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Journal articles on the topic 'Stirred tanks'

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Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Manshoor, Bukhari, Muhammad Faiq Mdsaufi, Izzuddin Zaman, and Amir Khalid. "CFD Analysis of Industrial Multi-Stage Impeller in Stirred Tank with Fractal Pattern Baffled and Impeller." Applied Mechanics and Materials 773-774 (July 2015): 337–42. http://dx.doi.org/10.4028/www.scientific.net/amm.773-774.337.

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This paper presents tool for analysis of CFD adapted for flows in multi-staged stirred vessels with fractal pattern baffled for industrial. In order to develop a good mixing process model for stirred tanks, several way have been investigated by using the computational fluid dynamic. Implementing fractal design into stirred tank’s baffle and impeller are believed to influence the flow characteristic inside the stirred tank. The mixing process will be conduct by using multi-stage stirred tanks. Hence, the study is to simulate a fractal pattern baffled stirred vessels with fractal base of impeller. Four models with a new concept and different design of stirred tank have been introduced and studied. The multi-stages stirred tanks will adapted with fractal base pattern concept. The simulation is carry out by using the standard k-ε turbulence model. The results have been analysis in order to prove that which one of that model is the most effective in mixing. The flows produced in stirred tank are different and relevant with each model. The velocity profiles also give a relevant and quite impressive result by each model. At the end, the results will be examined and compared with each data that use a common type of baffle and impeller design.

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2

Asencor, J., J. M. Gracia, and I. De Hoyos. "Stirred tanks: a didactic tool." International Journal of Mathematical Education in Science and Technology 24, no. 5 (September 1993): 617–29. http://dx.doi.org/10.1080/0020739930240502.

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3

Steiros, K. "Transient torque in stirred tanks." Journal of Fluid Mechanics 831 (October 13, 2017): 554–78. http://dx.doi.org/10.1017/jfm.2017.652.

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The transient dynamics of stirred tanks whose impeller speed undergoes smooth or step changes is investigated. First, a low-order model is developed, linking the impeller torque with the ‘extent’ of the solid-body rotation in the tank, derived from an angular momentum balance in a control volume around the impeller. Utilisation of this model enables the prediction of the torque ‘spike’ appearing after an impulsive change of the shaft speed, and of the torque evolution during a quasi-steady transition. For the case of a small impulsive change in the shaft speed, a characteristic spin-up time is also proposed. Torque measurements performed in an unbaffled stirred tank show considerable agreement with the theoretical predictions.

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4

Wu, J., B. Nguyen, G. Lane, S. Wang, R. Parthasarathy, and L. J. Graham. "Process Intensification in Stirred Tanks." Chemical Engineering & Technology 35, no. 7 (June 5, 2012): 1125–32. http://dx.doi.org/10.1002/ceat.201100712.

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5

Zivkovic, Goran, and Stevan Nemoda. "Modeling of bubble break-up in stirred tanks." Thermal Science 8, no. 1 (2004): 29–50. http://dx.doi.org/10.2298/tsci0401029z.

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The Lagrangian code LAG3D for dispersed phase flow modeling was implemented with the introduction of bubble break-up model. The research was restricted on bubbles with diameter less than 2 mm, i.e. bubbles which could be treated as spheres. The model was developed according to the approach of Martinez-Bazan model. It was rearranged and adjusted for the use in the particular problem of flow in stirred tanks. Developed model is stochastic one, based on the assumption that shear in the flow induces the break of the bubble. As a dominant parameter a dissipation of the turbulent kinetic energy was used. Computations were performed for two different types of the stirrer: Rushton turbine, and Pitch blade turbine. The geometry of the tank was kept constant (four blades). Two different types of liquids with very big difference in viscosity were used, i.e. silicon oil and dimethylsulfoxide, in order to enable computation of the flow in turbulent regime as well. As a parameter of the flow, the number of rotations of the stirrer was varying. As a result of the computation the fields of velocity of both phases were got, as well as the fields of bubble concentration bubble mean diameter and bubble Sauter diameter. To estimate the influence of the break-up model on the processes in the stirred tank a computations with and without this model were performed and compared. A considerable differences were found not only in the field of bubble diameter, but also in the field of bubble concentration. That confirmed a necessity of the introduction of such model. A comparison with the experiments performed with phase Doppler anemometry technique showed very good agreement in velocity and concentration profiles of the gas phase. The results for the average bubble diameter are qualitatively the same, but in almost all computations about 20% smaller bubble diameter was got than in the measurements.

