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Licensed Unlicensed Requires Authentication Published by De Gruyter June 23, 2016

Study of Dispersive and Distributive Mixing in a Converging Pipe

M. Mostafaiyan, S. Wiessner and G. Heinrich

Abstract

The creeping flow of a polymeric melt in a converging pipe is analyzed using an in-house finite element code. An introduced power-law model considers the shear thinning behavior of the viscous liquid. Furthermore, distributive and dispersive mixing processes are evaluated with the mean strain function and the Manas-Zloczower mixing index, respectively. Using a parametric study, the dependency of the mixing criteria on the rheological and geometrical factors is investigated. Finally, a new analytical expression for the evaluation of the distributive mixing is suggested, based on simplifying assumptions and a curve fitting method.


*Correspondence address, Mail address: Mehdi Mostafaiyan, Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, D-01069 Dresden, Germany. E-mail: ,

References

Alemaskin, K., Manas-Zloczower, I. and Kaufman, M., “Color Mixing in the Metering Zone of a Single Screw Extruder: Numerical Simulations and Experimental Validation”, Polym. Eng. Sci., 45, 10111020 (2005) 10.1002/pen.20368Search in Google Scholar

Ausias, G., Jarrin, J., and Vincent, M., “Optimization of the Tube-Extrusion Die for Short-Fiber-Filled Polymers”, Compos. Sci. Technol., 56, 719724 (1996) 10.1016/0266-3538(96)00012-7Search in Google Scholar

Bigg, D., Middleman, S., “Mixing in a Screw Extruder. A Model for Residence Time Distribution and Strain”, Ind. Eng. Chem. Fundam., 13, 6671 (1974) 10.1021/i160049a013Search in Google Scholar

Bigio, D. I., Boyd, J. D., Erwin, L. and Gailus, D. W., “Mixing Studies in the Single Screw Extruder”, Polym. Eng. Sci., 25, 305310 (1985) 10.1002/pen.760250510Search in Google Scholar

Bigio, D., Zerafati, S., “Parametric Study of a 2-D Model of the Nip Region in a Counter-Rotating, Non-Intermeshing Twin Screw Extruder”, Polym. Eng. Sci., 31, 14001410 (1991) 10.1002/pen.760311906Search in Google Scholar

Bird, R. B., Armstrong, R. C. and Hassager, O.: Dynamics of Polymeric Liquids. Fluid Mechanics, Volume 1, Wiley-Interscience Publication, John Wiley & Sons, New York (1987)Search in Google Scholar

Cheng, H., Manas-Zloczower, I., “Study of Mixing Efficiency in Kneading Discs of Co-Rotating Twin-Screw Extruders”, Polym. Eng. Sci., 37, 10821090 (1997) 10.1002/pen.11753Search in Google Scholar

Cheng, H., Manas-Zloczower, I., “Distributive Mixing in Conveying Elements of a ZSK-53 Co-Rotating Twin Screw Extruder”, Polym. Eng. Sci., 38, 926935 (1998) 10.1002/pen.10260Search in Google Scholar

Connelly, R. K., Kokini, J. L., “The Effect of Shear Thinning and Differential Viscoelasticity on Mixing in a Model 2D Mixer as Determined Using FEM with Particle Tracking”, J. Non-Newtonian Fluid Mech., 123, 117 (2004) 10.1016/j.jnnfm.2004.03.006Search in Google Scholar

Erwin, L., Mokhtarian, F., “Analysis of Mixing in Modified Single Screw Extruders”, Polym. Eng. Sci., 23, 4960 (1983) 10.1002/pen.760230202Search in Google Scholar

Fard, A. S., Famili, N. M. and Anderson, P. D., “A New Adaptation of Mapping Method to Study Mixing of Multiphase Flows in Mixers with Complex Geometries”, Comput. Chem. Eng., 32, 14711481 (2008) 10.1016/j.compchemeng.2007.06.023Search in Google Scholar

Funt, J.: Mixing of Rubber, RAPRRA Publication, Shawbury, UK (1977)Search in Google Scholar

Galaktionov, O. S., Anderson, P. D., Peters, G. W. M. and Tucker, C. L., “A Global, Multi-Scale Simulation of Laminar Fluid Mixing: The Extended Mapping Method”, Int. J. Multiphase Flow, 28, 497523 (2002) 10.1016/S0301-9322(01)00080-5Search in Google Scholar

Gale, M., “Compounding with Single-Screw Extruders”, Adv. Polym. Technol., 16, 251262 (1997) 10.1002/(SICI)1098-2329(199711)16:4<251::AID-ADV1>3.0.CO;2-USearch in Google Scholar

