Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

doi:10.1016/j.cjche.2021.11.008

中国化学工程学报 ›› 2022, Vol. 41 ›› Issue (1): 176-192.DOI: 10.1016/j.cjche.2021.11.008

Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

Qianqian Kang^1,2, Jinfan Liu⁵, Xin Feng^2,3,4, Chao Yang^2,3, Jingtao Wang¹

1 School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China;
2 Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
4 Innovation Academy for Green Manufacture, Chinese Academy of Sciences, Beijing 100190, China;
5 School of Chemical Engineering, Sichuan University, Chengdu 610065, China

收稿日期:2021-07-28 修回日期:2021-11-08 出版日期:2022-01-28 发布日期:2022-02-25
通讯作者: Xin Feng,E-mail address:xfeng@ipe.ac.cn;Jingtao Wang,E-mail address:wjingtao928@tju.edu.cn
基金资助:
Financial supports from National Key Research and Development Program (2020YFA0906804), the National Natural Science Foundation of China (21776282, 21978296 and 22078229), the NSFC Key Program (21938009) and major project (91934301), the National Key R&D Program of China (2019YFC1905805), Chemistry and Chemical Engineering Guangdong Laboratory Shantou (1922006), Innovation Academy for Green Manufacture, Chinese Academy of Sciences (IAGM2020C06) and Youth Innovation Promotion Association CAS are gratefully acknowledged.

Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

Qianqian Kang^1,2, Jinfan Liu⁵, Xin Feng^2,3,4, Chao Yang^2,3, Jingtao Wang¹

1 School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China;
2 Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
4 Innovation Academy for Green Manufacture, Chinese Academy of Sciences, Beijing 100190, China;
5 School of Chemical Engineering, Sichuan University, Chengdu 610065, China

Received:2021-07-28 Revised:2021-11-08 Online:2022-01-28 Published:2022-02-25
Contact: Xin Feng,E-mail address:xfeng@ipe.ac.cn;Jingtao Wang,E-mail address:wjingtao928@tju.edu.cn
Supported by:
Financial supports from National Key Research and Development Program (2020YFA0906804), the National Natural Science Foundation of China (21776282, 21978296 and 22078229), the NSFC Key Program (21938009) and major project (91934301), the National Key R&D Program of China (2019YFC1905805), Chemistry and Chemical Engineering Guangdong Laboratory Shantou (1922006), Innovation Academy for Green Manufacture, Chinese Academy of Sciences (IAGM2020C06) and Youth Innovation Promotion Association CAS are gratefully acknowledged.

摘要/Abstract

摘要： Laminar mixing in the stirred tank is widely encountered in chemical and biological industries. Isolated mixing regions (IMRs) usually exist when the fluid medium has high viscosity, which are not conducive to mixing. In this work, the researches on IMRs, enhancement of laminar mixing and the phenomenon of particle clustering within IMRs are reviewed. For most studies, the aim is to destroy IMRs and improve the chaotic mixing. To this end, the mechanism of chaotic mixing and the structure of IMRs were well investigated. The methods developed to destroy IMRs include off-centered agitation, dynamic mixing protocol, special designs of impellers, baffles, etc. In addition, the methods to characterize the shape and size of IMRs as well as mixing effect by experiments and simulations are summarized. However, IMRs are not always nuisance, and it may be necessary in some situations. Finally, the present engineering applications are summarized, and the prospect of the future application is predicted. For example, particle clustering will form in the co-existing system of chaotic mixing and IMRs, which can be used for solid–liquid separation and recovery of particles from high viscosity fluid.

