Asymptotic model for the dynamics of curved viscous fibres with surface tension

Journal of Fluid Mechanics

Volumn 622, Issue , 2009, Pages 345-369

  Marheineke, Nicole ^a   Wegener, Raimund ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; SURFACE TENSION;

ASYMPTOTIC MODEL; CAPILLARY NUMBERS; FREE END; NEWTONIANS; ROTATIONAL SPINNING PROCESS; SLENDER-BODY THEORY; TEMPORAL EVOLUTION; VISCOUS TRANSPORT;

FIBERS;

BOUNDARY CONDITION; COMPUTATIONAL FLUID DYNAMICS; FLOW MODELING; NEWTONIAN FLUID; ROTATING FLOW; SURFACE TENSION; TEMPORAL EVOLUTION; THEORETICAL STUDY; VISCOUS FLOW;

EID: 65649100473     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008005259     Document Type: Article

References (45)

1. ANTMAN, S. S. 2006 Nonlinear Problems of Elasticity. Springer.
2. BECHTEL, S. E., FOREST, M. G., HOLM, D. D. & LIN, K. J. 1988 One-dimensional closure models for three-dimensional incompressible viscoelastic free jets: Von Karman flow geometry and elliptical cross-section. J. Fluid Mech. 196, 241-262.
3. BISHOP, R. L. 1975 There is more than one way to frame a curve. Am. Math. Monthly 82 (3), 246-251.
4. BUCKMASTER, J. D., NACHMAN, A. & TING, L. 1975 The buckling and stretching of a viscida. J. Fluid Mech. 69 (1), 1-20.
5. CAROSELLI, R. F. 1999 Glass textile fibers. In Man-Made Fibers, Science and Technology (ed. H. F. Mark, S. M. Atlas & E. Cernia), vol. 3, pp. 361-389. Interscience.
6. CHIU-WEBSTER, S. & LISTER, J. R. 2006 The fall of a viscous thread onto a moving surface: A 'fluid-mechanical sewing machine'. J. Fluid Mech. 569, 89-111.
7. CUMMINGS, L. J. & HOWELL, P. D. 1999 On the evolution of non-axisymmetric viscous fibres with surface tension inertia and gravity. J. Fluid Mech. 389, 361-389.
8. DECENT, S. P., KING, A. C. & WALLWORK, I. M. 2002 Free jets spun from a prilling tower. J. Engng Math. 42, 265-282.
9. DECENT, S. P., SIMMONS, M., PARAU, E., WONG, D., KING, A. & PARTRIDGE, L. 2004 Liquid jets from a rotating orifice. In Proceedings of the 5th International Conference on Multiphase Flow, Yokohama, Japan.
10. DEWYNNE, J. N., HOWELL, P. D. & WILMOTT, P. 1994 Slender viscous fibers with inertia and gravity. Q. J. Mech. Appl. Math. 47, 541-555.
11. DEWYNNE, J. N., OCKENDON, J. R. & WILMOT, P. 1992 A systematic derivation of the leading-order equations for extensional flows in slender geometries. J. Fluid Mech. 244, 323-338.
12. DEWYNNE, J. N. & WILMOTT, P. 1993 Slender axisymmetric fluid jets. Math. Comput. Model. 18 (10), 69-82.
13. DO CARMO, M. P. 1998 Differentialgeometrie von Kurven und Flächen. Vieweg.
14. EGGERS, J. 1997 Nonlinear dynamics and breakup of free-surface flow. Rev. Mod. Phys. 69, 865-929.
15. EGGERS, J. & DUPONT, T. 2001 Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262 205-221.
16. ENTOV, V. M. & YARIN, A. L. 1984 The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91-111.
17. FINNICUM, D. S., WEINSTEIN, S. J. & RUSCHAK, K. J. 1993 The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity. J. Fluid Mech. 255, 647-665.
18. FOREST, M. G. & WANG, Q. 1994 Dynamics of slender viscoelastic free jets. SIAM J. Appl. Math. 54 (4), 996-1032.
19. FOREST, M. G., WANG, Q. & BECHTEL, S. E. 2000 1-D models for thin filaments of liquid crystalline polymers: Coupling of orientation and flow in the stability of simple solutions. Physics D 99 (4), 527-554.
20. FOREST, M. G. & ZHOU, H. 2001 Unsteady analyses of thermal glass fibre drawing process. Eur. J. Appl. Math. 12, 497-496.
