“…This is compounded by the fact that the bead can rotate about the fibre. Here, we use glycerol–water mixtures as the solvent for our polymer solutions, which are the same as used in our Newtonian experiments (Gabbard & Bostwick 2021 a ); however, adding polymer may slightly affect , leading to morphology differences near the transition point. Figure 2.Phase diagram of the bead symmetry as it depends upon the power-law index and fibre diameter for all experiments with .…”
Section: Resultsmentioning
confidence: 99%
“…Asymmetric bead morphologies were observed when either (i) shear-thinning, as quantified by the power-law index , or (ii) fibre diameter , were increased. Qualitative observations show that unlike the asymmetric morphology of Newtonian liquids (Gabbard & Bostwick 2021 a ), shear-thinning solutions can exhibit patterns containing both morphologies; small, static beads may be symmetric, while larger, faster beads are asymmetric. The asymmetric morphologies of Newtonian and shear-thinning liquids exhibit the same three flow regimes (isolated, Plateau–Rayleigh, convective), but shear-thinning significantly decreases the flow rate and increases the bead spacing at the transition points (i) between the isolated and Plateau–Rayleigh regimes, and (ii) between the Plateau–Rayleigh and convective regimes.…”
Section: Discussionmentioning
confidence: 95%
“…2011). Recently, we observed asymmetric morphologies in Newtonian flow down a fibre using high-surface-tension glycerol–water mixtures, with the azimuthal symmetry depending upon the surface tension and fibre diameter, and the bead properties following scaling laws much different to the corresponding symmetric patterns (Gabbard & Bostwick 2021 a ). The asymmetric morphology results in azimuthally asymmetric bead profiles like the ‘clamshell’ profile observed for static beads on a fibre; however, they are also axial asymmetric, resulting in a wide range of shapes.…”
Thin-film flow down a fibre exhibits rich dynamics and is relevant to applications such as desalination, fibre coating and fog harvesting. These flows are subject to instabilities that result in dynamic bead-on-fibre patterns. We perform an experimental study of shear-thinning flow down fibres using 20 different xanthan gum solutions as our working liquid. The bead-on-fibre morphology can be oriented either symmetrically or asymmetrically on the fibre, and this depends upon the surface tension, fibre diameter and liquid rheology, as defined by the Ostwald power-law index. For highly shear-thinning liquids, it is possible for the pattern to be complex and exhibit simultaneously both asymmetric large beads and symmetric small beads in the isolated and convective flow regimes. We quantify the transition between flow regimes and bead dynamics for the asymmetric morphology, and compare with Newtonian flow, as it depends upon the experimental parameters. Finally, the dimensionless bead frequency is shown to scale with the Bond number for all of our experimental data (symmetric and asymmetric).
“…This is compounded by the fact that the bead can rotate about the fibre. Here, we use glycerol–water mixtures as the solvent for our polymer solutions, which are the same as used in our Newtonian experiments (Gabbard & Bostwick 2021 a ); however, adding polymer may slightly affect , leading to morphology differences near the transition point. Figure 2.Phase diagram of the bead symmetry as it depends upon the power-law index and fibre diameter for all experiments with .…”
Section: Resultsmentioning
confidence: 99%
“…Asymmetric bead morphologies were observed when either (i) shear-thinning, as quantified by the power-law index , or (ii) fibre diameter , were increased. Qualitative observations show that unlike the asymmetric morphology of Newtonian liquids (Gabbard & Bostwick 2021 a ), shear-thinning solutions can exhibit patterns containing both morphologies; small, static beads may be symmetric, while larger, faster beads are asymmetric. The asymmetric morphologies of Newtonian and shear-thinning liquids exhibit the same three flow regimes (isolated, Plateau–Rayleigh, convective), but shear-thinning significantly decreases the flow rate and increases the bead spacing at the transition points (i) between the isolated and Plateau–Rayleigh regimes, and (ii) between the Plateau–Rayleigh and convective regimes.…”
Section: Discussionmentioning
confidence: 95%
“…2011). Recently, we observed asymmetric morphologies in Newtonian flow down a fibre using high-surface-tension glycerol–water mixtures, with the azimuthal symmetry depending upon the surface tension and fibre diameter, and the bead properties following scaling laws much different to the corresponding symmetric patterns (Gabbard & Bostwick 2021 a ). The asymmetric morphology results in azimuthally asymmetric bead profiles like the ‘clamshell’ profile observed for static beads on a fibre; however, they are also axial asymmetric, resulting in a wide range of shapes.…”
Thin-film flow down a fibre exhibits rich dynamics and is relevant to applications such as desalination, fibre coating and fog harvesting. These flows are subject to instabilities that result in dynamic bead-on-fibre patterns. We perform an experimental study of shear-thinning flow down fibres using 20 different xanthan gum solutions as our working liquid. The bead-on-fibre morphology can be oriented either symmetrically or asymmetrically on the fibre, and this depends upon the surface tension, fibre diameter and liquid rheology, as defined by the Ostwald power-law index. For highly shear-thinning liquids, it is possible for the pattern to be complex and exhibit simultaneously both asymmetric large beads and symmetric small beads in the isolated and convective flow regimes. We quantify the transition between flow regimes and bead dynamics for the asymmetric morphology, and compare with Newtonian flow, as it depends upon the experimental parameters. Finally, the dimensionless bead frequency is shown to scale with the Bond number for all of our experimental data (symmetric and asymmetric).
