Document Type : Research Paper



2 Iran University of Science and Technology


Laminar mixing of glycerin in a chaotic mixer is carried by means of the blob deformation method. The mixer was a cylindrical vessel with two rotational blades which move along two different circular paths with a stepwise motion protocol. The flow visualization was performed by marking of the free surface of the flow with a tracer. The effects of controlling parameters such as rotational speed of blades, blades length, and rotational speed amplitude on mixing efficiency and time were analyzed by measuring of the area covered by the tracer. The results revealed that increasing rotational speed intensifies stretching and folding phenomenon, and consequently better mixing can be obtained. Also, the better condition in flow kinematic was provided to blend as stepwise motion protocol with wider amplitude adopted. A reduction in mixing time could be observed as the blades with longer length were used. In addition, it was also found that the promotion of mixing by rotational speed is more effective than that of two other parameters. The quantitative data and qualitative observations proved the potential of proposed chaotic mixer in wide range of industrial processes including chemical reaction and food processing in which laminar mixing is required.

Graphical Abstract

Laminar mixing of high-viscous fluids by a cylindrical chaotic mixer


Main Subjects

[1] H. Aref, “Stirring by chaotic advection", Journal of Fluid Mechanic, Vol. 143, pp. 1-21, (1984).


[2] H. Aref, and S. Balachandar, “Chaotic advection in a Stokes flow”, Physics of Fluids, Vol. 29, No. 11, pp. 3515-3521, (1986).


[3] W. L. Chien, H. Rising, and J. M. Ottino, “Laminar mixing and chaotic mixing in several cavity flows”, Journal of Fluid. Mechanics, Vol. 170, pp. 355-377, (1986).


[4] D. J. Lamberto, F. J. Muzzio, P. D. Swanson, and A. L. Tonkovich, “Using time-dependent RPM to enhance mixing in stirred vessels”, Chemical Engineering Science, Vol. 51, No. 5, pp.733-741, (1996).


[5] W. G. Yao, H. Sato, K. Takahashi, and K. Koyama, “Mixing performance experiments in impeller stirred tanks subjected to unsteady rotational speeds”, Chemical Engineering Science, Vol. 53, No. 17, pp. 3031-3040, (1998).


[6] P. D. Swanson, and J. M. Ottino, “Comparative computational and experimental study of chaotic mixing of viscous fluids”, Journal of Fluid. Mechanics., Vol. 213, pp. 227-227, (1990).


[7] H. Aref, and S. Balachandar, “Chaotic advection in a Stokes flow”, Phys. Fluids., Vol. 29, No. 11, pp.3515–3521, (1986).


[8] P. Dutta, and R. Chevray, “Effect of diffusion on chaotic advection in Stokes flow”, Physics of Fluids, Vol. 3, No. 5, p.1440, (1991).


[9] J. A. Zambaux, J. L. Harion, S. Russeil, and P. Bouvier, “Combining two orthogonal secondary flows to enhance the mixing in an annular duct”, Chemical Engineering Research and Design, Vol. 94, pp.702-713, (2012).


[10] O. S. Galaktionov, V. V. Meleshko, G. W. M. Peters, H. E. H., Meijer, “Stokes flow in a rectangular cavity with a cylinder”, Fluid. Dynamic Research, Vol. 24, No. 2, pp.81-102, (1999)


[11] K. Takahashi, and M. Motoda, “Chaotic mixing created by Object inserted in a vessel agitated by an impeller”, Chemical Engineering Research and Design, Vol. 84, No. 4, pp.386-390, (2009).


[12] Z. Zhang, and G. Chen, “Liquid mixing enhancement by chaotic perturbations in stirred tanks”, Chaos, Soliton and Fractal, Vol. 36, No. 1, pp.144-149, (2008).


[13] Y. Kato, Y. Tada, M. Ban, Y. Nagatsu, S. Iwata, and K. Yanagimoto, “Improvement of Mixing Efficiencies of Conventional Impeller with Unsteady Speed in an Impeller Revolution”, Journal of Chemical Engineering of. Japan, Vol. 38, No. 9, pp. 688-691, (2005).


[14] K. Takahashi, H. Sekine, Y. Sugo, and Y. Takahata, “Nakamura M. Laminar Mixing in Stirred Tank Agitated by an Impeller Inclined”, International Journal of Chemical Engineering, doi:10.1155/2012/858329 (2012).


[15] Y. Hwu, “Chaotic stirring in a new type of mixer with rotating rigid blades”, European Journal of Mechanic B-Fluid, Vol. 27, No. 3, pp. 239-250, (2008).


[16] P. R. Mashaei, S. M. Hosseinalipour, M. J. Muslmani, N. M. Nouri, “Experimental study on chaotic mixing created by a new type of mixer with rotational blades”, Advances in Mechanical Engineering, doi: 10.1155/2012/543253, (2012).


[17] M. Robinson, and W. Cleary, “Flow and mixing performance in helical ribbon mixers”, Chemical Engineering Science., Vol. 84, pp. 382-398, (2012).


[18] Z. Liu, X. Zheng, D. Liu, Y. wang, and C. Tao, “Enhancement of liquid–liquid mixing in a mixer-settler by a double rigid-flexible combination impeller”, Chem. Eng. Process., Vol. 86, pp.69-77, (2014).


[19] F. Shirmohammadi, A. Tohidi, “Mixing enhancement using chaos theory in fluid dynamics: Experimental and numerical study”, Chemical Engineering and Processing: Process Intensification, In press, (2018).


[20] S. Y. Jung, K.H. Ahn, T. G. Kang, G. T. Park, S. U. Kim, “Chaotic Mixing in a Barrier-Embedded Partitioned Pipe Mixer”, AIChE Journal, Vol. 64, No. 2, pp.717-729, (2018).


[21] S. Jegatheeswaran, F. Ein-Mozaffari, and W. Jiangning, “Efficient Mixing of Yield-Pseudoplastic Fluids at Low Reynolds Numbers in the Chaotic SMX Static Mixer, Chemical Engineering Journal, Vol. 317, pp.215-231, (2017).


[22] T. C. Niederkorn, and J. M. Ottino, “Mixing of a viscoelastic fluid in time-periodic flow”, Journal of Fluid Mechanic, Vol. 256, pp. 243-268, (1993).


[23] S. M. Hosseinalipour, A. Tohidi, P. R. Mashaei, and A. S. Mujumdar, “Experimental investigation of mixing in a novel continuous chaotic mixer”, Koreaan Journal of Chemical Engineering, Vol. 31, No. 10, pp.1757-1765, (2014).


[24] Fox, Robert W. Alan, T. McDonald, and J. Philip Pritchard, Introduction to fluid mechanics (6th Ed.). Hoboken, NJ: Wiley (2006).


[25] P. R. Mashaei, Design and manufacturing of a chaotic mixer for non-Newtonian fluid, M.S. thesis, Iran University of Science and Technology, Tehran, Iran (2011).