Investigation of the Viscoelastic Effect on the Metzner and Otto Coefficient Through LDA  Velocity Measurements

Abstract

Abstract: The Metzner and Otto correlation is the single practical method for incorporating non-
Newtonian effects in the mixing process. In this article, the Metzner and Otto’ s idea, the
role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on
ks and the determination of ks for Rushton turbine impeller have been studied using the
direct method of the laser Doppler anemometry (LDA) velocity meusurement for the case of
viscoelastic liquids. The normalized mean tangential velocity profiles are independent of
Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the
variation of local shear rate against the impeller speed is better correlated by the power
equation, i.e. = ks＇. Nb＇, in the transition region, i.e. ～ 30 ＜ Re <～ 2000.Also, a
correlation between improved coefficient, ks＇, and the elasticity number of viscoelastic
liquids is given which is very helpful in designing of the mixing of both viscoelastic and
inelastic non-Newtonian fluids through relating rheological properties to kinematical and
dynamical parameters of the mixing process.

Key words: viscoelastic, mixing, Rushton turbine impeller, laser Doppler anemometry (LDA), Metzner and Otto coefficient

摘要： The Metzner and Otto correlation is the single practical method for incorporating non-
Newtonian effects in the mixing process. In this article, the Metzner and Otto’ s idea, the
role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on
ks and the determination of ks for Rushton turbine impeller have been studied using the
direct method of the laser Doppler anemometry (LDA) velocity meusurement for the case of
viscoelastic liquids. The normalized mean tangential velocity profiles are independent of
Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the
variation of local shear rate against the impeller speed is better correlated by the power
equation, i.e. = ks＇. Nb＇, in the transition region, i.e. ～ 30 ＜ Re <～ 2000.Also, a
correlation between improved coefficient, ks＇, and the elasticity number of viscoelastic
liquids is given which is very helpful in designing of the mixing of both viscoelastic and
inelastic non-Newtonian fluids through relating rheological properties to kinematical and
dynamical parameters of the mixing process.

关键词: viscoelastic;mixing;Rushton turbine impeller;laser Doppler anemometry (LDA);Metzner and Otto coefficient

M. Jahangiri, M. R. Golkar-Narenji, N. Montazerin, S. Savarmand. Investigation of the Viscoelastic Effect on the Metzner and Otto Coefficient Through LDA
Velocity Measurements[J]. .

M. Jahangiri, M. R. Golkar-Narenji, N. Montazerin, S. Savarmand. 用激光多普勒测速计（LDA）分析粘弹性对Metzner和Otto系数的影响[J]. CIESC Journal.

