Slip-enhanced Rayleigh–Plateau instability of a liquid film on a fibre

Abstract

Boundary conditions at a liquid–solid interface are crucial to dynamics of a liquid film coated on a fibre. Here, a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid–solid slip on the Rayleigh–Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier–Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner et al. (Nat. Commun., vol. 6, issue 1, 2015, 7409).

Inertia and slip effects on the instability of a liquid film coated on a fibre

“…where details of Δ ij are shown in Appendix C. This dispersion relation (3.27) is identical to the slip-modified Stokes model proposed by Zhao et al (2023a), which was derived directly from the Stokes equations (neglecting inertia in the NS equations). Numerical investigations are also performed to further support the theoretical analysis, illustrated in figure 3, where the predictions generated by (3.18) tend to converge towards the Stokes model as Oh increases (inertia declines).…”

“…Similar to the previous work on planar films (Münch, Wagner & Witelski 2005), different rescaling for the leading orders give different forms of the lubrication model. When inertia is neglected (Re 1), the one-equation model, which has been widely used in the previous works (Craster & Matar 2006;Haefner et al 2015;Zhang et al 2020;Zhao et al 2023a), can be obtained from the Stokes equations. The dimensionless format of the no-slip lubrication model is…”

“…To quantitatively compare the numerical observations with the theoretical predictions derived from (3.18), we conduct multiple independent simulations (10 for each case) with different initial conditions to collect statistical data of the dominant modes. This statistical approach was proposed by Zhao, Sprittles & Lockerby (2019) and has been employed in evaluating dominant modes of instability in various films (Zhao et al 2021;Zhao, Zhang & Si 2023b;Zhao et al 2023a). For each simulation, a discrete Fourier transform is applied to the interface position h(z, t) to obtain the power spectral density (PSD) of the perturbations.…”

“…More recent investigations delved into the dynamics of films on slippery fibres within non-isothermal conditions (Chao, Ding & Liu 2018) and under the influence of intermolecular forces (Ji et al 2019), employing more intricate lubrication models. Despite the extensive use of slip-modified lubrication models, their constraints have been exposed by Zhao, Zhang & Si (2023a) through linear instability analysis applied to the axisymmetric Stokes equations. The theoretical framework not only highlights an overestimation of the slip-enhanced perturbation growth rate as compared with classical lubrication models, but also reveals a slip-dependent dominant wavelength, deviating from the constant value posited by prior works using the lubrication method (Liao et al 2013;Haefner et al 2015;Halpern & Wei 2017;Chao et al 2018).…”

The Surfactant Role on a Droplet Passing through a Constricted Microchannel in a Pressure-Driven Flow: A Lattice Boltzmann Study

“…Initially (see τ = 137.39), the droplet front invades the constricted channel, and an obvious neck is observed near the entrance of the constricted channel. Then, the neck is snapped off, caused by the Rayleigh–Plateau instability − (see τ = 140.66). Subsequently, the first and second daughter droplets coalesce (see τ = 314.03 and 327.1).…”