Thermally-driven coalescence in thin liquid film flowing down a fibre

Ji, Hangjie; Falcon, Claudia; Sedighi, Erfan; Sadeghpour, Abolfazl; Ju, Y. Sungtaek; Bertozzi, Andrea L.

doi:10.1017/jfm.2021.198

Cited by 18 publications

(7 citation statements)

References 42 publications

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“…These models incorporate gravity and both stabilizing and destabilizing roles of surface tension by characterizing the axial and azimuthal curvature of the free surface. Numerical and analytical investigations for this type of models also revealed the dependence of the droplet dynamics on the substrate effects and external physical fields [12,14,22].…”

Section: Introductionmentioning

confidence: 86%

“…If flow rates are further reduced, the isolated droplet regime occurs where widely-spaced droplets coexist with small amplitude wave patterns. Similar regime transitions can also be triggered by varying the nozzle diameters or imposing a gradient to the liquid property along the fibre [8,12,13]. A good understanding of these dynamics is critical to the design and control of engineering systems that involve a stable train of travelling droplets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On travelling waves of a control-volume model for liquid films flowing down a fibre

Taranets¹,

Ji²,

Chugunova³

2023

Preprint

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This paper analytically investigates the solutions to a control-volume model for liquid films flowing down a vertical fibre. The dynamic evolution of the free surface is governed by a coupled degenerate nonlinear PDE system for the fluid film radius and the axial velocity. We prove the existence of weak solutions to the coupled system based on the application of a priori estimates derived for energy-entropy functionals. Existence of travelling wave solutions to the system is also established. Numerical studies are presented to illustrate the derived analytical results for both the dynamic PDE solutions and the travelling wave structures.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

On travelling waves of a control-volume model for liquid films flowing down a fibre

Taranets¹,

Ji²,

Chugunova³

2023

Preprint

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“…Elfring, Leal & Squires 2016; Manikantan & Squires 2020) characterized by the Marangoni number. Such non-uniformity in surface tension is known to cause bead coalescence cascades (Ji et al 2021). The sum of the shear forces created in both liquids (L 1 and L 2 ) must exactly equal the gradient of the surface tension, Δγ = τ L 1 − τ L 2 .…”

Section: Surface Tension Transfigurationmentioning

confidence: 99%

“…Such non-uniformity in surface tension is known to cause bead coalescence cascades (Ji et al. 2021). The sum of the shear forces created in both liquids must exactly equal the gradient of the surface tension, .…”

Section: Surface Tension Transfigurationmentioning

confidence: 99%

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

et al. 2022

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The unsteady effects of transitioning surface tension, $\gamma (t)$ , on the dynamics of capillary imbibition in channels of arbitrary shape are analytically investigated with a focus on rectangular and circular channels. With proper scaling, two unsteady models for $\gamma (t)$ are defined and used to highlight this transient behaviour. The convoluted dynamics at the flow front are correctly captured in the governing equations, which are rigorously analysed using unsteady eigenfunction expansion. Then, the final solution and data are obtained by employing the Runge–Kutta fourth-order scheme elegantly applied simultaneously to two derived nonlinear ordinary differential equations. Ultimately, the results are more accurate compared with previous studies. Dynamics and kinematic similarity between rectangular and circular channels are investigated and discussed and the conditions for equivalence in both channels are highlighted. Using a small parameter ( $\epsilon$ ) that stretches the time scale, we successfully use a robust asymptotic analysis to develop and capture the long-time dynamics. Ultimately, we recover the Lucas–Washburn regime analysed in Washburn (Phys. Rev., vol. 17, 1921, pp. 273–283), Lucas (Kolloidn. Z., vol. 23, 1918, pp. 15–22) for steady surface tension where the variations of depth and rate with time result in $h\thicksim t^{1/2}$ and $v \thicksim t^{-1/2}$ . In the end, the three forces, namely the inertia, $F_{v}$ , the viscous, $F_{\mu }$ , and the surface tension, $F_{\gamma }$ , are briefly analysed and used to highlight three main distinct regimes. We show that at early times, $F_{v}/F_{\gamma } \thicksim 1$ , whereas at a long time, $F_{\mu }/F_{\gamma } \thicksim -1$ .

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“…An evolution equation for the interface was derived by Craster & Matar (2006) using the long-wavelength approximation and provided good predictions for the shape and speed of drops flowing down a fibre. More recently, models have considered streamwise viscous diffusion (Ruyer-Quil et al 2009), slip-enhanced drop formation (Halpern & Wei 2017), disjoining pressure (Ji et al 2019) and thermal gradients (Khanum & Tiwari 2020;Ji et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Bead-on-fibre morphology in shear-thinning flow

Gabbard

Bostwick

2023

J. Fluid Mech.

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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).

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Thermally-driven coalescence in thin liquid film flowing down a fibre

Abstract: Abstract

Cited by 18 publications

References 42 publications

On travelling waves of a control-volume model for liquid films flowing down a fibre

On travelling waves of a control-volume model for liquid films flowing down a fibre

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

Bead-on-fibre morphology in shear-thinning flow

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