关键词: Laminar mixing, Stirred tank, Isolated mixing regions, Particle clustering, Solid-liquid separation

Abstract: Laminar mixing in the stirred tank is widely encountered in chemical and biological industries. Isolated mixing regions (IMRs) usually exist when the fluid medium has high viscosity, which are not conducive to mixing. In this work, the researches on IMRs, enhancement of laminar mixing and the phenomenon of particle clustering within IMRs are reviewed. For most studies, the aim is to destroy IMRs and improve the chaotic mixing. To this end, the mechanism of chaotic mixing and the structure of IMRs were well investigated. The methods developed to destroy IMRs include off-centered agitation, dynamic mixing protocol, special designs of impellers, baffles, etc. In addition, the methods to characterize the shape and size of IMRs as well as mixing effect by experiments and simulations are summarized. However, IMRs are not always nuisance, and it may be necessary in some situations. Finally, the present engineering applications are summarized, and the prospect of the future application is predicted. For example, particle clustering will form in the co-existing system of chaotic mixing and IMRs, which can be used for solid–liquid separation and recovery of particles from high viscosity fluid.

Key words: Laminar mixing, Stirred tank, Isolated mixing regions, Particle clustering, Solid-liquid separation

Qianqian Kang, Jinfan Liu, Xin Feng, Chao Yang, Jingtao Wang. Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank[J]. 中国化学工程学报, 2022, 41(1): 176-192.

Qianqian Kang, Jinfan Liu, Xin Feng, Chao Yang, Jingtao Wang. Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank[J]. Chinese Journal of Chemical Engineering, 2022, 41(1): 176-192.

