Systematic derivation of an asymptotic model for the dynamics of curved viscous fibers

Mathematical Methods in the Applied Sciences

Volumn 31, Issue 10, 2008, Pages 1153-1173

  Panda, Satyananda ^a   Marheineke, Nicole ^b   Wegener, Raimund ^a  

^a FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

^b Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Asymptotic expansions; Curved viscous fibers; Free boundary value problem; Navier stokes equations; Slender body theory

Indexed keywords

ASYMPTOTIC ANALYSIS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DYNAMICS; EQUATIONS OF MOTION; FIBER OPTICS; FIBERS; FLUID DYNAMICS; FLUID MECHANICS; INITIAL VALUE PROBLEMS; MOBILE TELECOMMUNICATION SYSTEMS; NUMERICAL ANALYSIS; SHIP STEERING EQUIPMENT; SURFACE CHEMISTRY; SURFACE TENSION; THREE DIMENSIONAL;

(001) PARAMETER; (060.2410) FIBERS; (1 1 0) SURFACE; APPLIED (CO); ASYMPTOTIC EXPANSIONS; ASYMPTOTIC MODELS; BALANCE LAWS; CENTER LINES; DISCRETIZATION; FIBER DYNAMICS; FIBER FLOW; FIBER MODELS; FINITE VOLUME APPROACH; FREE BOUNDARY VALUE PROBLEMS; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; INTRINSIC VELOCITY; NUMERICAL INVESTIGATIONS; ONE-DIMENSIONAL; ROTATIONAL EFFECTS; SLENDER BODY THEORY; STAGGERED GRIDS; SYSTEMATIC DERIVATION; TEMPERATURE DEPENDENCES; THREE DIMENSIONAL (3D); VISCOUS NEWTONIAN; VISCOUS TRANSPORT;

NAVIER STOKES EQUATIONS;

EID: 46749137266     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.962     Document Type: Article

References (37)

