Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter January 8, 2019

Chaotic mixing analysis of a novel single-screw extruder with a perturbation baffle by the finite-time Lyapunov exponent method

  • Jian Liu and Xiangzhe Zhu EMAIL logo


The single-screw extruder with a perturbation baffle is a novel piece of equipment for polymer processing, in which the polymer melts undergo complex chaotic mixing. In this paper, from a new Lagrangian perspective, the fluid transporting mechanism in chaotic flow of the unwound screw channel was analyzed based on the finite element method. Firstly, two-dimensional velocity distributions in the unwound screw channel were calculated based on the mesh superposition technique. Fluid particle evolution processes in the extruder were tracked based on the fourth-order Runge-Kutta scheme. The numerical method used in this paper was validated by grid independence and experiments obtained from literature. Moreover, the finite-time Lyapunov exponent (FTLE) and Poincaré sections were adopted to discuss the chaotic mixing in the novel single-screw extruder. The effects of baffle width and height on the manifold structures in the flow dynamic system were analyzed. The results show that the homoclinic point of the manifold structure can give rise to chaotic mixing in the single-screw extruder. The height of the baffle is an important parameter to control the chaotic strength. In a way, increasing the height of the baffle can enlarge the kink scale and increase the stretching and folding actions, which results in the decrease of regular regions and an increase of the mixing efficiency in the single-screw extruder.

Award Identifier / Grant number: 51473073

Award Identifier / Grant number: 50903042

Award Identifier / Grant number: 51303075

Funding statement: This work was supported by the National Natural Science Foundation of China (Funder Id: 10.13039/501100001809, grant nos. 51473073, 50903042 and 51303075); the Program for Liaoning Excellent Talents in University (grant no. LR2016022) and the Liaoning Province Natural Science Foundation (grant no. 2015020142).


[1] Chella R, Ottino JM. Ind. Eng. Chem. Res. 1985, 24, 170–180.10.1021/i100018a006Search in Google Scholar

[2] Xu BP. CHN Patent, 2007, No.101003176.Search in Google Scholar

[3] Aref H. J. Fluid Mech. 1984, 143, 1–21.10.1017/S0022112084001233Search in Google Scholar

[4] Ottino JM. Annu. Rev. Fluid Mech. 1990, 22, 207–254.10.1146/annurev.fl.22.010190.001231Search in Google Scholar

[5] Wiggins S. Phys. Today 1992, 45, 68–69.10.1063/1.2809741Search in Google Scholar

[6] Jana SC, Tiahjadi M, Ottino JM. AICHE J. 1994, 40, 1769–1781.10.1002/aic.690401102Search in Google Scholar

[7] Lee TH, Kwon TH. Adv. Polym. Tech. 1999, 18, 53–68.10.1002/(SICI)1098-2329(199921)18:1<53::AID-ADV6>3.0.CO;2-ZSearch in Google Scholar

[8] Kim SJ, Kwon TH. Adv. Polym. Tech. 1996, 15, 41–54.10.1002/(SICI)1098-2329(199621)15:1<41::AID-ADV4>3.0.CO;2-KSearch in Google Scholar

[9] Kim SJ, Kwon TH. Adv. Polym. Tech. 1996, 15, 55–69.10.1002/(SICI)1098-2329(199621)15:1<55::AID-ADV5>3.0.CO;2-JSearch in Google Scholar

[10] Hwang WR, Kwon TH. Polym. Eng. Sci. 2003, 43, 783–797.10.1002/pen.10065Search in Google Scholar

[11] Khakhar DV, Franjione JG, Ottino JM. Chem. Eng. Sci. 1987, 42, 2909–2926.10.1016/0009-2509(87)87056-2Search in Google Scholar

[12] Xu B, Liu Y, Yu H, Turng LS. Polym. Eng. Sci. 2014, 54, 198–207.10.1002/pen.23531Search in Google Scholar

[13] Connelly RK, Kokini JL. J. Food Eng. 2007, 79, 956–969.10.1016/j.jfoodeng.2006.03.017Search in Google Scholar

[14] Domingues N, Gasparcunha A, Covas JA. J. Polym. Eng. 2012, 32, 81–94.10.1515/polyeng-2012-0501Search in Google Scholar

[15] Dhakal P, Das SR, Poudyal H, Chandy AJ. J. Appl. Polym. Sci. 2016, 134, 2739–2748.10.1002/app.44250Search in Google Scholar

[16] Haller G. Physica D 2001, 149, 248–277.10.1016/S0167-2789(00)00199-8Search in Google Scholar

[17] Haller G. Physica D 2011, 240, 574–598.10.1016/j.physd.2010.11.010Search in Google Scholar

[18] Shadden SC, Dabiri JO, Marsden JE. Phys. Fluids 2006, 18, 047105.10.1063/1.2189885Search in Google Scholar

[19] Prants SV. Eur. Phys. J. Spec. Top. 2014, 223, 2723–2743.10.1140/epjst/e2014-02288-5Search in Google Scholar

[20] Olascoaga MJ, Haller GP. Proc. Natl. Acad. Sci. USA. 2012, 109, 4738–4743.10.1073/pnas.1118574109Search in Google Scholar

[21] Ali S, Shah M. Conference: IEEE conference on computer vision and pattern recognition, Minneapolis, 2007.Search in Google Scholar

[22] Santitissadeekorn N, Bohl D, Bollt EM. Int. J. Bifurcation Chaos Appl. Sci. Eng. 2011, 19, 993–1006.10.1142/S021812740902341XSearch in Google Scholar

[23] Robinson M, Cleary PW. AIChE J. 2011, 57, 581–598.10.1002/aic.12297Search in Google Scholar

[24] Haller G, Yuan G. Physica D 2000, 147, 352–370.10.1016/S0167-2789(00)00142-1Search in Google Scholar

[25] Farazmand M, Haller G. Chaos 2012, 22, 58–335.10.1063/1.3690153Search in Google Scholar PubMed

[26] Steller RT. Polym. Eng. Sci. 1990, 30, 400–407.10.1002/pen.760300704Search in Google Scholar

[27] Shin KC, White JL. Rubber Chem. Technol. 1997, 70, 264–270.10.5254/1.3538431Search in Google Scholar

[28] Onu K, Huhn F, Haller G. J. Comput. Sci. 2015, 7, 26–36.10.1016/j.jocs.2014.12.002Search in Google Scholar

[29] Wei XL, Dong WG. J. Chem. Eng. Chin. Univ. 2003, 17, 254–260.Search in Google Scholar

Received: 2018-02-09
Accepted: 2018-11-11
Published Online: 2019-01-08
Published in Print: 2019-02-25

©2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 29.11.2023 from
Scroll to top button