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6

Bhattacharya, S., D. Hebert, and S. M. Kresta. "Air Entrainment in Baffled Stirred Tanks." Chemical Engineering Research and Design 85, no. 5 (January 2007): 654–64. http://dx.doi.org/10.1205/cherd06184.

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7

Alves, S. S., C. I. Maia, J. M. T. Vasconcelos, and A. J. Serralheiro. "Bubble size in aerated stirred tanks." Chemical Engineering Journal 89, no. 1-3 (October 2002): 109–17. http://dx.doi.org/10.1016/s1385-8947(02)00008-6.

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8

Zamankhan, P. "Enhanced Mass Transfer in Stirred Tanks." Chemical Engineering & Technology 33, no. 3 (March 2010): 508–22. http://dx.doi.org/10.1002/ceat.200900347.

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9

Luo, Xiaotong, Jiachuan Yu, Bo Wang, and Jingtao Wang. "Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method." Processes 9, no. 5 (May 12, 2021): 849. http://dx.doi.org/10.3390/pr9050849.

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The heat transfer and hydrodynamics of particle flows in stirred tanks are investigated numerically in this paper by using a coupled CFD–DEM method combined with a standard k-e turbulence model. Particle–fluid and particle–particle interactions, and heat transfer processes are considered in this model. The numerical method is validated by comparing the calculated results of our model to experimental results of the thermal convection of gas-particle flows in a fluidized bed published in the literature. This coupling model of computational fluid dynamics and discrete element (CFD–DEM) method, which could calculate the particle behaviors and individual particle temperature clearly, has been applied for the first time to the study of liquid-solid flows in stirred tanks with convective heat transfers. This paper reports the effect of particles on the temperature field in stirred tanks. The effects on the multiphase flow convective heat transfer of stirred tanks without and with baffles as well as various heights from the bottom are investigated. Temperature range of the multiphase flow is from 340 K to 350 K. The height of the blade is varied from about one-sixth to one-third of the overall height of the stirred tank. The numerical results show that decreasing the blade height and equipping baffles could enhance the heat transfer of the stirred tank. The calculated temperature field that takes into account the effects of particles are more instructive for the actual processes involving solid phases. This paper provides an effective method and is helpful for readers who have interests in the multiphase flows involving heat transfers in complex systems.

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10

Saravanathamizhan, R., R. Paranthaman, N. Balasubramanian, and C. Ahmed Basha. "Tanks in Series Model for Continuous Stirred Tank Electrochemical Reactor." Industrial & Engineering Chemistry Research 47, no. 9 (May 2008): 2976–84. http://dx.doi.org/10.1021/ie071426q.

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11

Sahu, A. K., P. Kumar, A. W. Patwardhan, and J. B. Joshi. "CFD modelling and mixing in stirred tanks." Chemical Engineering Science 54, no. 13-14 (July 1999): 2285–93. http://dx.doi.org/10.1016/s0009-2509(98)00334-0.

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12

Mueller, Sean G., and Milorad P. Dudukovic. "Gas Holdup in Gas−Liquid Stirred Tanks." Industrial & Engineering Chemistry Research 49, no. 21 (November 3, 2010): 10744–50. http://dx.doi.org/10.1021/ie100542a.

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13

Tamburini, Alessandro, Andrea Cipollina, Giorgio Micale, Francesca Scargiali, and Alberto Brucato. "Particle Suspension in Vortexing Unbaffled Stirred Tanks." Industrial & Engineering Chemistry Research 55, no. 27 (June 29, 2016): 7535–47. http://dx.doi.org/10.1021/acs.iecr.6b00824.

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14

Deglon, D. A., and C. J. Meyer. "CFD modelling of stirred tanks: Numerical considerations." Minerals Engineering 19, no. 10 (August 2006): 1059–68. http://dx.doi.org/10.1016/j.mineng.2006.04.001.

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15

Micale, G., V. Carrara, F. Grisafi, and A. Brucato. "Solids Suspension in Three-Phase Stirred Tanks." Chemical Engineering Research and Design 78, no. 3 (April 2000): 319–26. http://dx.doi.org/10.1205/026387600527374.