Gogos, C. G., Tadmor, Z.: Principles of Polymer Processing, Wiley-Interscience Publication, John Wiley & Sons, Dunfermline (1979)Search in Google Scholar

Hannachi, A., Mitsoulis, E., “Deformation Fields and Residence Time Distributions in Polymer Melt Flows”, Int. Polym. Proc, 5, 244251 (1990) 10.3139/217.900244Search in Google Scholar

Hatzikiriakos, S. G., Mitsoulis, E., “Slip Effects in Tapered Dies”, Polym. Eng. Sci., 49, 19601969 (2009) 10.1002/pen.21430Search in Google Scholar

Kalyon, D. M., Sangani, H. N., “An Experimental Study of Distributive Mixing in Fully Intermeshing, Co-Rotating Twin Screw Extruders”, Polym. Eng. Sci., 29, 10181026 (1989) 10.1002/pen.760291508Search in Google Scholar

Kwon, T., Joo, J. and Kim, S., “Kinematics and Deformation Characteristics as a Mixing Measure in the Screw Extrusion Process”, Polym. Eng. Sci., 34, 174189 (1994) 10.1002/pen.760340303Search in Google Scholar

Li, T., Manas-Zloczower, I., “A Study of Distributive Mixing in Counterrotating Twin Screw Extruders”, Int. Polym. Proc., 10, 314320 (1995) 10.3139/217.950314Search in Google Scholar

Maheshri, J. C., Wyman, C. E., “Mixing in an Intermeshing Twin Screw Extruder Chamber: Combined Cross and Down Channel Flow”, Polym. Eng. Sci., 20, 601607 (1980) 10.1002/pen.760200904Search in Google Scholar

Manas-Zloczower, I.: Mixing and Compounding of Polymers: Theory and Practice, Hanser, Munich (2012)Search in Google Scholar

Mostafaiyan, M., Saeb, M. R., Ahmadi, Z., Khonakdar, H. A., Wagenknecht, U. and Heinrich, G., “A Numerical Study on Deformation of Newtonian Droplets through Converging Cylindrical Dies”, E-Polymers, 13, 4966 (2013) 10.1515/epoly-2013-0106Search in Google Scholar

Mostafaiyan, M., Wiessner, S. and Heinrich, G., “The Study of the Distributive Mixing in Converging Channels: Numerical Method and Analytical Approach”, Polym. Eng. Sci., 55, 22852292 (2015)10.1002/pen.24115Search in Google Scholar

Reddy, J. N., Gartling, D. K.: The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, London (2010)10.1201/9781439882573Search in Google Scholar

Shopov, P. J., Iordanov, Y. I., “Numerical Solution of Stokes Equations with Pressure and Filtration Boundary Conditions“, J. Comput. Phys., 112, 1223 (1994) 10.1006/jcph.1994.1078Search in Google Scholar

Tokihisa, M., Yakemoto, K., Sakai, T., Utracki, L. A., Sepehr, M., Li, J. and Simard, Y., “Extensional Flow Mixer for Polymer Nanocomposites”, Polym. Eng. Sci., 46, 10401050 (2006) 10.1002/pen.20542Search in Google Scholar

Wang, W., Manas-Zloczower, I., “Temporal Distributions: The Basis for the Development of Mixing Indexes for Scale-Up of Polymer Processing Equipment”, Polym. Eng. Sci., 41, 10681077 (2001) 10.1002/pen.10807Search in Google Scholar

Wang, W., Manas-Zloczower, I. and Kaufman, M., “Entropic Characterization of Distributive Mixing in Polymer Processing Equipment”, AIChE J., 49, 16371644 (2003) 10.1002/aic.690490704Search in Google Scholar

Wong, T. H., Manas-Zloczower, I., “Two-Dimensional Dynamic Study of the Distributive Mixing in an Internal Mixer”, Int. Polym. Proc., 9, 310 (1994) 10.3139/217.940003Search in Google Scholar

Yao, C. H., Manas-Zloczower, I., “Study of Mixing Efficiency in Roll-Mills”, Polym. Eng. Sci., 36, 305310 (1996) 10.1002/pen.10417Search in Google Scholar

Zhou, D., Yue, P. and Feng, J. J., “Viscoelastic Effects on Drop Deformation in a Converging Pipe Flow”, J. Rheol., 52, 469487 (2008) 10.1122/1.2837525Search in Google Scholar

Received: 2015-10-01
Accepted: 2016-02-06
Published Online: 2016-06-23
Published in Print: 2016-07-30

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