The Instability of Shear Thinning and Shear Thickening Spiralling Liquid Jets: Linear Theory

Uddin, Jamal; Decent, Stephen; Simmons, Mark

doi:10.1115/1.2238876

Cited by 22 publications

(44 citation statements)

References 16 publications

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“…Uddin et al [44], who studied the linear instability of rotating power law non-Newtonian liquid jets, is currently extending this nonlinear model to his case. Also, the full three-dimensional problem with both gravity and rotation can be studied in the same manner.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear viscous liquid jets from a rotating orifice

et al. 2006

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Abstract. A liquid jet follows a curved trajectory when the orifice from which the jet emerges is rotating. Surface tension driven instabilities cause the jet to lose coherence and break to form droplets. The sizes of the drops formed from such jets are in general not uniform, ranging from drops with diameters of the order of the jet diameter to droplets with diameters which are several orders of magnitude smaller. This presentation details a theoretical investigation of the effects of changing operating parameters on the break-up of curved liquid jets in stagnant air at room temperature and pressure. The Navier-Stokes equations are solved in this system with the usual viscous free surface boundary conditions, using an asymptotic method based upon a slender jet assumption, which is clearly appropriate from experimental observations of the jet. We also present nonlinear temporal simulations of the breakup of the liquid jets using our slender theory. These simulations based upon both a steady trajectory assumption, and the more general equations which allow for an unsteady trajectory, show all the breakup modes viewed in experiments. Satellite droplet formation is also considered.

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Section: Discussionmentioning

confidence: 99%

Nonlinear viscous liquid jets from a rotating orifice

et al. 2006

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Section: Introductionmentioning

confidence: 98%

“…Non-Newtonian fluids have been investigated by Uddin et al [8] by using the Power-Law model to examine the linear instability of a rotating liquid. Uddin et al [8] studied non-linear temporal solutions by using the finite difference scheme http://dx.doi.org/10.1016/j.apm.2014.12.011 0307-904X/Ó 2014 Elsevier Inc. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

Instability of viscoelastic curved liquid jets

Alsharif

Uddin

Afzaal

2015

Applied Mathematical Modelling

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a b s t r a c tThe industrial prilling process is a common technique to produce small pellets which are generated from the break-up of rotating liquid jets. In many cases the fluids used are molten liquid and/or contain small quantities of polymers and thus typically can be modelled as non-Newtonian liquids. Industrial scale set-ups are costly to run and thus mathematical modelling provides an opportunity to assess methods of improving efficiency and introduces greater levels of precision. In order to understand this process, we will consider a mathematical model to capture the essential physics related to a cylindrical drum, which is rotated about its axis. In this paper, we will model the viscoelastic nature of the fluid using the Oldroyd-B model. An asymptotic approach is used to simplify the governing equations into 1D equations. Moreover, a linear instability analysis is examined and the most unstable modes are found to grow along the jet. Furthermore, the non-linear instability is investigated by using a finite difference scheme to find break-up lengths and droplet formation.

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“…However, disturbances along the jet are much smaller, typically of the order of the jet radius a (which is comparable to when x = O(1)). Similar to Wallwork et al 16 and Uddin et al, 17 we consider travelling shortwavelength modes (or short waves) of the form exp(ωt + ikx), wheret = t/ andx = x/ are 1) are the frequency and the wavenumber of the disturbances. Therefore, we have a multiple scales formulation, with perturbations along the jet having wavelength of O( ), as required.…”

Section: Linear Temporal Instability Analysismentioning

confidence: 94%