (α d). The coefficients of variation profiles show that RL-TKSM has better mixing efficiency compared with LL-TKSM and perfect mixing could be achieved after seven mixing elements. The micro mixing efficiency of RL-TKSM is 1.06–1.14 times that of LL-TKSM, which indicates that RL-TKSM has excellent mixing and mass transfer performances.
Funding source: Shenyang Young and Middle-aged Science and Technology Innovation Talent Support Program
Award Identifier / Grant number: RC200032
Funding source: Natural Science Foundation of Liaoning Province
Award Identifier / Grant number: 2022-MS-290
Funding source: Distinguished Professor of Liaoning Province
Award Identifier / Grant number: LCH[2018]35
Funding source: Key Scientific Research Project of Education Department of Liaoning Province
Award Identifier / Grant number: LJKMZ20220773
Award Identifier / Grant number: LJKZ0429
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 21476142
Funding source: Talent Introduction Research Fund of China University of Petroleum (East China)
Award Identifier / Grant number: R20220113
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The authors acknowledge funding support for this research from the Key Scientific Research Project of Education Department of Liaoning Province (Nos. LJKZ0429, LJKMZ20220773), Shenyang Young and Middle-aged Science and Technology Innovation Talent Support Program (No. RC200032), National Natural Science Foundation of China (No. 21476142), Distinguished Professor of Liaoning Province (No. LCH [2018] 35), Natural Science Foundation of Liaoning Province (No. 2022-MS-290), and Talent Introduction Research Fund of China University of Petroleum (East China) (No. R20220113).
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Conflict of interest statement: The authors declare no conflicts of interest.
References
Altabash, G., M. Al-Hindi, and F. Azizi. 2020. “Intensifying the Absorption of CO2 in Water Using a Static Mixer. Part I: Effect of Measurement Technique.” Industrial & Engineering Chemistry Research 59 (25): 11691–704. https://doi.org/10.1021/acs.iecr.0c01269.Search in Google Scholar
Andersson, R., and B. Andersson. 2006. “On the Breakup of Fluid Particles in Turbulent Flows.” AIChE Journal 52 (6): 2020–30. https://doi.org/10.1002/aic.10831.Search in Google Scholar
Azizi, F., and A. M. Al Taweel. 2010. “Algorithm for the Accurate Numerical Solution of PBE for Drop Breakup and Coalescence under High Shear Rates.” Chemical Engineering Science 65 (23): 6112–27. https://doi.org/10.1016/j.ces.2010.08.034.Search in Google Scholar
Azizi, F., and A. M. Al Taweel. 2011. “Turbulently Flowing Liquid-Liquid Dispersions. Part I: Drop Breakage and Coalescence.” Chemical Engineering Journal 166 (2): 715–25. https://doi.org/10.1016/j.cej.2010.11.050.Search in Google Scholar
Azizi, F., and A. M. Al Taweel. 2015. “Mass Transfer in an Energy-Efficient High-Intensity Gas-Liquid Contactor.” Industrial & Engineering Chemistry Research 54 (46): 11635–52. https://doi.org/10.1021/acs.iecr.5b01078.Search in Google Scholar
Bakker, H., and A. Akker. 1994. “A Computational Model for the Gas-Liquid Flow in Stirred Reactors.” Chemical Engineering Research and Design 72 (A4): 594–606.Search in Google Scholar
Baumann, A., S. A. K. Jeelani, B. Holenstein, P. Stössel, and E. J. Windhab. 2012. “Flow Regimes and Drop Break-Up in SMX and Packed Bed Static Mixers.” Chemical Engineering Science 73 (7): 354–65. https://doi.org/10.1016/j.ces.2012.02.006.Search in Google Scholar
Brucato, A., F. Grisafi, and G. Montante. 1998. “Particle Drag Coefficients in Turbulent Fluids.” Chemical Engineering Science 53 (18): 3295–314. https://doi.org/10.1016/s0009-2509(98)00114-6.Search in Google Scholar