参考文献

[1] D.J. Lamberto, M.M. Alvarez, F.J. Muzzio, Computational analysis of regular and chaotic mixing in a stirred tank reactor, Chem. Eng. Sci. 56(16)(2001) 4887-4899.
[2] J. Dusting, J. Sheridan, K. Hourigan, A fluid dynamics approach to bioreactor design for cell and tissue culture, Biotechnol. Bioeng. 94(6)(2006)1196-1208.
[3] D. Bulnes-Abundis, L.M. Carrillo-Cocom, D. Aráiz-Hernández, A. García-Ulloa, M. Granados-Pastor, P.B. Sánchez-Arreola, G. Murugappan, M.M. Alvarez, A simple eccentric stirred tank mini-bioreactor:Mixing characterization and mammalian cell culture experiments, Biotechnol. Bioeng. 110(4)(2013)1106-1118.
[4] K.W. Norwood, A.B. Metzner, Flow patterns and mixing rates in agitated vessels, AIChE J. 6(3)(1960)432-437.
[5] S. Hashimoto, H. Ito, Y. Inoue, Experimental study on geometric structure of isolated mixing region in impeller agitated vessel, Chem. Eng. Sci. 64(24) (2009)5173-5181.
[6] N. Ohmura, T. Makino, T. Kaise, K. Kataoka, Transition of organized flow structure in a stirred vessel at low Reynolds numbers, J. Chem. Eng. Japan 36(12)(2003)1458-1463.
[7] Y.W. Fan, S.B. Wang, H. Wang, J.X. Xu, Q.T. Xiao, Y.G. Wei, Formation mechanism and chaotic reinforcement elimination of the mechanical stirring isolated mixed region, Int. J. Chem. React. Eng. 19(3)(2021)239-250.
[8] A.A. Abatan, J.J. McCarthy, W.L. Vargas, Particle migration in the rotating flow between co-axial disks, AIChE J. 52(6)(2006)2039-2045.
[9] T. Makino, N. Ohmura, K. Kataoka, Observation of isolated mixing regions in a stirred vessel, J. Chem. Eng. Jpn. 34(5)(2001)574-578.
[10] M.M. Alvarez, P.E. Arratia, F.J. Muzzio, Laminar mixing in eccentric stirred tank systems, Can. J. Chem. Eng. 80(4)(2008)546-557.
[11] D.J. Lamberto, F.J. Muzzio, P.D. Swanson, A.L. Tonkovich, Using timedependent RPM to enhance mixing in stirred vessels, Chem. Eng. Sci. 51(5) (1996)733-741.
[12] D.J. Lamberto, M.M. Alvarez, F.J. Muzzio, Experimental and computational investigation of the laminar flow structure in a stirred tank, Chem. Eng. Sci. 54(7)(1999)919-942.
[13] S. Wang, J. Wu, E. Bong, Reduced IMRs in a mixing tank via agitation improvement, Chem. Eng. Res. Des. 91(6)(2013)1009-1017.
[14] T. Makino, T. Kaise, K. Sasaki, N. Ohmura, K. Kataoka, Isolated mixing region in a Taylor-vortex-flow reactor, KAGAKU KOGAKU RONBUN. 27(5)(2001)566-573.
[15] Z. Zhong, G. Chen, Chaotic motion generation with applications to liquid mixing, In:Proceding of the 2005 European Conference on Circuit Theory& Design, Cork, Ireland, IEEE (2005)225-228.
[16] S. Woziwodzki, Ł. Jędrzejczak, Effect of eccentricity on laminar mixing in vessel stirred by double turbine impellers, Chem. Eng. Res. Des. 89(11)(2011) 2268-2278.
[17] S. Woziwodzki, Mixing of viscous Newtonian fluids in a vessel equipped with steady and unsteady rotating dual-turbine impellers, Chem. Eng. Res. Des. 92(3)(2014)435-446.
[18] T. Makino, T. Kaise, N. Ohmura, K. Kataoka, Laser-optical observation of chaotic mixing structure in a stirred vessel Laser Techniques for Fluid Mechanics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2002, pp. 399-410.
[19] S. Hashimoto, H. Ito, Y. Nakata, Y. Ishikawa, Y. Inoue, Geometric structure and formation condition of corded isolated-mixing region in impeller agitated vessel, J. Chem. Eng. Japan 44(11)(2011)845-851.
