Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation

Meng Tong; Wang Yu; Tian Yijuan; Qin Shuang; Lin Yuyan; Liu Peiqiao; Wang Yundong; Liu Zuohua

doi:null

Your Location：

Home >

Browse articles >

Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation

Updated：2026-05-14

- Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation
- Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation
- 中国化学工程学报（英文） 2026年90卷第2期页码：293-307
- Affiliations：
  
  School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China
  Department of Industrial Chemistry “Toso Montanari”, University of Bologna, Bologna 40131, Italy
  State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing 400044, China
  Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
- Author bio：
  
  Corresponding author. E-mail address: liuzuohua@cqu.edu.cn (Z. Liu).
- Funds：
  
  the Chongqing Natural Science Foundation Innovation and Development Joint Fund Project(CSTB2022NSCQ-LZX0014);Fundamental Research Funds for Central Universities(2022CDJQY-005;2023CDJXY-047)
- DOI：
  中图分类号：
- 收稿：2025-07-29，
  
  修回：2025-09-25，
  
  录用：2025-09-25，
  
  网络首发：2025-11-11，
  
  纸质出版：2026-02
- Accepted：
Scan QR Code
Meng Tong, Wang Yu, Tian Yijuan, 等. Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation[J]. 中国化学工程学报（英文）, 2026,90(2):293-307.

Meng Tong, Wang Yu, Tian Yijuan, et al. Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation[J]. Chinese Journal of Chemical Engineering, 2026, 90(2): 293-307.
Meng Tong, Wang Yu, Tian Yijuan, 等. Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation[J]. 中国化学工程学报（英文）, 2026,90(2):293-307. DOI：

Meng Tong, Wang Yu, Tian Yijuan, et al. Multiscale synergistic enhancement mechanism of solid—liquid mixing in multi-shaft stirred reactors under variable-speed operation[J]. Chinese Journal of Chemical Engineering, 2026, 90(2): 293-307. DOI：

摘要

Abstract

Research on the solid—liquid mixing process and its enhancement mechanisms in multi-shaft stirred reactors still face challenges that limit its industrial applications. This work employs the RNG

—

model combined with the EE-KTGF model to numerically simulate the solid—liquid mixing process within a multi-shaft stirred reactor

yielding satisfactory results when compared to experimental data. Comparative analysis of the solid—liquid mixing performance under four different operational conditions reveals that applying variable speed conditions to the bottom impeller results in a smaller solid concentration gradient

reduced particle settling rates

and an improvement in solid homogeneity by 2.74% to 3.22% compared to other operational conditions. This operational condition enables more effective suspension and uniform distribution of solid particles throughout the reactor

thereby enhancing overall mixing efficiency. Flow field analysis under different operational conditions indicates that applying variable speed to the bottom impeller significantly improves flow field stability

reduces axial back-mixing

and optimizes the axial distribution of solid particles. Further dynamic mode decomposition of the flow field and time series analysis of modal coefficients elucidate a multi-scale synerg

istic nesting chaos-enhanced mechanism characterized by “macroscopic stability

mesoscopic matching

and microscopic resonance”. This work provides a theoretical foundation for the design and operational optimization of multi-shaft stirred reactors.

关键词

Keywords

references

H. Chen, B. Ouyang, X.G. Yi, X.B. Zhang, Z.H. Luo, Insights into the impact of small particle liquid film on the spatiotemporal distribution of suspension in stirred reactors, Ind. Eng. Chem. Res. 63(30) (2024)13379—13388.

X.L. Li, H.L. Zhao, Z.M. Zhang, Y. Liu, T.A. Zhang, Numerical optimization for blades of intermig impeller in solid—liquid stirred tank, Chin. J. Chem. Eng. 29 (2021) 57—66.

L. Torrente-Murciano, J.B. Dunn, P.D. Christofides, J.D. Keasling, S.C. Glotzer, S. Y. Lee, K.M. van Geem, J. Tom, G.H. He, The forefront of chemical engineering research, Nat. Chem. Eng. 1(1) (2024)18—27.

V.M. Barabash, R.S. Abiev, N.N. Kulov, Theory and practice of mixing: a review, Theor. Found. Chem. Eng. 52 (4) (2018) 473—487.

P. Mishra, F. Ein-Mozaffari, Using computational fluid dynamics to analyze the performance of the maxblend impeller in solid—liquid mixing operations, Int. J. Multiphas. Flow 91(2017)194—207.

D.Y. Gu, Y.H. Song, H. Xu, L. Wen, M. Ye, CFD simulation and experimental analysis of solid—liquid mixing characteristics in a stirred tank with a selfsimilarity impeller, J. Taiwan Inst. Chem. Eng. 146 (2023) 104878.

A. Kazemzadeh, F. Ein-Mozaffari, A. Lohi, Effect of impeller type on mixing of highly concentrated slurries of large particles, Particuology 50 (2020) 88—99.