References

[1] Bird, R. B., Armstrong, R. C., Hassager, O., Dynamics of Polymeric Liquids, Vol. 1,
Fluid Mechanics, 2nd ed., John Wiley & Sons, New York (1987).
[2] Ozcan-Taskin, N.G., Nienow, A. W., "Mixing viscoelastic fluids with axial flow
impellers: flow fields and power consumption", Trans. IChem. E., 73, 49(1995).
[3] Haddad, Y. M., Viscoelasticity of Engineering Materials,Champman and Hall, London
(1995).
[4] Lee, K. C., Yianneskis, M., "Turbulenceproperties of the impeller stream of a Rushton
turbine", AIChE J., 44, 13(1998).
[5] Dyster, K. N., Koutsakos, E., Jaworski, Z., Nienow, A.W.,"An LDA study of the radial
discharge velocities generated by a Rushton turbine: Newtonian fluids, Re ≥ 5",
Trans.Inst. Chem. Eng., 71, 11 (1993).
[6] Costes, J., "Structure of generated flow by a Rushton turbine in abaffied tank", Thesis
Doctorat des Sciences, Institut National polytechnique, Tolouse, France, (1986). (in
French)
[7] Metzner, A. B., Otto, R. E., "Agitation of non-Newtonian fluids", AlChE J., 3 (1), 3
(1957).
[8] Magnusson, K., "The power requirement dependence of the effective shear rate while
stirring structurally viscous fluids", Iva. (Sweden), 23, 86 (1952). (in Swedish)
[9] Metzner, A. B., Taylor, J. S., "Flow patterns in agitated vessels", AIChE J., 6 (1),
109 (1960).
[10] Metzner, A. B., Fees, R. H., Ramos, H. L., Otto, R. E.,Tuthill, J. D., "Agitation of
viscous Newtonian and nonNewtonian fluids", AIChE J., 7 (1), 3 (1961).
[11] Hiraoka, S., Yamada, I., Mizoguchi, K., "Two dimensional model analyses of flow
behaviour of highly viscous nonNewtonian fluid in agitated vessel with paddle impeller",J.
Chem. Eng. Japan, 12 (1), 56 (1979).
[12] Carreau, P. J., Chhabra, R. P., Cheng, J., "Effect of rheological properties on power
consumption with helical ribbon agitators", AIChE J., 39 (9), 1421 (1993).
[13] Brito-De La Fuente, E, Choplin, L., Tanguy, P. A., "Mixing with helical ribbon
impellers: Effect of highly shear thinning behaviour and impeller geometry", Trans. IChem.
E.,75, 45 (1997).
[14] Ulbrecht, J. J., Carreau, P., "Mixing of viscous nonNewtonian liquids", In: Mixing of
liquids by Mechanical Agitation, Ulbrecht, J. J., Patterson, G. K., (eds.), Vol. 1,Gordon
and Breach Science Pub., New York, 93 (1985).
[15] Seyssiecq, I., Mrely-Alpa, F., Desplanches, H., GastonBonhomme, Y., "Power consumption
reduction in viscoelastic solutions", ENTROPIE, 31 (191), 19 (1995). (in French)
[16] Bartels, P.V., "An experimental study on turbulent mixing of viscoelastic fluids", Ph.
D. Thesis, Delft University, Delft(1988).
[17] Montazerin, N., Damangir, A., Mirian, S., "A new concept for squirrel-cage fan inlet",
Proc. Instn. Mech. Engrs.,212, 343 (1998).
[18] Johnson, D. A., Modarress, D., Owen, F. K., "An experimental verification of laser-
velocimeter sampling bias and its correlation", Trans. ASME J. Fluids Engng., 106, 5(1984).
[19] Golkar-Narenji, M. R., "Free coating of viscoelastic fluids",Ph. D. Thesis, University
of bradford, UK (1978).
[20] Stoots, C. M., Calabrese, R. V., "Mean velocity field relativeto a Rushton turbine
blade", AIChE J., 41 (1), 1(1995).
[21] Ulbrecht, J., "Mixing of viscoelastic fluids by mechanical agitation", Chem. Eng.,
June, 347 (1974).
[22] Skelland, A. H. P., "Mixing and agitation of non-Newtonian fluids", In: Handbook of
Fluids in Motion, Cheremisinoff,N. P., Gupta, R., eds., Ann Arbor Science, New York,
chap.7, pp. 179, (1983).
[23] Doraiswamy, D., Grenville, R. K., Etchells, A. W., "Twoscore years of the Metzner-Otto
correlation", Ind. Eng.Chem. Res., 33 (10), 2253 (1994).
[24] Calderbank, P. H., Moo-Young, M. B., "The prediction of power consumption in the
agitation of non-Newtonian fluids". Trans. Inst. Chem. Eng., 37, 26 (1959).
[25] Calderbank, P. H., Moo-Young, M. B., "The power characteristics of agitators for the
mixing of Newtonian and non-Newtonian fluids", Trans. Inst. Chem. Eng., 39, 337(1961).
[26] Ducla, J. M., Desplanches, H., Chevallier, J. L., "Effective viscosity of non-
Newtouian fiuids in a mechanically stirred tank", Chem. Eng. Commun., 21 (1), 29 (1983).
[27] Torrez, C., Andre, C., "Power consumption of a Rushton turbine mixing viscous
Newtonian and shear-thinning fluids: comparison between experimentaJ and numerical
results", Chem. Eng. Technol., 21,599 (1998).
[28] Solomon, J., Nienow, A. W., Pace, G. W., "Flow patterns in agitated plastic and
pseudoplastic", IChem. Eng. Symp.Ser. No. 64, Hemisphere Publbhing Corporation Bradford A1
(1981).
[29] Ranade, V. R., Ulbrecht, J. J., "Gas dispersion in agitated viscous inelastic and
viscoelastic liquids", 2nd Europ. Conf.on Mixing, Cambridge, F6, 83 (1977).
[30] Brito-De La Fuente, E., Leuliet, J. C., Choplln, L., Tanguy, P. A., "Mixing and
circulation times in rheologically complex fluids", IChem. Eng. Symp. Ser. No. 121, 75
(1990).

