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

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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.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 51766002, 11802066), Guangxi Natural Science Foundation (No. 2018GXNSFAA281331, 2018GXNSFBA138058), Guangxi Science and Technology Project (No. AD18281042, ZY20198017) and Innovation Project of Guangxi Graduate Education (Grant No. YCSW2021173, 2021YCXS013).

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  1. School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, China

    Bo Guo & Rong Liu

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  1. Bo Guo
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  2. Rong Liu
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Correspondence to Rong Liu.

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Guo, B., Liu, R. The Relative Periodic Orbit of Liquid Films Flowing down a Vertical Fiber. Microgravity Sci. Technol. 34, 3 (2022). https://doi.org/10.1007/s12217-021-09916-1

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