Z.W. Chen, Y.J. Wu, J. Wang, P.C. Luo, Study on the solid—liquid suspension behavior in a tank stirred by the long-short blades impeller, Chin. J. Chem. Eng. 47(2022)79—88.

X. Xiong, Z.H. Liu, C.Y. Tao, Y.D. Wang, F.Q. Cheng, H. Li, Reduced power consumption in stirred vessel with high solid loading by equipping punched baffles, Chin. J. Chem. Eng. 56(2023)203—214.

B.Q. Liu, Z.L. Xu, F.Y. Fan, B.L. Huang, Experimental study on the solid suspension characteristics of coaxial mixers, Chem. Eng. Res. Des. 133 (2018) 335—346.

Z.L. Xu, C. Yang, Z.Q. Zhang, B.Q. Liu, Z.J. Jin, Study on the numerical model of dense solid suspension driven by a coaxial mixer, Ind. Eng. Chem. Res. 60(4) (2021)1939—1951.

L. Zhang, K. Yang, M. Li, Q.T. Xiao, H. Wang, Enhancement of solid—liquid mixing state quality in a stirred tank by cascade chaotic rotating speed of main shaft, Powder Technol. 397(2022)117020.

F. Maluta, F. Alberini, A. Paglianti, G. Montante, A CFD study on the change of scale of Non-Newtonian stirred digesters at low Reynolds numbers, Chem. Eng. Res. Des. 205(2024)498—509.

T. Meng, Y. Wang, S.S. Wang, S. Qin, Q. Zhang, Y.D. Wang, C.Y. Tao, Y.Q. Xu, Z. H. Liu, Exploration of multishafts stirred reactors: an investigation on experiments and large eddy simulations for turbulent chaos and mixing characteristics, Ind. Eng. Chem. Res. 63 (5) (2024) 2441—2456.

T. Meng, Y. Wang, S. Qin, P.Q. Liu, Y.D. Wang, C.Y. Tao, Z.H. Liu, Complex flow field analysis in multi-shaft stirred reactors: dynamics of wave—vortex coupling revealed by POD and DMD methods, Chem. Eng. Sci. 301 (2025) 120753.

T. Meng, J. Yang, S.S. Wang, Y. Wang, S. Qin, Y.D. Wang, C.Y. Tao, Q. Zhang, Z.H. Liu, Multi-shaft stirred reactors mixing efficiency: rapid characterization strategy based on chaotic attractors, AIChE J. 70(10)(2024)e18510.

T. Meng, Y. Wang, S. Qin, P.Q. Liu, Q. Zhang, Y.D. Wang, C.Y. Tao, Z.H. Liu, From patterns to cocktails: a novel visualization method for turbulent flow fields in stirred reactors, Ind. Eng. Chem. Res. 63 (44)(2024)19320—19328.

S.S. Wang, T. Meng, Q. Zhang, C.Y. Tao, Y.D. Wang, Z.Q. Li, Z.H. Liu, A strategy for strengthening chaotic mixing of dual shaft eccentric mixers by changing Non-Newtonian fluids kinetic energy distribution, Chin. J. Chem. Eng. 69 (2024)122—134.

G.R. Kasat, A.R. Khopkar, V.V. Ranade, A.B. Pandit, CFD simulation of liquidphase mixing in solid—liquid stirred reactor, Chem. Eng. Sci. 63 (15) (2008) 3877—3885.

S.F. Wright, I. Zadrazil, C.N. Markides, A review of solid—fluid selection options for optical-based measurements in single-phase liquid, twophase liquid—liqui d and multiphase solid—liquid flows, Exp. Fluid 58 (9) (2017) 108.

S. Wiederseiner, N. Andreini, G. Epely-Chauvin, C. Ancey, Refractive-index and density matching in concentrated particle suspensions: a review, Exp. Fluid 50(5)(2011) 1183—1206.

M. Sharifi, B. Young, Review of applications of electrical resistance tomography to chemical engineering, Rev. Chem. Eng. 39 (4) (2023) 567—599.

C. Poelma, Ultrasound imaging velocimetry: a review, Exp. Fluid 58(1)(2016)3.

S.J. Li, L.T. Zhu, X.B. Zhang, Z.H. Luo, Recent advances in CFD simulations of multiphase flow processes with phase change, Ind. Eng. Chem. Res. 62 (28) (2023)10729—10786.

S. Hosseini, D. Patel, F. Ein-Mozaffari, M. Mehrvar, Study of solid- liquid mixing in agitated tanks through computational fluid dynamics modeling, Ind. Eng. Chem. Res. 49(9)(2010)4426—4435.

P.Y. Shi, R. Rzehak, Solid—liquid flow in stirred tanks: euler—euler/rans modeling, Chem. Eng. Sci. 227(2020)115875.

R.S.S. Raja Ehsan Shah, B. Sajjadi, A.A. Abdul Raman, S. Ibrahim, Solid—liquid mixing analysis in stirred vessels, Rev. Chem. Eng. 31 (2)(2015)119—147.

S. Subramaniam, S. Balachandar, Modeling Approaches and Computational Methods for Particle-Laden Turbulent Flows, Elsevier, Amsterdam (2023).