[20] M.M. Alvarez, J.M. Zalc, T. Shinbrot, P.E. Arratia, F.J. Muzzio, Mechanisms of mixing and creation of structure in laminar stirred tanks, AIChE J. 48(10) (2002)2135-2148.
[21] Y. Inoue, Y. Hirata, Numerical analysis of chaotic mixing in plane cellular flow. II. mixedness and final mixing pattern, KAGAKU KOGAKU RONBUNSHU 26(1) (2000)31-39.
[22] I.C. Christov, J.M. Ottino, R.M. Lueptow, Streamline jumping:A mixing mechanism, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(4 Pt 2)(2010) 046307.
[23] I.C. Christov, J.M. Ottino, R.M. Lueptow, Chaotic mixing via streamline jumping in quasi-two-dimensional tumbled granular flows, Chaos 20(2) (2010)023102.
[24] Y. Inoue, D. Takaoka, B. Okada, K. Natami, S. Hashimoto, Y. Hirata, Analysis of fluid mixing in an agitated vessel based on a streakline, KAGAKU KOGAKU RONBUNSHU 35(3)(2009)265-273.
[25] Y. Inoue, S. Hashimoto, Analysis of mechanism of laminar fluid mixing in 3-D mixing tank based on streakline lobes, KAGAKU KOGAKU RONBUNSHU 36(4) (2010)355-365.
[26] S. Hashimoto, K. Natami, Y. Inoue, Mechanism of mixing enhancement with baffles in impeller-agitated vessel, part I:A case study based on crosssections of streak sheet, Chem. Eng. Sci. 66(20)(2011)4690-4701.
[27] P.E. Arratia, J.P. Lacombe, T. Shinbrot, F.J. Muzzio, Segregated regions in continuous laminar stirred tank reactors, Chem. Eng. Sci. 59(7)(2004)1481-1490.
[28] H. Furukawa, S. Ohtani, Y. Kato, Y. Tada, Effects of location of baffle and clearance between baffle and vessel wall on isolated mixing regions, J. Chem. Eng. Japan 51(1)(2018)29-32.
[29] S. Hashimoto, R. Osaka, M. Kawamata, Analysis on laminar chaotic mixing based on configuration of streak lobes in an impeller-agitated vessel, Ind. Eng. Chem. Res. 51(19)(2012)6939-6947.
[30] D. Bulnes-Abundis, M.M. Alvarez, The simplest stirred tank for laminar mixing:Mixing in a vessel agitated by an off-centered angled disc, AIChE J. 59(8)(2013)3092-3108.
[31] M.M. Alvarez, A. Guzmán, M. Elías, Experimental visualization of mixing pathologies in laminar stirred tank bioreactors, Chem. Eng. Sci. 60(8-9) (2005)2449-2457.
[32] M. Alvarez, Using spatio-temporal asymmetry to enhance mixing in chaotic flows:From maps to stirred tanks Ph.D. Thesis, Rutgers The State University of New Jersey-New Brunswick, 2000.
[33] A.D. HarveyIII, D.H. WestIII, N.B. TufillaroIII, Evaluation of laminar mixing in stirred tanks using a discrete-time particle-mapping procedure, Chem. Eng. Sci. 55(3)(2000)667-684.
[34] J.M. Zalc, M.M. Alvarez, F.J. Muzzio, B.E. Arik, Extensive validation of computed laminar flow in a stirred tank with three Rushton turbines, AIChE J. 47(10)(2001)2144-2154.
[35] J.M. Zalc, E.S. Szalai, M.M. Alvarez, F.J. Muzzio, Using CFD to understand chaotic mixing in laminar stirred tanks, AIChE J. 48(10)(2002)2124-2134.
[36] J.R. Vallejos, Y. Kostov, A. Ram, J.A. French, M.R. Marten, G. Rao, Optical analysis of liquid mixing in a minibioreactor, Biotechnol. Bioeng. 93(5)(2006) 906-911.
[37] F. Cabaret, L. Fradette, P.A. Tanguy, Effect of shaft eccentricity on the laminar mixing performance of a radial impeller, Can. J. Chem. Eng. 86(6)(2008)971-977.
[38] D. Gu, Z. Liu, J. Li, Z. Xie, C. Tao, Y. Wang, Intensification of chaotic mixing in a stirred tank with a punched rigid-flexible impeller and a chaotic motor, Chem. Eng. Process. 122(2017)1-9.
[39] S. Woziwodzki, Unsteady mixing characteristics in a vessel with forwardreverse rotating impeller, Chem. Eng. Technol. 34(5)(2011)767-774.