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16

Khazam, Oscar, and Suzanne M. Kresta. "Mechanisms of solids drawdown in stirred tanks." Canadian Journal of Chemical Engineering 86, no. 4 (August 2008): 622–34. http://dx.doi.org/10.1002/cjce.20077.

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17

Arrua, Luis A., B. J. McCoy, and J. M. Smith. "Gas–liquid mass transfer in stirred tanks." AIChE Journal 36, no. 11 (November 1990): 1768–72. http://dx.doi.org/10.1002/aic.690361121.

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18

Kresta, Suzanne M., Deming Mao, and Vesselina Roussinova. "Batch blend time in square stirred tanks." Chemical Engineering Science 61, no. 9 (May 2006): 2823–25. http://dx.doi.org/10.1016/j.ces.2005.10.069.

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19

Busciglio, A., F. Grisafi, F. Scargiali, and A. Brucato. "Mixing dynamics in uncovered unbaffled stirred tanks." Chemical Engineering Journal 254 (October 2014): 210–19. http://dx.doi.org/10.1016/j.cej.2014.05.084.

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20

Wadnerkar, Divyamaan, Ranjeet P. Utikar, Moses O. Tade, and Vishnu K. Pareek. "CFD simulation of solid–liquid stirred tanks." Advanced Powder Technology 23, no. 4 (July 2012): 445–53. http://dx.doi.org/10.1016/j.apt.2012.03.007.

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21

Jones, Raymond M., Albert D. Harvey, and Sumanta Acharya. "Two-Equation Turbulence Modeling for Impeller Stirred Tanks." Journal of Fluids Engineering 123, no. 3 (March 5, 2001): 640–48. http://dx.doi.org/10.1115/1.1384568.

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In this study, the predictive performance of six different two-equation turbulence models on the flow in an unbaffled stirred tank has been investigated. These models include the low Reynolds number k-ε model of Rodi, W., and Mansour, N. N., “Low Reynolds Number k-ε Modeling With the Aid of Direct Simulation Data,” J. Fluid Mech., Vol. 250, pp. 509–529, the high and low Reynolds number k-ω models of Wilson, D. C., 1993, Turbulence Modeling for CFD, DCW Industries, La Canada, CA., the RNG k-ε model, and modified k-ω and k-ε models which incorporate a correction for streamline curvature and swirl. Model results are compared with experimental laser Doppler velocimetry (LDV) data for the turbulent velocity field in an unbaffled tank with a single paddle impeller. An overall qualitative agreement has been found between the experimental and numerical results with poor predictions observed in some parts of the tank. Discrepancies in model predictions are observed in the anisotropic regions of the flow such as near the impeller shaft and in the impeller discharge region where the model overpredicts the radial velocity component. These results are discussed and a strategy for improving two-equation models for application to impeller stirred tanks is proposed.

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22

Hasal, Pavel, Milan Jahoda, and Ivan Fořt. "Macro-instability: a chaotic flow component in stirred tanks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1864 (August 2, 2007): 409–18. http://dx.doi.org/10.1098/rsta.2007.2098.

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Chaotic features of the macro-instability (MI) of flow patterns in stirred tanks are studied in this paper. Datasets obtained by measuring the axial component of the fluid velocity and the tangential force affecting the baffles are used. Two geometrically identical, flat-bottomed cylindrical mixing tanks (diameter of 0.3 m) stirred with either pitched blade turbine impellers or Rushton turbine impeller are used in the experiments, and water and aqueous glycerol solutions are used as the working liquids. First, the presence of the MI component in the data is examined by spectral analysis. Then, the MI components are identified in the data using the proper orthogonal decomposition (POD) technique. The attractors of the macro-instability are reconstructed using either the POD eigenmodes or a method of delays and finally the attractor invariants are evaluated. The dependence of the correlation dimension and maximum Lyapunov exponent on the vessel operational conditions is determined together with their distribution within the tank. No significant spatial variability of the correlation dimension value is observed. Its value is strongly influenced by impeller speed and by the vessel–impeller geometry. More profound spatial distribution is displayed by the maximum Lyapunov exponent taking distinctly positive values. These two invariants, therefore, can be used to locate distinctive regions with qualitatively different MI dynamics within the stirred tank.