Buffo, A., M. Vanni, P. Renze, and D. L. Marchisio. 2016. “Empirical Drag Closure for Polydisperse Gas-Liquid Systems in Bubbly Flow Regime: Bubble Swarm and Micro-scale Turbulence.” Chemical Engineering Research and Design 113: 284–303. https://doi.org/10.1016/j.cherd.2016.08.004.Search in Google Scholar
Cao, X. W., K. R. Yang, H. C. Wang, and J. Bian. 2022. “Gas-Liquid-Hydrate Flow Characteristics in Vertical Pipe Considering Bubble and Particle Coalescence and Breakage.” Chemical Engineering Science 252 (28): 117249. https://doi.org/10.1016/j.ces.2021.117249.Search in Google Scholar
Chabanon, E., N. Sheibat-Othman, O. Mdere, J. P. Valour, S. Urbaniak, and F. Puel. 2017. “Drop Size Distribution Monitoring of Oil-In-Water Emulsions in SMX+ Static Mixers: Effect of Operating and Geometrical Conditions.” International Journal of Multiphase Flow 92: 61–9. https://doi.org/10.1016/j.ijmultiphaseflow.2017.03.001.Search in Google Scholar
Gao, Z. M., D. Y. Li, A. Buffo, W. Podgórska, and D. L. Marchisio. 2016. “Simulation of Droplet Breakage in Turbulent Liquid–Liquid Dispersions with CFD-PBM: Comparison of Breakage Kernels.” Chemical Engineering Science 142 (13): 277–88. https://doi.org/10.1016/j.ces.2015.11.040.Search in Google Scholar
Gaurav, T. K., A. Prakash, and C. Zhang. 2022. “CFD Modeling of the Hydrodynamic Characteristics of a Bubble Column in Different Flow Regimes.” International Journal of Multiphase Flow 147: 103902. https://doi.org/10.1016/j.ijmultiphaseflow.2021.103902.Search in Google Scholar
Ghanem, A., T. Lemenand, D. D. Valle, and H. Peerhossaini. 2014. “Static Mixers: Mechanisms, Applications, and Characterization Methods – A Review.” Chemical Engineering Research and Design 92 (2): 205–28. https://doi.org/10.1016/j.cherd.2013.07.013.Search in Google Scholar
Goldshmid, J., M. Samet, and M. Wagner. 1986. “Turbulent Mixing at High Dilution Ratio in a Sulzer-Koch Static Mixer.” Industrial & Engineering Chemistry Process Design and Development 25 (1): 108–16. https://doi.org/10.1021/i200032a017.Search in Google Scholar
Grace, J. R., T. Wairegi, and T. H. Nguyen. 1976. “Shapes and Velocities of Single Drops and Bubbles Moving Freely through Immiscible Liquids.” Transactions of the American Institute of Chemical Engineers 54 (3): 167–73.Search in Google Scholar
Guan, X. P., and N. Yang. 2017. “Bubble Properties Measurement in Bubble Columns: From Homogeneous to Heterogeneous Regime.” Chemical Engineering Research and Design 127: 103–12. https://doi.org/10.1016/j.cherd.2017.09.017.Search in Google Scholar
Guo, X., Z. Huang, and J. Sun. 2020. “Evolution and Interaction Characteristics of Liquid Flow and Bubbles in a Jet Bubbling Column.” Industrial & Engineering Chemistry Research 59 (48): 21217–30. https://doi.org/10.1021/acs.iecr.0c04178.Search in Google Scholar
Guo, X. F., Q. Zhou, J. Li, and C. X. Chen. 2016. “Implementation of an Improved Bubble Breakup Model for TFM-PBM Simulations of Gas-Liquid Flows in Bubble Columns.” Chemical Engineering Science 152 (2): 255–66. https://doi.org/10.1016/j.ces.2016.06.032.Search in Google Scholar
Haddadi, M. M., S. H. Hosseini, D. Rashtchian, and G. Ahmadi. 2020. “CFD Modeling of Immiscible Liquids Turbulent Dispersion in Kenics Static Mixers: Focusing on Droplet Behavior.” Chinese Journal of Chemical Engineering 28 (2): 348–61. https://doi.org/10.1016/j.cjche.2019.07.020.Search in Google Scholar
Han, L. C., H. A. Luo, and Y. J. Liu. 2011. “A Theoretical Model for Droplet Breakup in Turbulent Dispersions.” Chemical Engineering Science 66 (4): 766–76. https://doi.org/10.1016/j.ces.2010.11.041.Search in Google Scholar
