Structure-controlled bifurcation in mathematical modelling of fibre spinning

• Autorzy: Ziabicki, A. , Jarecki, L.
• Konferencja: International Conference on Continuous and Discrete Modelling in Mechanics (05-09.09.2005 ; Warsaw ; Poland)
• Języki publikacji: EN

Abstrakty

EN

In the mathematical model of melt spinning of fibres from crystallizing polymers the set of conservation equations is completed with structure-controlled constitutive equations and structure evolution equations describing kinetics of stress-induced crystallization. In a definite range of conditions, bifurcation of solutions is observed. Maximum filament velocity is limited and the same boundary conditions yield different steady-state dynamic and structure profiles. Bifurcation is observed when stress-induced crystallization leads to rapid solidification of the material. Critical conditions for bifurcation in melt spinning are analyzed and physical mechanism of such a behaviour is discussed.

Słowa kluczowe

PL

przędzenie włókien polimeru ze stopu; model matematyczny; równania ewolucji struktury; równania konstytutywne; równania zachowania; modelowania komputerowe; symulacja numeryczna

EN

melt spinning of fibres; mathematical model; structures evolution equations; constitutive equations; conservation equations; computer modelling; numerical simulation

• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 4-5
• Strony: 459-475
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Ziabicki, A.

autor

Jarecki, L.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warsaw, Poland,

Bibliografia

• 1. L. JARECKI, A. ZIABICKI, A. BUM, Dynamics of hot-tube spinning from crystallizing polymer melts, Comput. Theoret. Polymer Sci., 10, 63-72, 2000.
• 2. L. JARECKI, A. ZIABICKI,Viscosity effects in computer modelling of fiber spinning from crystallizing polymer melts [in English], Polimery, 49, 101, 2004.
• 3. A. BLIM, E. OŁDAK, A. WASIAK, L. JARECKI, Effect of zone heating on the structure of PET fibers and the dynamics of melt spinning [in Polish], Polimery, 50, 48-59, 2005.
• 4. A. ZIABICKI, L. JARECKI, A. WASIAK, Dynamic modelling of melt spinning, Comput. Theoret. Polymer Sci., 8, 143-157, 1998.
• 5. S. KASE, T. MATSUO, Studies on melt spinning. I. Fundamental equations on the dynamics of melt spinning, J. Polymer Sci., A3, 2541, 1965; II, Steady-state and transient solutions of fundamental equations compared with experimental results, J. Appl. Polymer Sci., 11, 251-287, 1968.
• 6. A. ZIABICKI, Kinetics of polymer crystallization and molecular orientation in the course of melt spinning Appl. Polymer Symposia, 6 l, 1967; Crystallization of polymers in variable external conditions, Colloid and Polymer Sci., 274, 209, 1996.
• 7. K. NAKAMURA , T. WATANABE, K. KATAYAMA, T. AMANO, Some aspects of non-isothermal crystallization of polymers, I. Relationship between crystallization temperature, crystallinity and cooling conditions, J. Appl. Polymer Sci., 16, 1077-1099, 1972; II. Consideration of the isokinetic condition, ibid, 17, 1031-1041, 1973.
• 8. Y.G. LIN, D.T. MALLIN, J.C.W. CHIEN, H.H. WINTER, Dynamic mechanical measurement of crystallization induced gelation in thermoplastic polypropylene, Macromolecules, 24, 850, 1991.
• 9. G. FLOUDAS, L. HILLIOU, D. LELLINGER, I. ALIG, Shear-induced crystallization in poly-e-caprolactone, Macromolecules, 30, 6466, 2000.
• 10. C. SCHWITTAY, M. MOURS, H.H. WINTER, Rheological expression of physical gelation in polymers, Faraday Disc., 101, 93-104, 1995.
• 11. A. ZIABICKI, The mechanisms of neck-like deformation in high-speed melt spinning. 2. Effects of polymer crystallization, J. Non-Newtonian Fluid Mech., 30, 157-168, 1988.
• 12. I.M. KRIEGER, T. J. DOUGHERTY, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol., 3, 137-152, 1959.
• 13. A. ZIABICKI, L. JARECKI, [in:] High Speed Fiber Spinning, A. ZIABICKI, H. KAWAI, [Eds.], Wiley, N.Y. p. 225, 1985.
• 14. G.C. ALFONSO, M.P. VERDONA, A. WASIAK, Crystallization kinetics of oriented polyethylene terephthalate in the glassy state, Polymer, 19, 711-716, 1978.
• 15. A. ZIABICKI, [in:] Fundamentals of Fiber Formation Wiley, London, p. 113, 1976.
• 16. A. MAKRADI, S. AHZI, RV. GREGORY, Effects of non-isothermal oriented crystallization on the velocity and elongational viscosity profiles during the melt spinning of HDPE fibers, Polymer Engineering and Sci., 41, 1107-1114, 2001.
• 17. A.K. DOUFAS, A. J. McHuGH, C. MILLER, Simulation of melt spinning including flow-induced crystallization. I. Model development and predictions, J. Non-Newtonian Fluid Mech., 92, 27, 2000; II. Quantitative comparisons with industrial spinline data, 92, 81, 2000.
• 18. K. KANNAN, K.R. RAJAGOPAL, Simulation of fiber spinning including flow-induced crystallization, J. Rheol, 49, 683, 2005.
• 19. J.A. KULKARNI, A.N. BERIS, A model for the necking phenomenon in high-speed fiber spinning based on flow-induced crystallization, J. Rheol., 42, 971-994, 1998.