1. Wong D, Simmons M, Decent S, Parau E, King A. Break up dynamics and drop size distributions created from curved liquid jets. International Journal of Multiphase Flow 2004; 30:499-520.
2. Caroselli R. Glass textile fibers. In Man-made Fibers, Science and Technology, vol. 3, Mark H, Atlas S, Cernia E (eds). Interscience: New York, 1999; 361-389.
3. Geyling F, Homsey G. Extensional instabilities of the glass fiber drawing process. Glass Technology 1980; 21:95-102.
4. Pearson J, Matovich M. Spinning a molten threadline. Stability. Industrial and Engineering Chemistry Fundamentals 1969; 8:605-609.
5. Matovich M, Pearson J. Spinning a molten threadline. Steady-state isothermal viscous flows. Industrial and Engineering Chemistry Fundamentals 1969; 8:512.
6. Dewynne J, Ockendon J, Wilmott P. On a mathematical model for fiber tapering. SIAM Journal on Applied Mathematics 1989; 49:983-990.
7. Pearson J. Mechanics of Polymer Processing. Elsevier: Amsterdam, 1985.
8. Decent S, Simmons M, Parau E, Wong D, King A, Partridge L. Liquid jets from a rotating orifice. Proceedings of the 5th International Conference on Multiphase Flow, ICMF 04, Yokohama, Japan, 2004.
9. Wallwork IM, Decent SP, King AC, Schulkes FRS, Trouton RMSM. The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory. Journal of Fluid Mechanics 2002; 459:43-65.
10. Hohmann M, Shin M, Rutledge G, Brenner M. Electrospinning and electrically forced jets. I. Stability theory. Physics of Fluids 2001; 13:2201-2220.
11. Shah F, Pearson J. On the stability of non-isothermal fibre spinning. Industrial and Engineering Chemistry Fundamentals 1972; 11:145-149.
12. Schultz W, Davis S. One-dimensional liquid fibres. Journal of Rheology 1982; 26:331-345.
13. Gospodinov P, Roussinov V. Nonlinear instability during the isothermal drawing of optical fibers. International Journal of Multiphase Flow 1993; 19:1153-1158.
14. Yarin A, Gospodinov P, Gottlieb O, Graham M. Newtonian glass fiber drawing: chaotic variation of the cross-sectional radius. Physics of Fluids 1999; 11:3201-3208.
15. Forest M, Zhou H. Unsteady analyses of thermal glass fibre drawing process. European Journal of Applied Mathematics 2001; 12:479-496.
16. Eggers J, Dupont T. Drop formation in a one-dimensional approximation of the Navier-Stokes equation. Journal of Fluid Mechanics 2001; 262:205-221.
17. Partridge L, Wong D, Simmons M, Parau E, Decent S. Experimental and theoretical description of the break up of curved liquid jets in the prilling process. Chemical Engineering Research and Design 2005; 83(A11): 1267-1275.
18. Stokes Y, Tuck E. The role of inertia in extensional fall of viscous drop. Journal of Fluid Mechanics 2004; 498:205-225.
19. Stokes Y, Tuck E, Schwartz L. Extensional fall of a very viscous fluid drop. Quarterly Journal of Mechanics and Applied Mathematics 2000; 53:565-582.
20. Howell P, Siegel M. The evolution of a slender non-axisymmetric drop in an extensional flow. Journal of Fluid Mechanics 2004; 521:155-180.
21. Forest M, Wang Q, Bechtel S. Id Models for thin filaments of liquid crystalline polymers: coupling of orientation and flow in the stability of simple solutions. Physica D 2000; 99:527-554.
22. Forest M, Wang Q. Dynamics of slender viscoelastic free jets. SIAM Journal on Applied Mathematics 1994; 54:996-1032.
23. Bechtel S, Forest M, Holm D, Lin K. One-dimensional closure models for three-dimensional incompressible viscoelastic free jets: von Karman flow geometry and elliptical cross-section. Journal of Fluid Mechanics 1988; 196:241-262.
24. Dewynne J, Wilmott P. Slender axisymmetric fluid jets. Mathematical and Computer Modelling 1993; 18:69-82.
25. Cummings L, Howell P. On the evolution of non-axissymetric viscous fibres with surface tension inertia and gravity. Journal of Fluid Mechanics 1999; 389:361-389.
26. Entov V, Yarin A. The dynamics of thin liquid jets in air. Journal of Fluid Mechanics 1984; 140:91-111.
27. Dewynne J, Ockendon J, Wilmot P. A systematic derivation of the leading-order equations for extensional flows in slender geometries. Journal of Fluid Mechanics 1992; 244:323-338.
28. Howell PD. Extensional thin layer flows. Ph.D. Thesis, St Catherine's College, Oxford, 1994.
29. Dewynne J, Howell P, Wilmott P. Slender viscous fibers with inertia and gravity. Quarterly Journal of Mechanics and Applied Mathematics 1994; 47:541-555.
30. Decent S, King A, Wallwork I. Free jets spun from a prilling tower. Journal of Engineering Mathematics 2002; 42:265-282.
31. Ribe N. Coiling of viscous jets. Proceedings of the Royal Society of London, Series A 2004; 2051:3223-3239.
32. Antman S. Nonlinear Problems of Elasticity. Springer: Berlin, 1995.
33. Bishop R. There is more than one way to frame a curve. American Mathematical Monthly 1975; 82:246-251.
34. Panda S. The dynamics of viscous fibers. Ph.D. Thesis, Technische Universität Kaiserslautern, 2006.
35. Trouton FRS. On the coefficient of viscous traction and its relation to that of viscosity. Proceedings of the Royal Society of London, Series A 1906; 77:426-440.
36. Sierou A, Lister J. Self-similar solutions for viscous capillary pinch-off. Journal of Fluid Mechanics 2003; 497:381-403.
37. Yarin A. Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman: New York, 1993.