J. Capecelatro, O. Desjardins, An Euler—Lagrange strategy for simulating particle-laden flows, J. Comput. Phys. 238(2013)1—31.

S.M. Peker, S.S. Helvaci, Solid—Liquid Two Phase Flow, Elsevier, Amsterdam (2011).

L. Xie, Z.H. Luo, Modeling and simulation of the influences of particle—particle interactions on dense solid—liquid suspensions in stirred vessels, Chem. Eng. Sci. 176(2018)439—453.

S. Hosseini, D. Patel, F. Ein-Mozaffari, M. Mehrvar, Study of solid—liquid mixing in agitated tanks through electrical resistance tomography, Chem. Eng. Sci. 65(4)(2010)1374—1384.

D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic Press, Boston(1994).

Z. Yang, T. Holemans, B. Lagrain, B. Sels, M. Vanierschot, A solid—liquid mixing reactor based on swirling flow technology, Chem. Eng. Sci. 280(2023) 119054.

F. Maluta, A. Paglianti, G. Montante, RANS-based predictions of dense solid—liquid suspensions in turbulent stirred tanks, Chem. Eng. Res. Des. 147 (2019)470—482.

P.R. Spalart, Strategies for turbulence modelling a nd simulations, Int. J. Heat Fluid Flow 21 (3)(2000)252—263.

L.T. Zhu, X.Z. Chen, B. Ouyang, W.C. Yan, H. Lei, Z. Chen, Z.H. Luo, Review of machine learning for hydrodynamics, transport, and reactions in multiphase flows and reactors, Ind. Eng. Chem. Res. 61(28)(2022)9901—9949.

D.Y. Gu, C.S. Li, X.L. Gu, J. Wang, Solid—liquid mixing characteristics in a fractal cut impeller stirred reactor with dense solid loading, Chem. Eng. Process. Process Intensif. 196(2024)109655.

Z. Yang, T. Holemans, B. Lagrain, B. Sels, M. Vanierschot, A draft tube to improve mixing in swirling flow-based solid—liquid mixing reactors, Chem. Eng. Res. Des. 206(2024)226—241.

Z.L. Xu, C. Yang, L.X. Wan, B.Q. Liu, Numerical investigation on the intensification of coaxial slurry mixing systems, Chem. Eng. Process. Process Intensif. 192 (2023) 109514.

T. Meng, A. Paglianti, F. Alberini, G. Montante, Y. Wang, Z.H. Liu, Investigating coupling and intensification mechanisms in multi-shaft digesting stirring reactors using POD, AIChE J. (2025)e70028.

A. de Lamotte, A. Delafosse, S. Calvo, D. Toye, Identifying dominant spatial and time characteristics of flow dynamics within free-surface baffled stirredtanks from CFD simulations, Chem. Eng. Sci. 192 (2018) 128— 142.

S.C. Zhao, W. Li, J.L. Zhang, Investigation of the temporal and spatial flow features within the high-shear mixer by modal decomposition techniques, AIChE J. 69(3) (2023)e17967.

J. Jin, Y. Fan, PIV experimental study on flow structure and dynamics of square stirred tank using modal decomposition, Kor. J. Chem. Eng. 37 (5) (2020)755—765.

W.H. Weheliye, N. Cagney, G. Rodriguez, M. Micheletti, A. Ducci, Mode decomposition and Lagrangian structures of the flow dynamics in orbitally shaken bioreactors, Phys. Fluids 30(3)(2018)033603.

ANSYS Inc, ANSYS FLUENT Theory Guide Inc. Release 19.2, ANSYS Academic, Research(2019).

J.M. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow, AIChE J. 36 (4)(1990)523—538.

A.D. Burns, T. Frank, I. Hamill, J.M. Shi, The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows, In: 5th International Conference on Multiphase Flow, Yokohama, Japan(2004).

A. de Lamotte, A. Delafosse, S. Calvo, D. Toye, Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor, Chem. Eng. Sci. 178(2018)348—366.

X.M. de Wit, M. Fruchart, T. Khain, F. Toschi, V. Vitelli, Pattern formation by turbulent casc ades, Nature 627(8004)(2024)515—521.

T. Savage, N. Basha, J. McDonough, J. Krassowski, O. Matar, E.A. del Rio Chanona, Machine learning-assisted discovery of flow reactor designs, Nat. Chem. Eng. 1(8)(2024)522—531.

D. Zhang, B. Ouyang, Z.H. Luo, Reaction process optimization based on interpretable machine learning and metaheuristic optimization algorithms, Chin. J. Chem. Eng. 84(2025)77—85.

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

Removal of deposited metal particles on a horizontal surface by vertical submerged impinging jets

CFD simulation of hydrodynamics and mixing performance in dual shaft eccentric mixers

Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller

Numerical study on solid suspension characteristics of a coaxial mixer in viscous systems

3D hydrodynamics involving multiple eccentric impellers in unbaffled cylindrical tank