Melt flow of biopolymer through the cavities of an extruder die: Mathematical modelling

Alexander N. Ostrikov; Abdymanap A. Ospanov; Vitaly N. Vasilenko; Nurzhan Zh. Muslimov; Aigul K. Timurbekova; Gulnara B. Jumabekova; Alexander N. Ostrikov; Abdymanap A. Ospanov; Vitaly N. Vasilenko; Nurzhan Zh. Muslimov; Aigul K. Timurbekova; Gulnara B. Jumabekova

doi:10.3934/mbe.2019142

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2875-2905. doi: 10.3934/mbe.2019142

Previous Article Next Article

Research article

Melt flow of biopolymer through the cavities of an extruder die: Mathematical modelling

1.
Voronezh State University of Engineering Technologies, Voronezh, Russian Federation
2.
Kazakh National Agrarian University, Almaty, Republic of Kazakhstan
3.
Taraz innovative-humanities university, Taraz, Republic of Kazakhstan
4.
M.Kh. Dulaty Taraz State University, Taraz, Republic of Kazakhstan

Received: 13 December 2018 Accepted: 07 March 2019 Published: 09 April 2019

This is an analytical solution of the two-dimensional non-isothermal mathematical model describing the change in the velocity profile of a cylindrical extrusion die. This solution is based on the following assumptions. The two-dimensional melt flow is asymmetric. A melt viscosity anomaly may take place. Heat generated by viscous friction is a factor affecting the melt flow. The melt flow moving towards the metering section is in a steady state. Neither mass forces nor inertia forces are present. Velocity gradients along the channel are neglected. The mathematical model was built up from the incompressibility equation, motion equations, energy equation, and the rheological equation. This model depicted a non-isothermal flow of rheological fluid moving through the cylindrical extrusion die. A diagram was drawn. It depicts the melt velocities at a die entrance in different cross-sectional views. Computer testing was performed to verify the obtained solutions and compare them with the real extrusion process. Difference between calculated and experimental data was below 14%. Results allow concluding a matching of numerical results with experimental data, and so the possibility of using a built-up model in an extrusion die design for single-screw extruders.
- mathematical modelling,
- extrusion,
- melt flow,
- polymer processing,
- die,
- extruder
Citation: Alexander N. Ostrikov, Abdymanap A. Ospanov, Vitaly N. Vasilenko, Nurzhan Zh. Muslimov, Aigul K. Timurbekova, Gulnara B. Jumabekova. Melt flow of biopolymer through the cavities of an extruder die: Mathematical modelling[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2875-2905. doi: 10.3934/mbe.2019142

Related Papers:

Abstract

This is an analytical solution of the two-dimensional non-isothermal mathematical model describing the change in the velocity profile of a cylindrical extrusion die. This solution is based on the following assumptions. The two-dimensional melt flow is asymmetric. A melt viscosity anomaly may take place. Heat generated by viscous friction is a factor affecting the melt flow. The melt flow moving towards the metering section is in a steady state. Neither mass forces nor inertia forces are present. Velocity gradients along the channel are neglected. The mathematical model was built up from the incompressibility equation, motion equations, energy equation, and the rheological equation. This model depicted a non-isothermal flow of rheological fluid moving through the cylindrical extrusion die. A diagram was drawn. It depicts the melt velocities at a die entrance in different cross-sectional views. Computer testing was performed to verify the obtained solutions and compare them with the real extrusion process. Difference between calculated and experimental data was below 14%. Results allow concluding a matching of numerical results with experimental data, and so the possibility of using a built-up model in an extrusion die design for single-screw extruders.

References

[1]	L.G. Vinnikova, Extrusion processing of products with dietary fiber, Food Ind., 11 (1991), 51–55.
[2]	A.N. Ostrikov, S.V. Shakhov, A.A, Ospanov, et al., Mathematical modeling of product melt flow in the molding channel of an extruding machine with meat filling feeding, J. Food Process Eng., 41 (2018), e12874.
[3]	J.M. McKelvey, Polymer processing, translated from English, Khimiya Publishing House, (1965), 444.
[4]	M. Walter, Extrusion dies for plastics and rubber: Design and engineering computations, translated from English, Professiya Publishing House, (2007), 472.
[5]	I.R. Raupov and A.M. Shagiakhmetov, The results of the complex rheological studies of the cross-linked polymer composition and the grounding of its injection volume, Int. J. Civil Eng. Tech., 10 (2019), 493–509.
[6]	A.N. Ostrikov, O.V. Abramov, V.N. Vasilenko, et al., Mathematical modeling of anomalously viscous flow in the channels of extruders, Publishing and Printing Center of Voronezh State University, (2010), 240.
[7]	A. Ospanov, L. Gaceu, A. Timurbekova, et al., Innovative technologies of grain crops processing, (2014), 439.
[8]	A.N. Ostrikov, O.V. Abramov and R. Nenakhov, Patent 2142361 Russian Federation, Extrusion die with adjustable profile of a forming channel. (Application No. 98118397). http://www1.fips.ru/fips_servl/fips_servlet?DB=RUPAT&DocNumber=2142361&TypeFile=html
[9]	A.N. Ostrikov, O.V. Abramov, R.V. Nenakho, et al., Patent 2161556 Russian Federation, Extruder for the production of shaped article with adjustable profile of a forming channel (Application No. 99114877). http://www1.fips.ru/fips_servl/fips_servlet?DB=RUPAT&DocNumber=2161556&TypeFile=html
[10]	V.P. Pervadchuk, N.M. Trufanova and V.I. Yankov, The mathematical model and numerical analysis of heat transfer processes involving polymer melting in plasticizing extruders, J. eng. phy. thermophysics, 1 (1985), 75–78.
[11]	V.V. Skachkov, R.V. Torner, Yu.V. Stungur, et al., Modeling and optimization of polymer extrusion, Chemistry, Khimiya Publishing House, (1984), 152.
[12]	T. Zehev and C.G. Gogos, Principles of Polymer Processing, 2nd Edition, John Wiley & Sons, (2013), 624.
[13]	R.V. Torner, Theoretical bases of polymer processing, Khimiya Publishing House, (1977), 460.
[14]	D.H. Chang, Rheology in polymer processing, Khimiya Publishing House, (1979), 368.
[15]	V.I. Yankov, V.I. Pervadchuk and V.I. Boyarchenko, Processing of Fiber-Forming Polymers, Khimiya Publishing House, (1989), 320.
[16]	C. Rauwendaal, Polymer extrusion, (1990), 568.
[17]	M. Kristiawan, L. Chaunier, G. Della Valle, et al., Modeling of starchy melts expansion by extrusion, Trends food sci. technol., 48 (2016), 13–26.
[18]	J.M. Bouvier and O.H. Campanella, Extrusion processing technology: Food and non-food biomaterials, John Wiley & Sons, (2014).
[19]	L. Chaunier, S. Guessasma, S. Belhabib, et al., Material extrusion of plant biopolymers: Opportunities & challenges for 3D printing, (2017).
[20]	Q.T. Ho, J. Carmeliet, A.K. Datta, et al., Multiscale modeling in food engineering, J. food Eng., 114 (2013), 279–291.
[21]	K. Lamnawar, A. Maazouz, G. Cabrera, et al., Interfacial tension properties in biopolymer blends: From deformed drop retraction method (DDRM) to shear and elongation rheology-application to blown film extrusion, Int. Polymer Process, 33 (2018), 411–424.
[22]	J.M. Buick, Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder, Chem. Eng. Sci., 64 (2009), 52–58.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)