Heyouni, A., M. Roustan, and Z. Do-Quang. 2002. “Hydrodynamics and Mass Transfer in Gas-Liquid Flow through Static Mixers.” Chemical Engineering Science 57 (16): 3325–33. https://doi.org/10.1016/s0009-2509(02)00202-6.Search in Google Scholar
Hirschberg, S., R. Koubek, F. Moser, and J. Schöck. 2009. “An Improvement of the Sulzer SMX™ Static Mixer Significantly Reducing the Pressure Drop.” Chemical Engineering Research and Design 87 (4): 524–32. https://doi.org/10.1016/j.cherd.2008.12.021.Search in Google Scholar
Hosseini, S. M., K. Razzaghi, and F. Shahraki. 2019. “Design and Characterization of a Low-Pressure-Drop Static Mixer.” AIChE Journal 65 (3): 1126–33. https://doi.org/10.1002/aic.16505.Search in Google Scholar
Ishii, M., and N. Zuber. 1979. “Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows.” AIChE Journal 25 (5): 843–55. https://doi.org/10.1002/aic.690250513.Search in Google Scholar
Juan, P. V., K. Lyes, and K. M. Omar. 2022. “Current Advances in Liquid-Liquid Mixing in Static Mixers: A Review.” Chemical Engineering Research and Design 177: 694–731. https://doi.org/10.1016/j.cherd.2021.11.016.Search in Google Scholar
Khan, I., M. J. Wang, Y. P. Zhang, W. X. Tian, G. H. Su, and S. Z. Qiu. 2020. “Two-phase Bubbly Flow Simulation Using CFD Method: A Review of Models for Interfacial Forces.” Progress in Nuclear Energy 125: 103360. https://doi.org/10.1016/j.pnucene.2020.103360.Search in Google Scholar
Lebaz, N., and N. Sheibat-Othman. 2019. “A Population Balance Model for the Prediction of Breakage of Emulsion Droplets in SMX+ Static Mixers.” Chemical Engineering Journal 361 (1): 625–34. https://doi.org/10.1016/j.cej.2018.12.090.Search in Google Scholar
Lebaz, N., F. Azizi, and N. Sheibat-Othman. 2022. “Modeling Droplet Breakage in Continuous Emulsification Using Static Mixers in the Framework of the Entire Spectrum of Turbulent Energy.” Industrial & Engineering Chemistry Research 61 (1): 541–53. https://doi.org/10.1021/acs.iecr.1c03529.Search in Google Scholar
Liang, X. F., H. Pan, Y. H. Su, and Z. H. Luo. 2016. “CFD-PBM Approach with Modified Drag Model for the Gas-Liquid Flow in a Bubble Column.” Chemical Engineering Research and Design 112: 88–102. https://doi.org/10.1016/j.cherd.2016.06.014.Search in Google Scholar
Liao, Y. X., and D. Lucas. 2009. “A Literature Review of Theoretical Models for Drop and Bubble Breakup in Turbulent Dispersions.” Chemical Engineering Science 64 (15): 3389–406. https://doi.org/10.1016/j.ces.2009.04.026.Search in Google Scholar
Liu, L., H. Y. Zhang, H. J. Yan, T. Ziegenhein, H. Hessenkemper, P. Zhou, and D. Lucas. 2021. “Experimental Studies on Bubble Aspect Ratio and Corresponding Correlations under Bubble Swarm Condition.” Chemical Engineering Science 236 (8): 116551. https://doi.org/10.1016/j.ces.2021.116551.Search in Google Scholar
Luo, H. A., and H. F. Svendsen. 1996. “Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions.” AIChE Journal 42 (5): 1225–33. https://doi.org/10.1002/aic.690420505.Search in Google Scholar
Liu, Z. P., E. Hitimana, M. G. Olsen, J. C. Hill, and R. O. Fox. 2017. “Turbulent Mixing in the Confined Swirling Flow of a Multi-Inlet Vortex Reactor.” AIChE Journal 63 (6): 2409–19. https://doi.org/10.1002/aic.15572.Search in Google Scholar
Mahmoodi, H., K. Razzaghi, and F. Shahraki. 2020. “Improving Mixing Performance by Curved-Blade Static Mixer.” AIChE Journal 66 (11): e17034. https://doi.org/10.1002/aic.17034.Search in Google Scholar