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23

Carletti, Claudio, Siniša Bikić, Giuseppina Montante, and Alessandro Paglianti. "Mass Transfer in Dilute Solid–Liquid Stirred Tanks." Industrial & Engineering Chemistry Research 57, no. 18 (April 23, 2018): 6505–15. http://dx.doi.org/10.1021/acs.iecr.7b04730.

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24

Özcan-Taskin, Gül, and Geoff McGrath. "Draw Down of Light Particles in Stirred Tanks." Chemical Engineering Research and Design 79, no. 7 (October 2001): 789–94. http://dx.doi.org/10.1205/026387601753191966.

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25

Distelhoff, M. F. W., A. J. Marquis, J. M. Nouri, and J. H. Whitelaw. "Scalar mixing measurements in batch operated stirred tanks." Canadian Journal of Chemical Engineering 75, no. 4 (August 1997): 641–52. http://dx.doi.org/10.1002/cjce.5450750401.

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26

Brucato, Alberto, and Valerio Brucato. "Unsuspended mass of solid particles in stirred tanks." Canadian Journal of Chemical Engineering 76, no. 3 (June 1998): 420–27. http://dx.doi.org/10.1002/cjce.5450760311.

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27

Kresta, Suzanne. "Turbulence in stirred tanks: Anisotropic, approximate, and applied." Canadian Journal of Chemical Engineering 76, no. 3 (June 1998): 563–76. http://dx.doi.org/10.1002/cjce.5450760329.

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28

Rao, Achanta Ramakrishna. "Prediction of Reaeration Rates in Square, Stirred Tanks." Journal of Environmental Engineering 125, no. 3 (March 1999): 215–23. http://dx.doi.org/10.1061/(asce)0733-9372(1999)125:3(215).

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29

Kilander, J., S. Blomström, and A. Rasmuson. "Scale-up behaviour in stirred square flocculation tanks." Chemical Engineering Science 62, no. 6 (March 2007): 1606–18. http://dx.doi.org/10.1016/j.ces.2006.06.002.

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30

Mali, R. G., and A. W. Patwardhan. "Characterization of onset of entrainment in stirred tanks." Chemical Engineering Research and Design 87, no. 7 (July 2009): 951–61. http://dx.doi.org/10.1016/j.cherd.2009.01.010.

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31

Kulkarni, A. L., and A. W. Patwardhan. "Effect of scale on entrainment in stirred tanks." Chemical Engineering Research and Design 90, no. 8 (August 2012): 1031–37. http://dx.doi.org/10.1016/j.cherd.2011.11.012.

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32

Shu, Shuli, and Ning Yang. "GPU-accelerated large eddy simulation of stirred tanks." Chemical Engineering Science 181 (May 2018): 132–45. http://dx.doi.org/10.1016/j.ces.2018.02.011.

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33

Alopaeus, Ville, Pasi Moilanen, and Marko Laakkonen. "Analysis of stirred tanks with two-zone models." AIChE Journal 55, no. 10 (October 2009): 2545–52. http://dx.doi.org/10.1002/aic.11850.

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34

Hao, Zong Rui, Juan Xu, Hai Yan Bie, and Zhong Hai Zhou. "Numerical Simulation of the Effects of Baffle on Flow Field in a Stirred Tank." Advanced Materials Research 732-733 (August 2013): 432–35. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.432.

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Flow characteristics of stirred tanks with different structures were calculated by taking RNG k-ε model as the turbulent flow model. The results showed that at the same rotational speed, a large number of axial and radial vortexes were formed in the stirred tank with the baffle. The velocity in the blade area was high, and it decreased rapidly with the increasing distance to the blade. The double peak area of the radial velocity was formed in the stirred tank with baffle, and the high and low speed cycles were obtained in the cross-section. The baffle increased not only the axial circulation of the liquid in the tank but also the radial circulation, which help to mix the liquid.

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35

Shi, Lei, Shen Jie Zhou, Feng Ling Yang, and Fan Jin Hu. "Numerical Simulation of Turbulent Mixing for Dislocated Blades in a Stirred Tank." Advanced Materials Research 354-355 (October 2011): 559–63. http://dx.doi.org/10.4028/www.scientific.net/amr.354-355.559.