Investigation of the Viscoelastic Effect on the Metzner and Otto Coefficient Through LDA
Velocity Measurements

用激光多普勒测速计（LDA）分析粘弹性对Metzner和Otto系数的影响

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Erqi WANG, Shuzhou PENG, Zhen YANG, Yuanyuan DUAN. Evaluation of vapor-liquid equilibrium models for mixtures containing HFOs [J]. CIESC Journal, 2023, 74(8): 3216-3225.
[2]	Kexin HUANG, Tong LI, Anqi LI, Mei LIN. Mode decomposition of flow field in T-junction with rotating impeller [J]. CIESC Journal, 2023, 74(7): 2848-2857.
[3]	Feng LIU, Quan WANG, Panyu WU, Guo WEI, Xiang HE. Effect of internal phase particle size on vibration resistance of on-site mixed emulsion explosive matrix [J]. CIESC Journal, 2022, 73(9): 4217-4225.
[4]	Yuehui HOU, Xuan LIU, Yingjiang LIAN, Mei HAN, Chaoqun YAO, Guangwen CHEN. Synthesis process of trinitrophloroglucinol in an ultrasonic microreactor [J]. CIESC Journal, 2022, 73(8): 3597-3607.
[5]	Huibo MENG, Tong MENG, Yanfang YU, Zongyong WANG, Jianhua WU. Turbulent heat transfer and mixing enhancement characteristics in Ross LPD static mixer [J]. CIESC Journal, 2022, 73(8): 3541-3552.
[6]	Wenkai CHENG, Xianming ZHANG, Jiajun WANG, Lianfang FENG. Numerical simulation of hydrodynamics and mixing characteristics in a horizontal single-shaft kneader [J]. CIESC Journal, 2022, 73(5): 1995-2007.
[7]	Hongfei LIU, Xueliang LI, Juntao QIAN, Jin LIU, Guocheng DU, Jian CHEN. Hydrodynamics and mass transfer in rocking T25 cell culture flasks [J]. CIESC Journal, 2022, 73(4): 1546-1556.
[8]	Zirui WU, Rui SUN, Lingfeng SHI, Hua TIAN, Xuan WANG, Gequn SHU. A comparative and predictive study of the mixing rules for the vapor-liquid equilibria of CO₂-based mixtures [J]. CIESC Journal, 2022, 73(4): 1483-1492.
[9]	Xing TIAN, Jiayue ZHANG, Zhigang GUO, Jian YANG, Qiuwang WANG. Flow and heat transfer characteristics of particles flowing along the plate with different mixing elements [J]. CIESC Journal, 2022, 73(11): 4884-4892.
[10]	Weixing JIN, Jun YAN, Chenglin E, Yiping FAN, Chunxi LU. Mixing/separation characteristics of great different particles in gas-solid fluidized bed [J]. CIESC Journal, 2022, 73(11): 4872-4883.
[11]	Zuohua LIU, Yilin ZHOU, Xia XIONG, Changyuan TAO, Yundong WANG. Chaotic mixing intensification and flow field structure instability in stirred reactor by counter-flow pitched-blade turbine [J]. CIESC Journal, 2022, 73(1): 222-231.
[12]	Wenkai CHENG, Xianming ZHANG, Jiajun WANG, Lianfang FENG. Numerical simulation of mixing process in different opposite-rotating horizontal twin-shaft kneaders [J]. CIESC Journal, 2022, 73(1): 162-174.
[13]	Jing ZHAO, Bogeng LI, Zhiyang BU, Hong FAN. Research on residence time distribution of the low-viscous polymer fluid in microchannel [J]. CIESC Journal, 2021, 72(8): 4030-4038.
[14]	DONG Xiaorui, WANG Kai, LUO Guangsheng. Microreaction continuous synthesis of gold nanoparticles [J]. CIESC Journal, 2021, 72(7): 3823-3831.
[15]	LI Wenjin, ZHOU Yongjun, YUAN Mingyue, HE Hua, SUN Jianping. Comparative study of the flow characteristics in several frame-type impeller stirred tanks [J]. CIESC Journal, 2021, 72(4): 1998-2005.