Meinecke, M., A. Kilzer, and E. Weidner. 2020. “Imaging Method for Mass Transport Measurements in a Two-Phase Bubbly Flow of Supercritical CO2 and Viscous Liquids in a Static Mixer.” Journal of Supercritical Fluids 159 (1): 104757. https://doi.org/10.1016/j.supflu.2020.104757.Search in Google Scholar
Meng, H. B., F. Wang, Y. F. Yu, M. Y. Song, and J. H. Wu. 2014. “A Numerical Study of Mixing Performance of High-Viscosity Fluid in Novel Static Mixers with Multitwisted Leaves.” Industrial & Engineering Chemistry Research 53 (10): 4084–95. https://doi.org/10.1021/ie402970v.Search in Google Scholar
Meng, H. B., J. B. Wang, Y. F. Yu, Z. Y. Wang, and J. H. Wu. 2021. “CFD-PBM Numerical Study on Liquid-Liquid Dispersion in the Q-Type Static Mixer.” Industrial & Engineering Chemistry Research 60 (49): 18121–35. https://doi.org/10.1021/acs.iecr.1c02906.Search in Google Scholar
Meng, H. B., M. Q. Han, Y. F. Yu, Z. Y. Wang, and J. H. Wu. 2020a. “Numerical Evaluations on the Characteristics of Turbulent Flow and Heat Transfer in the Lightnin Static Mixer.” International Journal of Heat and Mass Transfer 156: 119788. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119788.Search in Google Scholar
Meng, H. B., Y. N. Hao, Y. F. Yu, Z. G. Li, and J. H. Wu. 2020b. “Experimental Study of Gas-Liquid Two-phase Bubbly Flow Characteristics in a Static Mixer with Three Twisted Leaves.” Korean Journal of Chemical Engineering 37 (11): 1859–66. https://doi.org/10.1007/s11814-020-0609-z.Search in Google Scholar
Meng, H. B., T. Meng, Y. F. Yu, Z. Y. Wang, and J. H. Wu. 2022. “Experimental and Numerical Investigation of Turbulent Flow and Heat Transfer Characteristics in the Komax Static Mixer.” International Journal of Heat and Mass Transfer 194 (15): 123006. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123006.Search in Google Scholar
Meng, H. B., Y. J. Yao, Y. F. Yu, B. W. Shi, and P. C. Ding. 2023. “Enhancement Analysis of Turbulent Flow and Heat Transfer of Supercritical CO2 in a Static Mixer with Three Helical Blades.” Korean Journal of Chemical Engineering 40 (1): 79–90. https://doi.org/10.1007/s11814-022-1312-z.Search in Google Scholar
Menter, F. R. 1994. “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications.” AIAA Journal 32 (8): 1598–605. https://doi.org/10.2514/3.12149.Search in Google Scholar
Nie, Y. Y., S. F. Zhao, P. J. Yu, Y. M. Wei, R. Z. Hu, W. He, N. Zhu, Y. G. Li, D. Ji, and K. Guo. 2023. “Improvement of Mass and Heat Transfer Efficiency in a Scale-Up Microfluidic Mixer Designed by CFD Simulation.” Canadian Journal of Chemical Engineering, https://doi.org/10.1002/cjce.24855.Search in Google Scholar
Rabha, S., M. Schubert, F. Grugel, M. Banowski, and U. Hampel. 2015. “Visualization and Quantitative Analysis of Dispersive Mixing by a Helical Static Mixer in Upward Co-Current Gas-Liquid Flow.” Chemical Engineering Journal 262 (15): 527–40. https://doi.org/10.1016/j.cej.2014.09.019.Search in Google Scholar
Roghair, I., M. V. S. Annaland, and H. J. A. M. Kuipers. 2013. “Drag Force and Clustering in Bubble Swarms.” AIChE Journal 59 (5): 1971–800. https://doi.org/10.1002/aic.13949.Search in Google Scholar
Saatdjian, E., A. J. S. Rodrigo, and J. P. B. Mota. 2012. “On Chaotic Advection in a Static Mixer.” Chemical Engineering Journal 187: 289–98. https://doi.org/10.1016/j.cej.2012.01.122.Search in Google Scholar
Scala, M., L. Gamet, L. M. Malbec, and H. Z. Li. 2020. “Hydrodynamics of Gas-Liquid Dispersion in Transparent Sulzer Static Mixers SMXTM.” Chemical Engineering Science 213 (23): 115398. https://doi.org/10.1016/j.ces.2019.115398.Search in Google Scholar
Schiller, L., and A. Naumann. 1935. “A Drag Coefficient Correlation.” Zeitschrift des Vereines Deutscher Ingenieure 779: 318–20.Search in Google Scholar
