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Extrusion of fluid cylinders of arbitrary shape with surface tension and gravity

  • Hayden Tronnolone (a1), Yvonne M. Stokes (a1) and Heike Ebendorff-Heidepriem (a2)

Abstract

A model is developed for the extrusion in the direction of gravity of a slender fluid cylinder from a die of arbitrary shape. Both gravity and surface tension act to stretch and deform the geometry. The model allows for an arbitrary but prescribed viscosity profile, while the effects of extrudate swell are neglected. The solution is found efficiently through the use of a carefully selected axial Lagrangian coordinate and a transformation to a reduced-time variable. Comparisons between the model and extruded glass microstructured optical fibre preforms show that surface tension has a significant effect on the geometry but the model does not capture all of the behaviour observed in practice. Experimental observations are used in conjunction with the model to argue that some deformation, due neither to surface tension nor gravity, occurs in or near the die exit. Methods are considered to overcome deformation due to surface tension.

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Corresponding author

Email address for correspondence: hayden.tronnolone@adelaide.edu.au

References

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Boyd, K., Ebendorff-Heidepriem, H., Monro, T. M. & Munch, J. 2012 Surface tension and viscosity measurement of optical glasses using a scanning CO2 laser. Opt. Mater. Express 2 (8), 11011110.
Buchak, P., Crowdy, D. G., Stokes, Y. M. & Ebendorff-Heidepriem, H. 2015 Elliptical pore regularisation of the inverse problem for microstructured optical fibre fabrication. J. Fluid Mech. 778, 538.
Chen, M. J., Stokes, Y. M., Buchak, P., Crowdy, D. G. & Ebendorff-Heidepriem, H. 2015 Microstructured optical fibre drawing with active channel pressurisation. J. Fluid Mech. 783, 137165.
Chen, M. J., Stokes, Y. M., Buchak, P., Crowdy, D. G., Foo, H. T. C., Dowler, A. & Ebendorff-Heidepriem, H. 2016 Drawing tubular fibres: experiments versus mathematical modelling. Opt. Mater. Express 6 (1), 166180.
Crowdy, D. G. 2002 Exact solutions for the viscous sintering of multiply-connected fluid domains. J. Engng Maths 42 (3–4), 225242.
Crowdy, D. G. & Tanveer, S. 1998 A theory of exact solutions for annular viscous blobs. J. Nonlinear Sci. 8 (4), 375400.
Crowdy, D. G., Tanveer, S. & Vasconcelos, G. L. 2005 On a pair of interacting bubbles in planar Stokes flow. J. Fluid Mech. 541, 231261.
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, 361389.
Ebendorff-Heidepriem, H. & Monro, T. M. 2007 Extrusion of complex preforms for microstructured optical fibers. Opt. Express 15 (23), 8692.
Ebendorff-Heidepriem, H. & Monro, T. M. 2012 Analysis of glass flow during extrusion of optical fiber preforms. Opt. Mater. Express 2 (3), 304320.
Ebendorff-Heidepriem, H., Moore, R. C. & Monro, T. M. 2008 Progress in the fabrication of the next-generation soft glass microstructured optical fibers. AIP Conf. Proc. 1055 (1), 9598.
Ebendorff-Heidepriem, H., Schuppich, J., Dowler, A., Lima-Marques, L. & Monro, T. M 2014 3D-printed extrusion dies: a versatile approach to optical material processing. Opt. Mater. Express 4 (8), 14941504.
Goursat, É. J.-B. 1898 Sur l’équation ΔΔu = 0. Bull. Soc. Maths France 26, 233237.
Griffiths, I. M. & Howell, P. D. 2007 The surface-tension-driven evolution of a two-dimensional annular viscous tube. J. Fluid Mech. 593, 181208.
Griffiths, I. M. & Howell, P. D. 2008 Mathematical modelling of non-axisymmetric capillary tube drawing. J. Fluid Mech. 605, 181206.
Hopper, R. W. 1990 Plane Stokes flow driven by capillarity on a free surface. J. Fluid Mech. 213, 349375.
Knight, J. C. 2003 Photonic crystal fibres. Nature 424 (6950), 847851.
Manning, S.2011 A study of tellurite glasses for electro-optic optical fibre devices. PhD thesis, School of Chemistry and Physics, University of Adelaide.
Monro, T. M. & Ebendorff-Heidepriem, H. 2006 Progress in microstructured optical fibres. Annu. Rev. Mater. Res. 36 (1), 467495.
Richardson, S. 1992 Two-dimensional slow viscous flows with time-dependent free boundaries driven by surface tension. Eur. J. Appl. Maths 3, 193207.
Stokes, Y. M., Buchak, P., Crowdy, D. G. & Ebendorff-Heidepriem, H. 2014 Drawing of micro-structured fibres: circular and non-circular tubes. J. Fluid Mech. 755, 176203.
Stokes, Y. M., Crowdy, D. G., Tronnolone, H., Ebendorff-Heidepriem, H. & Monro, T. M. 2012 Towards understanding of geometrical structure in microstructured optical fibres. In International Congress of Theoretical and Applied Mechanics (23rd: 2012: Beijing, China), (ed. Y. Bai, J. Wang & D. Fang), FM10-013. Available at http://fluid.ippt.pan.pl/ conference_proceedings/ICTAM2012/.
Trabelssi, M., Ebendorff-Heidepriem, H., Richardson, K. A., Monro, T. M. & Joseph, P. F. 2015 Computational modeling of hole distortion in extruded microstructured optical fiber glass preforms. J. Lightwave Technol. 33 (2), 424431.
Tronnolone, H.2016 Extensional and surface-tension-driven fluid flows in microstructured optical fibre fabrication. PhD thesis, School of Mathematical Sciences, University of Adelaide.
Tronnolone, H., Stokes, Y. M., Foo, H. T. C. & Ebendorff-Heidepriem, H. 2016 Gravitational extension of a fluid cylinder with internal structure. J. Fluid Mech. 790, 308338.
van de Vorst, G. A. L. 1993 Integral method for a two-dimensional Stokes flow with shrinking holes applied to viscous sintering. J. Fluid Mech. 257, 667689.
Wilson, S. D. R. 1988 The slow dripping of a viscous fluid. J. Fluid Mech. 190, 561570.
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Extrusion of fluid cylinders of arbitrary shape with surface tension and gravity

  • Hayden Tronnolone (a1), Yvonne M. Stokes (a1) and Heike Ebendorff-Heidepriem (a2)

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