[40] Z. Liu, C. Chen, R. Liu, C. Tao, Y. Wang, Chaotic mixing enhanced by rigidflexible impeller in stirred vessel, CIESC J. 65(2014)61-70.(in Chinese)
[41] F.J. Muzzio, P.D. Swanson, J.M. Ottino, The statistics of stretching and stirring in chaotic flows, Phys. Fluids A:Fluid Dyn. 3(5)(1991)822-834.
[42] Z.G. Sun, G. Xi, X. Chen, A numerical study of stir mixing of liquids with particle method, Chem. Eng. Sci. 64(2)(2009)341-350.
[43] K.C. Ng, E.Y.K. Ng, Laminar mixing performances of baffling, shaft eccentricity and unsteady mixing in a cylindrical vessel, Chem. Eng. Sci. 104(2013)960-974.
[44] M.N. Noui-Mehidi, N. Ohmura, J. Wu, B.V. Nguyen, N. Nishioka, T. Takigawa, Characterisation of isolated mixing regions in a stirred vessel, Int. J. Chem. React. Eng. 6(1)(2008)1-10.
[45] M.M. Alvarez-Hernández, T. Shinbrot, J. Zalc, F.J. Muzzio, Practical chaotic mixing, Chem. Eng. Sci. 57(17)(2002)3749-3753.
[46] Y. Kato, Y. Tada, M. Ban, Y. Nagatsu, K. Yanagimoto, Application of asymmetric impellers to mixing at unsteady speed within a single revolution, KAGAKU KOGAKU RONBUNSHU 33(1)(2007)16-19.
[47] W.M. Yek, M.N. Noui-Mehidi, R. Parthasarathy, Intensification of flow characteristics in a laminar flow stirred tank using modified impeller designs, J. Chem. Eng. Japan 43(1)(2010)13-16.
[48] Z. Driss, S. Karray, H. Kchaou, M. Abid, CFD simulation of the laminar flow in stirred tanks generated by double helical ribbons and double helical screw ribbons impellers, Open Eng. 1(4)(2011)413-422.
[49] Y. Zhang, J. He, Numerically simulating influence of undulating motion mode of biomimetic fish fin on its motion performance, Mech. Sci. and Technol. 32(3)(2013)435-440.
[50] R.L. Campbell, E.G. Paterson, Fluid-structure interaction analysis of flexible turbomachinery, J. Fluids Struct. 27(8)(2011)1376-1391.
[51] J.Y. Dieulot, G. Delaplace, R. Guerin, J.P. Brienne, J.C. Leuliet, Laminar mixing performances of a stirred tank equipped with helical ribbon agitator subjected to steady and unsteady rotational speed, Chem. Eng. Res. Des. 80(4)(2002)335-344.
[52] J.Y. Dieulot, N. Petit, P. Rouchon, G. Delaplace, An arrangement of ideal zones with shifting boundaries as a way to model mixing processes in unsteady stirring conditions in agitated vessels, Chem. Eng. Sci. 60(20)(2005)5544-5554.
[53] S. Senda, Y. Komoda, Y. Hirata, H. Takeda, H. Suzuki, R. Hidema, Characteristics of flow filed induced by a rotationally reciprocating plate impeller, J. Chem. Eng. Japan 49(4)(2016)341-349.
[54] Y. Hirata, T. Dote, T. Yoshioka, Y. Komoda, Y. Inoue, Performance of chaotic mixing caused by reciprocating a disk in a cylindrical vessel, Chem. Eng. Res. Des. 85(5)(2007)576-582.
[55] Y. Komoda, Y. Inoue, Y. Hirata, Mixing performance by reciprocating disk in cylindrical vessel, J. Chem. Eng. Japan 33(6)(2000)879-885.
[56] Y. Komoda, Y. Inoue, Y. Hirata, Characteristics of laminar flow induced by reciprocating disk in cylindrical vessel, J. Chem. Eng. Japan 34(7)(2001)919-928.
[57] P. Mavros, Flow visualization in stirred vessels-A review of experimental techniques, Chem. Eng. Res. Des. 79(A2)(2001)113-127.
[58] J.Q. Zhang, X.W. Li, R.B. He, J. Liang, Study on double-shaft mixing paddle undergoing planetary motion in the laminar flow mixing system, Adv. Mech. Eng. 7(7)(2015), 168781401559260.