Shi, W. B., J. Yang, G. Li, X. G. Yang, Y. Zong, and X. Y. Cai. 2018. “Modelling of Breakage Rate and Bubble Size Distribution in Bubble Columns Accounting for Bubble Shape Variations.” Chemical Engineering Science 187 (21): 391–405. https://doi.org/10.1016/j.ces.2018.05.013.Search in Google Scholar
Shi, W. B., X. G. Yang, M. Sommerfeld, J. Yang, X. Y. Cai, G. Li, and Y. Zong. 2019. “Modelling of Mass Transfer for Gas-Liquid Two-Phase Flow in Bubble Column Reactor with a Bubble Breakage Model Considering Bubble-Induced Turbulence.” Chemical Engineering Journal 371 (1): 470–85. https://doi.org/10.1016/j.cej.2019.04.047.Search in Google Scholar
Sun, Z. Q., K. Zhang, W. H. Li, Q. Chen, and N. B. Zheng. 2020. “Investigations of the Turbulent Thermal-Hydraulic Performance in Circular Heat Exchanger Tubes with Multiple Rectangular Winglet Vortex Generators.” Applied Thermal Engineering 168 (5): 114838. https://doi.org/10.1016/j.applthermaleng.2019.114838.Search in Google Scholar
Tang, Q., X. Y. Qin, H. F. Dong, X. P. Zhang, X. D. Wang, and K. S. Wang. 2019. “Novel Drag Coefficient Models of Ionic Liquid – Spherical Particle System.” Chemical Engineering Science 204 (31): 177–85. https://doi.org/10.1016/j.ces.2019.04.017.Search in Google Scholar
Tas-Koehler, S., Y. X. Liao, and U. Hampel. 2021a. “A Critical Analysis of Drag Force Modelling for Disperse Gas-Liquid Flow in a Pipe with an Obstacle.” Chemical Engineering Science 246 (31): 117007. https://doi.org/10.1016/j.ces.2021.117007.Search in Google Scholar
Tas-Koehler, S., M. Neumann-Kipping, Y. X. Liao, E. Krepper, and U. Hampel. 2021b. “CFD Simulation of Bubbly Flow Around an Obstacle in a Vertical Pipe with a Focus on Breakup and Coalescence Modelling.” International Journal of Multiphase Flow 135: 103528. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103528.Search in Google Scholar
Tomiyama, A., I. Kataoka, I. Zun, and T. Sakaguchi. 1998. “Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions.” JSME International Journal Ser B-Fluids and Thermal Engineering 41 (2): 472–9. https://doi.org/10.1299/jsmeb.41.472.Search in Google Scholar
Troshko, A. A., and Y. A. Hassan. 2001. “A Two-Equation Turbulence Model of Turbulent Bubbly Flows.” International Journal of Multiphase Flow 27 (11): 1965–2000. https://doi.org/10.1016/s0301-9322(01)00043-x.Search in Google Scholar
Wang, T., Z. H. Xia, and C. X. Chen. 2019. “Coupled CFD-PBM Simulation of Bubble Size Distribution in a 2D Gas-Solid Bubbling Fluidized Bed with a Bubble Coalescence and Breakup Model.” Chemical Engineering Science 202 (20): 208–21. https://doi.org/10.1016/j.ces.2019.03.045.Search in Google Scholar
Wang, T. F. 2011. “Simulation of Bubble Column Reactors Using CFD Coupled with a Population Balance Model.” Frontiers of Chemical Science and Engineering 5 (2): 162–72. https://doi.org/10.1007/s11705-009-0267-5.Search in Google Scholar
Wang, T. F., and J. F. Wang. 2007. “Numerical Simulations of Gas-Liquid Mass Transfer in Bubble Columns with a CFD-PBM Coupled Model.” Chemical Engineering Science 62 (24): 7107–18. https://doi.org/10.1016/j.ces.2007.08.033.Search in Google Scholar
Wu, Y. X., H. Chen, and X. F. Song. 2022. “Experimental and Numerical Study on the Bubble Dynamics and Flow Field of a Swirl Flow Microbubble Generator with Baffle Internals.” Chemical Engineering Science 263 (14): 118066. https://doi.org/10.1016/j.ces.2022.118066.Search in Google Scholar
Xing, C. T., T. F. Wang, K. Y. Guo, and J. F. Wang. 2015. “A Unified Theoretical Model for Breakup of Bubbles and Droplets in Turbulent Flows.” AIChE Journal 61 (4): 1391–403. https://doi.org/10.1002/aic.14709.Search in Google Scholar