21. GEYLING, F. T. & HOMSEY, G. M. 1980 Extensional instabilities of the glass fiber drawing process. Glass Technol. 21, 95-102.
22. GOSPODINOV, P. & ROUSSINOV, V. 1993 Nonlinear instability during the isothermal drawing of optical fibers. Intl J. Multiph. Flow 19, 1153-1158.
23. GÖTZ, T., KLAR, A., UNTERREITER, A. & WEGENER, R. 2008 Numerical evidence for the non-existencing of solutions of the equations describing rational spinning. Math. Models Meth. Appl. Sci. 18 (10), 1-16.
24. HOWELL, P. D. 1994 Extensional thin layer flows. PhD thesis, St. Catherine's College, Oxford.
25. HOWELL, P. D. & SIEGEL, M. 2004 The evolution of a slender non-axisymmetric drop in an extensional flow. J. Fluid Mech. 521, 155-180.
26. MARHEINEKE, N. & WEGENER, R. 2007 Dynamics of curved viscous fibers with surface tension. Berichte des Fraunhofer ITWM 115
27. MATOVICH, M. A. & PEARSON, J. R. A. 1969 Spinning a molten threadline. Steady-state isothermal viscous flows. Ind. Engng Chem. Fundam. 8 (3), 512-520.
28. PANDA, S. 2006 The dynamics of viscous fibers. PhD thesis, Technische Universität Kaiserslautern.
29. PANDA, S., MARHEINEKE, N. & WEGENER, R. 2008 Systematic derivation of an asymptotic model for the dynamics of curved viscous fibers. Math. Meth. Appl. Sci. 31, 1153-1173.
30. PARTRIDGE, L., WONG, D. C. Y., SIMMONS, M. J. H., PARAU, E. I. & DECENT, S. P. 2005 Experimental and theoretical description of the break up of curved liquid jets in the prilling process. Chem. Engng Res. Des. 83 (11), 1267-1275.
31. PEARSON, J. R. A. 1985 Mechanics of Polymer Processing. Elsevier.
32. PEARSON, J. R. A. & MATOVICH, M. A. 1969 Spinning a molten threadline. Stability. Ind. Engng Chem. Fundam. 8 (3), 605-609.
33. RIBE, N. M. 2004 Coiling of viscous jets. Proc. R. Soc. Lond. A 2051, 3223-3239.
34. RIBE, N. M., HABIBI, M. & BONN, D. 2006a Stability of liquid rope coiling. Phys. Fluids 18, 084102.
35. RIBE, N. M., LISTER, J. R. & CHIU-WEBSTER, S. 2006b Stability of a dragged viscous thread: Onset of 'stitching' in a fluid-mechanical 'sewing machine'. Phys. Fluids 18, 124105.
36. SCHULTZ, W. W. & DAVIS, S. H. 1982 One-dimensional liquid fibres. J. Rheol. 26, 331-345.
37. SHAH, F. T. & PEARSON, J. R. A. 1972 On the stability of non-isothermal fibre spinning. Ind. Engng Chem. Fundam. 11, 145-149.
38. SIEROU, A. & LISTER, J. R. 2003 Self-similar solutions for viscous capillary pinch-off. J. Fluid Mech. 497, 381-403.
39. STOKES, Y. M. & TUCK, E. O. 2004 The role of inertia in extensional fall of viscous drop. J. Fluid Mech. 498, 205-225.
40. STOKES, Y. M., TUCK, E. O. & SCHWARTZ, L. W. 2000 Extensional fall of a very viscous fluid drop. Q. J. Mech. Appl. Math. 53 (4), 565-582.
41. TROUTON, F. R. S. 1906 On the coefficient of viscous traction and its relation to that of viscosity. Proc. R. Soc. Lond. A 77, 426-440.
42. WALLWORK, I. M., DECENT, S. P., KING, A. C. & SCHULKES, R. M. S. M. 2002 The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory. J. Fluid Mech. 459, 43-65.
43. WONG, D. C. Y., SIMMONS, M. J. H., DECENT, S. P., PARAU, E. I. & KING, A. C. 2004 Break up dynamics and drop size distributions created from curved liquid jets. Intl J. Multiph. Flow 30, 499-520.
44. YARIN, A. L. 1993 Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman.
45. YARIN, A. L., GOSPODINOV, P., GOTTLIEB, O. & GRAHAM, M. D. 1999 Newtonian glass fiber drawing: Chaotic variation of the cross-sectional radius. Phys. Fluids 11 (11), 3201-3208.