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

Tronnolone, Hayden; Stokes, Yvonne M.; Ebendorff-Heidepriem, Heike

doi:10.1017/jfm.2016.729

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…A similar approach has also been used to consider gravitational extension (Tronnolone et al. 2016) and extrusion (Tronnolone, Stokes & Ebendorff-Heidepriem 2017). The asymptotic techniques applied in studies of this type have been shown to be accurate by Chen et al.…”

Section: Introductionmentioning

confidence: 99%

“…This approach has been generalised to consider internal pressurisation of holes (Chen et al 2015), the inverse problem of designing the die for a desired output thread (Buchak et al 2015), and explicit thermal effects (Stokes, Wylie & Chen 2019). A similar approach has also been used to consider gravitational extension (Tronnolone et al 2016) and extrusion (Tronnolone, Stokes & Ebendorff-Heidepriem 2017). The asymptotic techniques applied in studies of this type have been shown to be accurate by Chen et al (2016).…”

Section: Introductionmentioning

confidence: 99%

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Stability of drawing of microstructured optical fibres

et al. 2023

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We consider the stability of the drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape that evolves due to axial drawing, inertia and surface tension effects. Despite the complicated geometry of the boundaries, we use asymptotic techniques to determine a particularly convenient formulation of the equations of motion that is well-suited to stability calculations. We will determine an explicit asymptotic solution for steady states with (a) large surface tension and negligible inertia, and (b) large inertia. In both cases, we will show that complicated boundary layer structures can occur. We will use linear stability analysis to show that the presence of an axisymmetric hole destabilises the flow for finite capillary number and which answers a question raised in the literature. However, our formulation allows us to go much further and consider arbitrary hole structures or non-axisymmetric shapes, and show that any structure with holes will be less stable than the case of a solid axisymmetric thread. For a solid axisymmetric thread, we will also determine a closed-form expression that delineates the unconditional instability boundary in which case the thread is unstable for all draw ratios. We will determine how the detailed effects of the microstructure affect the stability, and show that they manifest themselves only via a single function that occurs in the stability problem and hence have a surprisingly limited effect on the stability.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of drawing of microstructured optical fibres

et al. 2023

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“…Extrusion is an important manufacturing technique used to produce a wide variety of products including cereal (Lach 2006), pet food (Quang 2008), polymer foams (Feng & Bertelo 2004), artificial wine corks (O'Brien & Ehrenfreund 1976;Silva et al 2011) and optical fibres (Taroni et al 2013;Tronnolone, Stokes & Ebendorff-Heidepriem 2017). The global extruded-snack-food market alone was valued at $80.6 billion USD in 2018, and is growing as the demand for ready-to-eat food products increases, according to a report by IMARC Group (2019).…”

Section: Introductionmentioning

confidence: 99%

“…2011) and optical fibres (Taroni et al. 2013; Tronnolone, Stokes & Ebendorff-Heidepriem 2017). The global extruded-snack-food market alone was valued at $80.6 billion USD in 2018, and is growing as the demand for ready-to-eat food products increases, according to a report by IMARC Group (2019).…”

Section: Introductionmentioning

confidence: 99%

Extensional flow of a compressible viscous fluid

McPhail,

Oliver,

Parker

et al. 2023

J. Fluid Mech.

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We derive reduced models for extrusion problems where it is necessary to account for fluid compressibility. We consider the two-dimensional extensional flow of a compressible viscous fluid and discuss two specific applications: weakly compressible fluids and bubbly liquid–gas mixtures that behave as a single compressible fluid. The mathematical model we present consists of equations for conservation of mass, conservation of momentum and a closure relationship between the pressure and density. The most substantial differences between compressible extrusion problems is in the closure relationship. By integrating the conservation equations across the fluid cross-section and exploiting a slender aspect ratio, we derive reduced equations for conservation of mass and conservation of momentum in the direction of flow. The reduced system of equations relating cross-sectionally averaged quantities is closed by a relationship between the averaged pressure and density, which will differ substantially depending on the application. We demonstrate the utility of a reduced model for both the weakly compressible fluid and bubbly mixture applications; namely, in providing valuable quantitative insights without needing to solve a complicated free-boundary problem.

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Coupled fluid and energy flow in fabrication of microstructured optical fibres

Stokes

Wylie

2019

J. Fluid Mech.

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We consider the role of heating and cooling in the steady drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape. The internal holes and the external boundary evolve as a result of the axial drawing and surface-tension effects. The heating and cooling affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We use asymptotic techniques to show that, under a suitable transformation, this complicated three-dimensional free boundary problem can be formulated in such a way that the transverse aspect of the flow can be reduced to the solution of a standard Stokes flow problem in the absence of axial stretching. The solution of this standard problem can then be substituted into a system of three ordinary differential equations that completely determine the flow. We use this approach to develop a very simple numerical method that can determine the way that thermal effects impact on the drawing of threads by devices that either specify the fibre tension or the draw ratio. We also develop a numerical method to solve the inverse problem of determining the initial cross-sectional geometry, draw tension and, importantly, heater temperature to obtain a desired cross-sectional shape and change in cross-sectional area at the device exit. This precisely allows one to determine the pattern of air holes in the preform that will achieve the desired hole pattern in the stretched fibre.

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

Cited by 7 publications

References 23 publications

Stability of drawing of microstructured optical fibres

Stability of drawing of microstructured optical fibres

Extensional flow of a compressible viscous fluid

Coupled fluid and energy flow in fabrication of microstructured optical fibres

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