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

Abstract

The dynamics of coating flows down a vertical fiber is investigated experimentally. An oscillatory flow has been observed in experiments, which corresponds to a relative periodic orbit (RPO) in nonlinear dynamics. This type of RPO manifests as a periodic process in which a large droplet swallows small droplets, and then the film behind the large droplet evolves into new small droplets. In order to understand the physical mechanisms of RPOs, we studied the transition from travelling waves (TWs) to RPOs for different physical parameters, including the dynamic viscosities, fiber diameters and flow rates. The experimental results show that such a process is periodic, and there exists a critical flow rate at which the RPOs appear. It is interesting that a small-scale RPO has been observed in experiments when the flow rate is much smaller than the critical flow rate at which the normal-scale RPO appears. As the flow rate is decreased further, the relative periodic orbits transformed into an irregular state. This indicates that the appearance of multi-scale RPOs is a transition from an ordered state to a disordered state.

Investigation of the Dynamics of a Coating Flow on a Vertical Fiber Immersed in Surrounding Liquid Phase

“…Regular small droplets appear between adjacent large droplets, and then small droplets reappear after the large droplets swallowing the small droplets. This flow has been identified as an oscillatory travelling wave corresponding to the relative periodic orbit in nonlinear dynamics [10,11]. As the flow rate increases, in Fig.…”

“…The RPO solution has been used for capturing the wave speed and oscillatory dynamics in the unsteady flow regime [10,17]. Recently, Guo et al [11] studied experimentally the periodic nature of the flow regime (c) in both time and space.…”