[59] K. Takahashi, M. Motoda, Chaotic mixing created by object inserted in a vessel agitated by an impeller, Chem. Eng. Res. Des. 87(4)(2009)386-390.
[60] W.M. Yek, M.N. Noui-Mehidi, R. Parthasarathy, S.N. Bhattacharya, J. Wu, N. Ohmura, N. Nishioka, Enhanced mixing of Newtonian fluids in a stirred vessel using impeller speed modulation, Can. J. Chem. Eng. 87(6)(2009)839-846.
[61] F. Cabaret, L. Fradette, P.A. Tanguy, New turbine impellers for viscous mixing, Chem. Eng. Technol. 31(12)(2008)1806-1815.
[62] K. Takahashi, D. Shigihara, Y. Takahata, Laminar mixing in eccentric stirred tank with different bottom, J. Chem. Eng. Japan 44(12)(2011)931-935.
[63] J. Karcz, J. Szoplik, An effect of the eccentric position of the propeller agitator on the mixing time, Chem. Pap. 58(1)(2004)9-14.
[64] J. Karcz, M. Cudak, J. Szoplik, Stirring of a liquid in a stirred tank with an eccentrically located impeller, Chem. Eng. Sci. 60(8-9)(2005)2369-2380.
[65] G. Ascanio, E. Brito-de la Fuente, R. Yatomi, P.A. Tanguy, Design considerations in laminar fluid mixing with unconventional geometries, Front. Sci. Eng. 2(2012)15.
[66] S. Wang, J. Wu, N. Ohmura, Inclined-shaft agitation for improved viscous mixing, Ind. Eng. Chem. Res. 52(33)(2013)11741-11751.
[67] K. Takahashi, Y. Takahata, K. Kurisaka, H. Sekine, Mixing performance experiments in an agitated vessel equipped with a pitched paddle subjected to unsteady agitation, J. Chem. Eng. Japan 44(11)(2011)852-858.
[68] T. Nomura, T. Uchida, K. Takahashi, Enhancement of mixing by unsteady agitation of an impeller in an agitated vessel, J. Chem. Eng. Japan 30(5)(1997) 875-879.
[69] M. Yoshida, Y. Nagai, K. Yamagiwa, A. Ohkawa, S. Tezura, Turbulent and laminar mixings in an unbaffled agitated vessel with an unsteadily angularly oscillating impeller, Ind. Eng. Chem. Res. 48(3)(2009)1665-1672.
[70] M. Yoshida, M. Shigeyama, T. Hiura, K. Yamagiwa, A. Ohkawa, S. Tezura, Liquid-phase mixing in an unbaffled agitated vessel with an unsteady forward-reverse rotating impeller, Asia-Pacific Jrnl Chem. Eng 2(6)(2007) 659-664.
[71] Y. Kato, Y. Tada, M. Ban, Y. Nagatsu, S. Iwata, K. Yanagimoto, Improvement of mixing efficiencies of conventional impeller with unsteady speed in an impeller revolution, J. Chem. Eng. Japan 38(9)(2005)688-691.
[72] Y. Murakami, T. Hirose, T. Yamato, H. Fujiwara, M. Ohshima, Improvement in mixing of high viscosity liquid by additional up-and-down motion of a rotating impeller, J. Chem. Eng. Japan 13(4)(1980)318-323.
[73] M.J. Clifford, S.M. Cox, Smart baffle placement for chaotic mixing, Nonlinear Dyn. 43(1-2)(2006)117-126.
[74] Y. Kato, Y. Tada, S. Nakamichi, Y. Nagatsu, S. Iwata, S. Iwaishi, S. Kajihara, Y.S. Lee, S.T. Koh, Evaluation of unsteady mixing performance using a servo motor, KAGAKU KOGAKU RONBUNSHU 32(6)(2006)465-470.
[75] N.H. Shahirudin, N. Alatengtuya, T. Kumagai, N. Horie, Ohmura, Effect of temperature change on geometric structure of isolated mixing regions in stirred vessel, Int. J. Chem. Eng. 2012(2012)1-6.
[76] M. Rice, J. Hall, G. Papadakis, M. Yianneskis, Investigation of laminar flow in a stirred vessel at low Reynolds numbers, Chem. Eng. Sci. 61(9)(2006)2762-2770.
[77] M. Irene Sánchez Cervantes, J. Lacombe, F.J. Muzzio, M.M. Álvarez, Novel bioreactor design for the culture of suspended mammalian cells. Part I: Mixing characterization, Chem. Eng. Sci. 61(24)(2006)8075-8084.