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Mixing efficiency is an important parameter in the design of many industrial processes in stirred tanks. In this study, CFD technology was used to simulate the mixing process inside the stirred tank with dislocated blades and standard turbine. Calculations were performed to study the effects of agitator speed and the configuration of impellers on mixing efficiency. The results showed that the flow field in the stirred tank with the dislocated blades is better than the standard turbine, and the flow number of the dislocated blades had been improved while the power number had been reduced. According to calculation results of Wr, we found the mixing efficiency of the dislocated blades had been improved about 4 times than that of standard turbine.

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36

Gimbun, Jolius, Shi Yan Liew, Zoltan K. Nagy, and Chris D. Rielly. "Three-Way Coupling Simulation of a Gas-Liquid Stirred Tank using a Multi-Compartment Population Balance Model." Chemical Product and Process Modeling 11, no. 3 (September 1, 2016): 205–16. http://dx.doi.org/10.1515/cppm-2015-0076.

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Abstract Modelling of gas-liquid stirred tanks is very challenging due to the presence of strong bubble-liquid interactions. Depending upon the needs and desired accuracy, the simulation may be performed by considering one-way, two-way, three-way or four-way coupling between the primary and secondary phase. Accuracy of the prediction on the two-phase flow generally increases as the details of phase interactions increase but at the expense of higher computational cost. This study deals with two-way and three-way coupling of gas-liquid flow in stirred tanks which were then compared with results via four-way coupling. Population balance model (PBM) based on quadrature method of moments (QMOM) was implemented in a multi-compartment model of an aerated stirred tank to predict local bubble size. The multi-compartment model is regarded as three-way coupling because the local turbulent dissipation rates and flow rates were obtained from a two-way computational fluid dynamics (CFD) simulation. The predicted two-phase flows and local bubble size showed good agreement with experimental data.

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37

Ochieng, Aoyi, and Maurice Onyango. "CFD simulation of the hydrodynamics and mixing time in a stirred tank." Chemical Industry and Chemical Engineering Quarterly 16, no. 4 (2010): 379–86. http://dx.doi.org/10.2298/ciceq100211040o.

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Hydrodynamics and mixing efficiency in stirred tanks influence power draw and are therefore important for the design of many industrial processes. In the present study, both experimental and simulation methods were employed to determine the flow fields in different mixing tank configurations in single phase system. The laser Doppler velocimetry (LDV) and computational fluid dynamics (CFD) techniques were used to determine the flow fields in systems with and without a draft tube. There was a reasonable agreement between the simulation and experimental results. It was shown that the use of a draft tube with the Rushton turbine and hydrofoil impeller resulted in a reduction in the homogenization energy by 19.2% and 17.7%, respectively. This indicates that a reduction in the operating cost can be achieved with the use of a draft tube in a stirred tank and there would be a greater cost reduction in a system stirred by the Rushton turbine compared to that stirred by a propeller.

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38

Paglianti, Alessandro, Francesco Maluta, and Giuseppina Montante. "Particles dissolution and liquid mixing dynamics by Electrical Resistance Tomography." Transactions of the Institute of Measurement and Control 42, no. 4 (May 9, 2019): 647–54. http://dx.doi.org/10.1177/0142331219842318.

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Salt particles dissolution in slurry stirred tanks provides an ambitious challenge for the application of Electrical Resistance Tomography in the process industry, because the presence of high loadings of inert particles requires a purposely developed post-processing method of the experimental data. For the optimization of the working conditions of the dissolution process, two characteristic times are required: the time for the liquid homogenization in the tank and the time required for the complete dissolution of the salt particles. The former time has been experimentally determined in previous investigations both in stirred tanks working with single-phase and with multiphase mixtures. The latter characteristic time has not been analyzed so far, due to the lack of experimental procedures for distinguishing it from the former. In this work, a novel approach for the simultaneous identification of the two characteristic times is presented. The impact of the new procedure is significant for the production processes, since it offers a tool for identifying when the soluble particle size has an impact on the dissolution dynamics, and when the stirred tank dynamics is influenced by the liquid homogenization only, and therefore a reduction of the particle size does not speed up the process accomplishment.

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39

Ochieng, Aoyi, and Mrice Onyango. "CFD simulation of solids suspension in stirred tanks: Review." Chemical Industry 64, no. 5 (2010): 365–74. http://dx.doi.org/10.2298/hemind100714051o.

