A Mathematical Model for the Melt Spinning of Polymer Fibers

Andreassen, Erik; Gundersen, Elisabeth; Hinrichsen, Einar L.; Langtangen, Hans Petter

doi:10.1007/978-1-4612-1984-2_9

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…The flow of thin viscous filaments is relevant to a variety of industrial processes such as the drawing and spinning of polymer and glass fibers [1,2,3], and to natural phenomena such as formation of Pele's hair by lava ejected at high speed by volcanoes [4]. In art, Jackson Pollock took advantage of the coiling instability of a thin viscous fluid, the paint, impinging a surface, the canvas, to produce a variety of decorative patterns by a fluid-mechanical process [5].…”

Section: Contextmentioning

confidence: 99%

A discrete geometric approach for simulating the dynamics of thin viscous threads

Audoly

Clauvelin

Brun

et al. 2013

Journal of Computational Physics

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We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations is established formally in the limit of a vanishing discretization length. The discrete models lends itself naturally to numerical implementation. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous jets in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.

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Section: Contextmentioning

confidence: 99%

A discrete geometric approach for simulating the dynamics of thin viscous threads

Audoly

Clauvelin

Brun

et al. 2013

Journal of Computational Physics

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“…Understanding the motion of this viscous thread is a gateway to simulation tools whose utility spans film-making, gaming, and engineering; for example, in over 30% of worldwide textile manufacturing processes, threads of viscous liquid polymers (often incorporating recycled materials) are entangled to form nonwoven fabric used in baby diapers, bandages, envelopes, upholstery, air ("HEPA") filters, surgical gowns, high-traffic carpets, erosion control, felt, frost protection, and tea sachets [Andreassen et al 1997].…”

Section: Introductionmentioning

confidence: 99%

Discrete viscous threads

Bergou

Audoly

Vouga

et al. 2010

TOG

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Figure 1: A thin thread of viscous fluid is poured onto a moving belt, creating a dazzling AbstractWe present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating-without approximation-all but an O(n) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluidmechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

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A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack

Bruaset

Langtangen

1997

Numerical Methods and Software Tools in Industrial Mathematics

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A Mathematical Model for the Melt Spinning of Polymer Fibers

Cited by 8 publications

References 14 publications

A discrete geometric approach for simulating the dynamics of thin viscous threads

A discrete geometric approach for simulating the dynamics of thin viscous threads

Discrete viscous threads

A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack

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