Liquid Films Falling Down a Vertical Fiber: Modeling, Simulations and Experiments

Yadong Ruan,Lekha Duvvoori,Ali Nadim,Marina Chugunova

doi:10.3390/fluids6080281

Yadong Ruan, Lekha Duvvoori + Show 2 more

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https://doi.org/10.3390/fluids6080281

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Abstract

We provide a new framework for analyzing the flow of an axisymmetric liquid film flowing down a vertical fiber, applicable to fiber coating flows and those in similar geometries in heat exchangers, water treatment, and desalination processes. The problem considered is that of a viscous liquid film falling under the influence of gravity and surface tension on a solid cylindrical fiber. Our approach is different from existing ones in that we derive our mathematical model by using a control-volume approach to express the conservation of mass and axial momentum in simple and intuitively appealing forms, resulting in a pair of equations that are reminiscent of the Saint-Venant shallow-water equations. Two versions of the model are obtained, one assuming a plug-flow velocity profile with a linear drag force expression, and the other using the fully-developed laminar velocity profile for a locally uniform film to approximate the drag. These can, respectively, model high- and low-Reynolds number regimes of flow. Linear stability analyses and fully nonlinear numerical simulations are presented that show the emergence of traveling wave solutions representing chains of identical droplets falling down the fiber. Physical experiments with safflower oil on a fishing line are also undertaken and match the theoretical predictions from the laminar flow model well when machine learning methods are used to estimate the parameters.

Highlights

Liquid choice, fiber radius, and inlet geometry, three typical flow regimes have been observed [10,11,12,13]: (a) the convective instability regime, where bead coalescence happens repeatedly; (b) the traveling wave regime, where a steady train of beads flows down the fiber at a constant speed; and (c) the isolated droplet regime, where widely spaced large droplets are separated by small wave patterns
Our one-dimensional two-equation model for an axisymmetric liquid film falling down a vertical fiber consists of the equations for the conservation of mass (9) and axial momentum (6) for plug flow, or the corresponding pair (12) and (10) for laminar flow
Our setup was modeled after those presented in other papers examining droplet flow on a vertical fiber, e.g., Kliakhandler et al [19] and Craster and Matar [18]

Summary

Introduction

Driven by the effects of Rayleigh–Plateau instability and gravity, a wide range of dynamics can be observed [1,2,3,4,5]. These include the formation of discontinuous bead-like droplets, periodic traveling wave-like patterns, and irregularly coalescing droplets. The study of these dynamics has widespread applications in heat and mass exchangers, desalination [6,7,8], and particle capturing systems [9], attracting much attention over the past two decades. Further analysis of the traveling wave patterns in regime (b) is expected to provide insights into many engineering applications that utilize steady trains of beads

Results

Discussion

Conclusion