“…In all of the studies in the literature, the fibre is concentric with the liquid column, and the initial stage of any unstable regime exhibits an axisymmetric growth of the interface undulations. The recent work of Gabbard & Bostwick (2021) addresses the evolution of asymmetric beads when the film thickness is initially non-homogeneous around the fibre. In their case, they outlined the thresholds between the three regimes of isolated beads, and regular and irregular beads trains.…”
We study a gravity-driven viscous flow coating a vertical cylindrical fibre. The destabilisation of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh–Plateau and Kapitza instabilities in the limit of small Bond numbers
$Bo$
. Here, we focus on quasi-inertialess flows (large Ohnesorge number
$Oh$
) and conduct a linear stability analysis on a unidirectional flow along a rigid eccentric fibre for intermediate to large
$Bo$
. We show the existence of two unstable modes, namely pearl and whirl modes. The pearl mode depicts asymmetric beads, similar to that of the Rayleigh–Plateau instability, whereas a single helix forms along the axis in the whirl mode instability. The geometric and hydrodynamic thresholds of the whirl mode instability are investigated, and phase diagrams showing the transition thresholds between different regimes are presented. Additionally, an energy analysis is carried out to elucidate the whirl formation mechanism. This analysis reveals that despite the unfavourable capillary energy cost, the asymmetric interface shear distribution, caused by the fibre eccentricity, has the potential to sustain a whirling interface. In general, small fibre radius and large eccentricity tend to foster the whirl mode instability, while reducing
$Bo$
tends to favour the dominance of the pearl mode instability. Finally, we compare the predictions of our model with the results of some illustrative experiments, using highly viscous silicone oils flowing down fibres. Whirling structures are observed for the first time, and the measured wavenumbers match our stability analysis prediction.
“…Liquid film flow is a typical, low-speed flow with rich dynamical behaviors, such as interfacial instability, isolated waves, and liquid film rupture (Ruyer-Quil and Kalliadasis (2012); Boulogne et al (2013); Gabbard and Bostwick (2021); Qur (2003Qur ( , 2007). It is widely applied to 3D printing, falling film condensation (Halpern and Wei (2017)), heat and mass transfer (Zeng et al (2017); Davalos-Orozco (2018)), etc., which has attracted intensive research on the flow mechanism of the flow by domestic and foreign scholars (Ruyer-Quil and Kalliadasis (2012); Hinch and Yu (2011); Frenkel (2007); Demekhin (1999); Richter and Bestehorn (2019); Nave et al (2010); Kalliadasis and Chang (1994)).…”
Direct simulations on the dynamics of a liquid film coating on the outer surface of a vertical fiber are performed in the present paper. A domain mapping technique has been used on solving the Navier-Stokes problem in stream function form and predicts the dynamics of the various flow regimes with remarkable accuracy. We investigated the morphologies that develop in the coating flow down fiber and analyze the effects of Bond number and fiber diameter on the maximum liquid film height and drop speed. The results showed that the Bond number and fiber diameter have a significant effect on the instability. The transition between the Plateau-Rayleigh and convective regimes occurs at the conditions when the flow transitions from absolutely to convectively unstable.
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