[78] G. Segré, A. Silberberg, Radial particle displacements in poiseuille flow of suspensions, Nature 189(4760)(1961)209-210.
[79] G. Segre, A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow, J. Fluid Mech. 14(1962)115-157.
[80] J.S. Halow, G.B. Wills, Radial migration of spherical particles in couette systems, AIChE J. 16(2)(1970)281-286.
[81] A. Nadim, R.G. Cox, H. Brenner, Transport of sedimenting Brownian particles in a rotating Poiseuille flow, Phys. Fluids 28(12)(1985)3457.
[82] J.F. Morris, J.F. Brady, Pressure-driven flow of a suspension:Buoyancy effects, Int. J. Multiph. Flow 24(1)(1998)105-130.
[83] B.P. Ho, L.G. Leal, Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech. 65(2)(1974)365-400.
[84] D. Leighton, A. Acrivos, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech. 181(1987)415.
[85] A. Ramachandran, D.T. Leighton, The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions, J. Fluid Mech. 603(2008)207-243.
[86] A. Crisanti, M. Falcioni, A. Provenzale, A. Vulpiani, Passive advection of particles denser than the surrounding fluid, Phys. Lett. A 150(2)(1990)79-84.
[87] J. Magnaudet, Small inertial effects on a spherical bubble, drop or particle moving near a wall in a time-dependent linear flow, J. Fluid Mech. 485(2003) 115-142.
[88] J. Ye, M.C. Roco, Particle rotation in a Couette flow, Phys. Fluids A:Fluid Dyn. 4(2)(1992)220-224.
[89] R.L. Schiek, E.S.G. Shaqfeh, Cross-streamline migration of slender Brownian fibres in plane Poiseuille flow, J. Fluid Mech. 332(1997)23-39.
[90] M.R. Maxey, The motion of small spherical particles in a cellular flow field, Phys. Fluids 30(7)(1987)1915.
[91] N. Nishioka, Y. Tago, T. Takigawa, M. Noui-Mehidi, J. Wu, N. Ohmura, Particle migration in a stirred vessel at low Reynolds numbers, in:AIDIC Conference Series:Selected Papers of the Eighth Italian Conference on Chemical and Process Engineering, Milano, Italy, 2007, pp. 243-247.
[92] N. Nishioka, Observation of inertial particle motion in laminar flow in a stirred vessel, 1, Memoirs of the Graduate School of Engineering Kobe University, 2009, pp. 48-51.
[93] S. Wang, R.L. Stewart, G. Metcalfe, Visualization of the trapping of inertial particles in a laminar mixing tank, Chem. Eng. Sci. 143(2016)99-104.
[94] G. Metcalfe, Push and pull:Attractors and repellors of a dynamical system can localize inertial particles, Granul. Matter 21(4)(2019)1-8.
[95] G. Haller, T. Sapsis, Where do inertial particles go in fluid flows?, Phys D: Nonlinear Phenom. 237(5)(2008)573-583.
[96] T. Sapsis, G. Haller, Instabilities in the dynamics of neutrally buoyant particles, Phys. Fluids 20(1)(2008)017102.
[97] T. Sapsis, G. Haller, Clustering criterion for inertial particles in twodimensional time-periodic and three-dimensional steady flows, Chaos 20(1)(2010)017515.
[98] S. Wang, G. Metcalfe, R.L. Stewart, J. Wu, N. Ohmura, X. Feng, C. Yang, Solid-liquid separation by particle-flow-instability, Energy Environ. Sci. 7(12) (2014)3982-3988.
[99] R. Grenville, A. Nienow, Handbook of industrial mixing, John Wiley&Sons Inc, 2004, pp. 507-542.
[100] O. Paireau, P. Tabeling, Enhancement of the reactivity by chaotic mixing, Phys. Rev. E 56(2)(1997)2287.
[101] Z. Liu, X. Yang, Z. Xie, R. Liu, C. Tao, Y. Wang, Chaotic mixing performance of high-viscosity fluid synergistically intensified by flexible impeller and floating particles, CIESC J. 64(2013)2794-2800.(in Chinese)

Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Zewen Chen, Yongjun Wu, Jian Wang, Peicheng Luo. Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller[J]. 中国化学工程学报, 2022, 47(7): 79-88.
[2]	Yongjun Wu, Pan You, Peicheng Luo. Effect of pitched short blades on the flow characteristics in a stirred tank with long-short blades impeller[J]. 中国化学工程学报, 2022, 45(5): 143-152.
[3]	Weipeng Lu, Xuefeng Yan. Balanced multiple weighted linear discriminant analysis and its application to visual process monitoring[J]. 中国化学工程学报, 2021, 36(8): 128-137.
[4]	Xiaolong Li, Hongliang Zhao, Zimu Zhang, Yan Liu, Ting'an Zhang. Numerical optimization for blades of Intermig impeller in solid-liquid stirred tank[J]. 中国化学工程学报, 2021, 29(1): 57-66.
[5]	Xiaoxia Duan, Xin Feng, Chong Peng, Chao Yang, Zaisha Mao. Numerical simulation of micro-mixing in gas-liquid and solid-liquid stirred tanks with the coupled CFD-E-model[J]. 中国化学工程学报, 2020, 28(9): 2235-2247.
[6]	Mohammad Bagher Sabeti, Mohammad Amin Hejazi, Afzal Karimi. Enhanced removal of nitrate and phosphate from wastewater by Chlorella vulgaris: Multi-objective optimization and CFD simulation[J]. 中国化学工程学报, 2019, 27(3): 639-648.
[7]	Meng Li, Yangbo Tan, Jianglong Sun, De Xie, Zeng Liu. Drawdown mechanism of light particles in baffled stirred tank for the KR desulphurization process[J]. Chinese Journal of Chemical Engineering, 2019, 27(2): 247-256.
[8]	Facheng Qiu, Zuohua Liu, Renlong Liu, Xuejun Quan, Changyuan Tao, Yundong Wang. Experimental study of power consumption, local characteristics distributions and homogenization energy in gas–liquid stirred tank reactors[J]. Chinese Journal of Chemical Engineering, 2019, 27(2): 278-285.
[9]	Meng Li, Yangbo Tan, Yufeng Liu, Jianglong Sun, De Xie, Zeng Liu. Effects of geometrical and physical factors on light particles dispersion by agitation characteristic curve[J]. 中国化学工程学报, 2019, 27(10): 2313-2324.
[10]	Xiaoxia Duan, Xin Feng, Chao Yang, Zaisha Mao. CFD modeling of turbulent reacting flow in a semi-batch stirred-tank reactor[J]. Chinese Journal of Chemical Engineering, 2018, 26(4): 675-683.
[11]	Basim O. Hasan. Breakage of drops and bubbles in a stirred tank:A review of experimental studies[J]. , 2017, 25(6): 698-711.
[12]	Dongyue Li, Antonio Buffo, Wioletta Podgórska, Daniele L. Marchisio, Zhengming Gao. Investigation of droplet breakup in liquid-liquid dispersions by CFD-PBM simulations:The influence of the surfactant type[J]. , 2017, 25(10): 1369-1380.
[13]	Dongyue Li, Antonio Buffo, Wioletta Podgórska, Daniele L. Marchisio, Zhengming Gao. Investigation of droplet breakup in liquid-liquid dispersions by CFD-PBM simulations:The influence of the surfactant type[J]. , 2017, 25(10): 1369-1380.
[14]	Shengbin Di, Ji Xu, Qi Chang, Wei Ge. Numerical simulation of stirred tanks using a hybrid immersed-boundary method[J]. , 2016, 24(9): 1122-1134.
[15]	M. Moayeri Kashani, S. H. Lai, S. Ibrahim, P. Moradi Bargani. Design factors affecting the dynamic performance of soil suspension in an agitated, baffled tank[J]. , 2016, 24(12): 1664-1673.