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Many chemical reactions are carried out using stirred tanks, and the efficiency of such systems depends on the quality of mixing, which has been a subject of research for many years. For solid-liquid mixing, traditionally the research efforts were geared towards determining mixing features such as off-bottom solid suspension using experimental techniques. In a few studies that focused on the determination of solids concentration distribution, some methods that have been used have not been accurate enough to account for some small scale flow mal-distribution such as the existence of dead zones. The present review shows that computational fluid dynamic (CFD) techniques can be used to simulate mixing features such as solids off-bottom suspension, solids concentration and particle size distribution and cloud height. Information on the effects of particle size and particle size distribution on the solids concentration distribution is still scarce. Advancement of the CFD modeling is towards coupling the physical and kinetic data to capture mixing and reaction at meso- and micro-scales. Solids residence time distribution is important for the design; however, the current CFD models do not predict this parameter. Some advances have been made in recent years to apply CFD simulation to systems that involve fermentation and anaerobic processes. In these systems, complex interaction between the biochemical process and the hydrodynamics is still not well understood. This is one of the areas that still need more attention.

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40

ZHOU, Guozhong, Minghui XIE, Min LIU, Huaxiao WU, Xiangli LONG, and Peiqing YU. "Dissolution Characteristics of Hydrophobically Associating Polyacrylamide in Stirred Tanks." Chinese Journal of Chemical Engineering 18, no. 1 (February 2010): 170–74. http://dx.doi.org/10.1016/s1004-9541(08)60339-0.

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41

Kim, Yong H., and Larry A. Glasgow. "Simulation of aggregate growth and breakage in stirred tanks." Industrial & Engineering Chemistry Research 26, no. 8 (August 1987): 1604–9. http://dx.doi.org/10.1021/ie00068a018.

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42

N. Sharma, Rajendra, and Abdullah A. Shaikh. "Solids suspension in stirred tanks with pitched blade turbines." Chemical Engineering Science 58, no. 10 (May 2003): 2123–40. http://dx.doi.org/10.1016/s0009-2509(03)00023-x.

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43

Patwardhan, Ashwin W., and Jyeshtharaj B. Joshi. "Relation between Flow Pattern and Blending in Stirred Tanks." Industrial & Engineering Chemistry Research 38, no. 8 (August 1999): 3131–43. http://dx.doi.org/10.1021/ie980772s.

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44

Hollander, E. D., J. J. Derksen, H. M. J. Kramer, G. M. Van Rosmalen, and H. E. A. Van den Akker. "A numerical study on orthokinetic agglomeration in stirred tanks." Powder Technology 130, no. 1-3 (February 2003): 169–73. http://dx.doi.org/10.1016/s0032-5910(02)00261-9.

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45

Okufi, S., E. S. Perez De Ortiz, and H. Sawistowski. "Scale-up of liquid-liquid dispersions in stirred tanks." Canadian Journal of Chemical Engineering 68, no. 3 (June 1990): 400–406. http://dx.doi.org/10.1002/cjce.5450680308.

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46

Chin, Ching-Ju, Sotira Yiacoumi, and Costas Tsouris. "Shear-Induced Flocculation of Colloidal Particles in Stirred Tanks." Journal of Colloid and Interface Science 206, no. 2 (October 1998): 532–45. http://dx.doi.org/10.1006/jcis.1998.5737.

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47

Jahoda, Milan, and Václav Machoň. "Homogenization of liquids in tanks stirred by multiple impellers." Chemical Engineering & Technology 17, no. 2 (April 1994): 95–101. http://dx.doi.org/10.1002/ceat.270170205.

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48

Paglianti, Alessandro, Claudio Carletti, and Giuseppina Montante. "Liquid Mixing Time in Dense Solid-Liquid Stirred Tanks." Chemical Engineering & Technology 40, no. 5 (March 2, 2017): 862–69. http://dx.doi.org/10.1002/ceat.201600595.

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49

Lane, G. L., M. P. Schwarz, and G. M. Evans. "Numerical modelling of gas–liquid flow in stirred tanks." Chemical Engineering Science 60, no. 8-9 (April 2005): 2203–14. http://dx.doi.org/10.1016/j.ces.2004.11.046.

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50

Zhang, Zhong, and Guanrong Chen. "Liquid mixing enhancement by chaotic perturbations in stirred tanks." Chaos, Solitons & Fractals 36, no. 1 (April 2008): 144–49. http://dx.doi.org/10.1016/j.chaos.2006.06.024.

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