Yang, G. Y., H. H. Zhang, J. J. Luo, and T. F. Wang. 2018. “Drag Force of Bubble Swarms and Numerical Simulations of a Bubble Column with a CFD-PBM Coupled Model.” Chemical Engineering Science 192 (31): 714–24. https://doi.org/10.1016/j.ces.2018.07.012.Search in Google Scholar
Yang, N., Z. Wu, J. Chen, Y. Wang, and J. Li. 2011. “Multi-Scale Analysis of Gas-Liquid Interaction and CFD Simulation of Gas-Liquid Flow in Bubble Columns.” Chemical Engineering Science 66 (14): 3212–22. https://doi.org/10.1016/j.ces.2011.02.029.Search in Google Scholar
Zhang, H. H., K. Y. Guo, Y. L. Wang, A. Sayyar, and T. F. Wang. 2020a. “Numerical Simulations of the Effect of Liquid Viscosity on Gas-Liquid Mass Transfer of a Bubble Column with a CFD-PBM Coupled Model.” International Journal of Heat and Mass Transfer 161: 120229. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120229.Search in Google Scholar
Zhang, H. H., A. Sayyar, Y. L. Wang, and T. F. Wang. 2020b. “Generality of the CFD-PBM Coupled Model for Bubble Column Simulation.” Chemical Engineering Science 219 (29): 115514. https://doi.org/10.1016/j.ces.2020.115514.Search in Google Scholar
Zhang, X. B., R. Q. Zheng, and Z. H. Luo. 2020c. “CFD-PBM Simulation of Bubble Columns: Effect of Parameters in the Class Method for Solving PBEs.” Chemical Engineering Science 226 (23): 115853. https://doi.org/10.1016/j.ces.2020.115853.Search in Google Scholar
Zhang, X. B., W. C. Yan, and Z. H. Luo. 2020d. “CFD-PBM Simulation of Bubble Columns: Sensitivity Analysis on the Non-Drag Forces.” Industrial & Engineering Chemistry Research 59 (41): 18674–682. https://doi.org/10.1021/acs.iecr.0c02759.Search in Google Scholar
Zhang, X. B., and Z. H. Luo. 2020. “Effects of Bubble Coalescence and Breakup Models on the Simulation of Bubble Columns.” Chemical Engineering Science 226 (23): 115850. https://doi.org/10.1016/j.ces.2020.115850.Search in Google Scholar
Zhang, X. B., and Z. H. Luo. 2021. “Local Gas-Liquid Slip Velocity Distribution in Bubble Columns and its Relationship with Heat Transfer.” AIChE Journal 67 (1): e17032. https://doi.org/10.1002/aic.17032.Search in Google Scholar
Zhao, S. F., R. Hu, Y. Y. Nie, L. Z. Sheng, W. He, N. Zhu, Y. G. Li, D. Ji, and K. Guo. 2022a. “Intensification of Mixing Efficiency and Reduction of Pressure Drop in a Millimeter Scale T-Junction Mixer Optimized by an Elliptical Array Hole Structure.” Chemical Engineering and Processing – Process Intensification 178: 109034. https://doi.org/10.1016/j.cep.2022.109034.Search in Google Scholar
Zhao, S. F., L. Z. Sheng, W. He, N. Zhu, Y. G. Li, D. Ji, and K. Guo. 2022b. “Design and Optimization of a Novel Ellipsoidal Baffle Mixer with High Mixing Efficiency and Low Pressure Drop.” Journal of Chemical Technology and Biotechnology 97 (11): 3121–31. https://doi.org/10.1002/jctb.7179.Search in Google Scholar
Zhao, S. F., Y. M. Wei, P. J. Yu, Y. Nie, R. Z. Hu, W. He, N. Zhu, Y. G. Li, D. Ji, and K. Guo. 2022c. “High Throughput Millifluidics Mixer with Double Triangle Baffle for Improvement of Mixing Performance and Reduction of Flow Resistance Designed by Grey Relational Analysis.” Chemical Engineering and Processing – Process Intensification 181: 109166. https://doi.org/10.1016/j.cep.2022.109166.Search in Google Scholar
Zidouni, F., E. Krepper, R. Rzehak, S. Rabha, M. Schubert, and U. Hampel. 2015. “Simulation of Gas-Liquid Flow in a Helical Static Mixer.” Chemical Engineering Science 137 (1): 476–86. https://doi.org/10.1016/j.ces.2015.06.052.Search in Google Scholar
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