Instabilities and bifurcations of liquid films flowing down a rotating fibre

Abstract

Abstract

Coating flows down a vertical fibre: towards the full Navier–Stokes problem

“…However, when the fibre radius is small, e.g. , we observe a different phenomenon in that the wave speed can be slightly reduced for a larger droplet when , which, perhaps, is due to the circulation flow in the large droplet (Liu & Ding 2020). Furthermore, we examined the dependence of the travelling wave solution on the Bond number by fixing the Laplace number at .…”

“…To solve the Navier–Stokes equations (2.1)–(2.3) subject to a moving boundary at , we employ a domain mapping technique adapted from Richter & Bestehorn (2019) (see Liu & Ding 2020): where is the thickness of the film. Hence, the domain of fluid is mapped into a rectangular region , where is the axial length of the domain, which is also the wavelength of a typical travelling wave in the present study.…”

“…Ten Chebyshev modes and Fourier modes were utilized to ensure numerical accuracy in the present study. Details of the numerical method can be found in the appendix of Liu & Ding (2020). It should be mentioned that the present study considers a periodic domain such that the nozzle effect and irregular bead coalescence dynamics in the convective instability regime will not be characterized.…”

“…Very recently, Richter & Bestehorn (2019) used a domain mapping method to simulate the dynamics of a vibrating liquid film on a horizontal plane. The domain mapping method is to map the time-varying domain into a time-independent rectangular domain, which has been recently extended to a liquid film flowing down a rotating cylinder by Liu & Ding (2020). The main advantage of the domain mapping method is that there is no need to update the grid at every time step.…”

The Relative Periodic Orbit of Liquid Films Flowing down a Vertical Fiber

“…Recently, many authors have devoted to studying the coating flow on a vertical cylindrical fiber in more complicated situations, e.g. in a radial electric field (Li et al 2009;Wray et al 2013;Ding et al 2014;Liu et al 2018), a heated fiber (Liu and Liu 2014;Dávalos 2017;Dávalos 2019;Dong et al 2020), and a rotating fiber (Liu and Ding 2020). These flows are driven by a Plateau-Rayleigh mechanism modified by the existence of gravity and different destabilizing body force which play roles in the formation of bead-like structures and a series of stable or oscillatory travelling waves (De Ryck and Quéré 1996;Zuccher 2008;Duprat et al 2009).…”