Unstable waves on a curved non-Newtonian liquid jet

Hawkins, V; Gurney, Christopher James; Decent, Stephen; Simmons, Mark; Uddin, Jamal

doi:10.1088/1751-8113/43/5/055501

Cited by 14 publications

(13 citation statements)

References 23 publications

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“…All the studies that were described in the previous paragraph were done for the spirally or curved Newtonian jets. On the non-Newtonian counterpart efforts, there have been a number of investigations including those by Uddin et al [14,15], Uddin & Decent [18], Hawkins et al [19], Alsharif & Uddin [24] and Riahi [25]. Uddin et al [14] studied spirally non-Newtonian rotating liquid jets using power-law model and determined linear instability of such flows.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear rotating viscoelastic jets during forcespinning process

Riahi

2018

Proc. R. Soc. A.

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In the usual forcespinning (FS) process, a fluid jet is forced through an orifice of a rotating spinneret leading to the formation of a jet with curved centreline. In this paper, we investigate the properties of nonlinear viscoelastic jets during the FS process. We apply scaling and perturbation techniques to determine the modelling system for the viscoelastic jets, subjected to the Giesekus constitutive equations for the stress tensor. We calculate numerically the expressions for the nonlinear steady solutions for the jet quantities such as radius, speed, stretching rate, strain rate, tensile force and trajectory. We determine these quantities for different values of the parameters such as those representing the effects due to rotation, surface tension, viscosity, jet drag and viscoelasticity. We find, in particular, that the fibre jet radius decreases and the tensile force increases with the jet arc length as well as with increasing the effects of rotation and viscoelasticity. Both viscosity and surface tension indicate stabilizing effect on the viscoelastic jet. In addition, strain rate, stretching rate and the jet speed increase with the arc length, viscoelasticity and rotation rate.

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Section: Introductionmentioning

confidence: 99%

Nonlinear rotating viscoelastic jets during forcespinning process

Riahi

2018

Proc. R. Soc. A.

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“…There also exist a number of relevant studies concerning non-Newtonian fluids, e.g. Uddin, Decent & Simmons (2008), Uddin & Decent (2009), Hawkins et al (2010), and Marheineke et al (2016). Although the majority of the previous studies have examined jet breakup through stability analyses, the analysis methods can well be used to study the trajectory and thinning of the radius of curved jets.…”

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confidence: 99%

Regularized string model for nanofibre formation in centrifugal spinning methods

et al. 2017

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We develop a general regularized thin-fibre (string) model to predict the properties of non-Newtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shear-thinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number (Rb), the Reynolds number (Re), the Weber number (We), the Froude number (Fr) and a power-law index (m), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small Rb, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as Re increases or m decreases. At larger arc lengths, a relatively large We results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length.

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“…the asymptotic analysis assumes that the jets are slender and the jet ruptures when s = O (1). The experimental observations of W02, Wong et al (2004), Partridge et al (2005) and Hawkins et al (2010) confirm that these simplifying assumptions are a reasonable starting point in order to describe the physical problem.…”

Section: Mathematical Approaches and Approximationsmentioning

confidence: 52%

“…The equations agree at O (1) as has already been shown in this paper, but there are O (ε) terms including ones proportional to κ 2 in (5.2)-(5.4) in SS17 which are absent in D02. In experiments such as those in W02, Wong et al (2004), Partridge et al (2005) and Hawkins et al (2010), ε ≈ 0.01. In the industrial applications such as prilling that have motivated the work (e.g.…”

Section: Discussionmentioning

confidence: 96%

“…The deviation between the es vector described by W02/D02 (vector shown by a solid-line arrow and labelled es) and the es vector derived by SS17 (vector shown by a dotted-line arrow) is exaggerated in the Figure to aid visibility. et al (2005), Pȃrȃu et al (2006Pȃrȃu et al ( , 2007, Uddin et al (2006Uddin et al ( , 2008aUddin et al ( ,b, 2009, Decent et al (2009), Gurney et al (2010), Hawkins et al (2010), Uddin & Decent (2012)) then the base vectors will remain exactly orthogonal throughout the jet. However, when gravity is included in the model, as in D02, then the jet's centreline falls out of the horizontal plane and has non-zero torsion.…”

Section: Mathematical Approaches and Approximationsmentioning

confidence: 98%

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On mathematical approaches to modelling slender liquid jets with a curved trajectory

et al. 2018

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Slender liquid jets that have a curved trajectory have been examined in a range of papers using a method introduced in Wallwork et al. (Proc. IUTAM Symp. on Free-Surface Flows, 2000, Kluwer; J. Fluid Mech., vol. 459, 2002, pp. 43–65) and Decent et al. (J. Engng Maths, vol. 42, 2002, pp. 265–282), for jets that emerge from an orifice on the surface of a rotating cylindrical container, successfully comparing computational results to measurements arising from laboratory experiments. Wallwork et al. (2000, 2002) and Decent et al. (2002) based their analyses on the slenderness of the jet, and neglected the torsion of the centreline of the jet, which is valid since in most situations examined the torsion is zero or small. Shikhmurzaev & Sisoev (J. Fluid Mech., vol. 819, 2017, pp. 352–400) used differential geometry and incorporated the torsion. This paper shows that these two methods produce identical results at leading order when the torsion is zero or when the torsion is $O(1)$, in an asymptotic framework based upon the slenderness of the jet, and shows that the method of Wallwork et al. (2000, 2002) and Decent et al. (2002) is accurate for parameters corresponding to scenarios previously examined and also when the torsion is $O(1)$. It is shown that the method of Shikhmurzaev & Sisoev (2017) should be used when the torsion is asymptotically large or when the jet is not slender.

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Unstable waves on a curved non-Newtonian liquid jet

Cited by 14 publications

References 23 publications

Nonlinear rotating viscoelastic jets during forcespinning process

Nonlinear rotating viscoelastic jets during forcespinning process

Regularized string model for nanofibre formation in centrifugal spinning methods

On mathematical approaches to modelling slender liquid jets with a curved trajectory

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