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

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.

Hydrodynamics of Two-Phase Gas-Very Viscous Liquid Flow in Heat Exchange Conditions

This paper presents the results of analyses of the impact of heat transfer conditions on the hydrodynamics of downward co-current annular flow in vertical tubes of very viscous liquid and gas. The research was conducted within the range of gas velocities of 0–30.0 m/s and liquid velocities of 0.001–0.254 m/s, while the viscosity was in the unprecedented range of 0.046–3.5 Pas. The research demonstrates that the volume and nature of the liquid waves with various amplitudes and frequencies arising on the surface of the film are relative to the flow rate and viscosity of the gas phase. At the same time, we found that, under the condition of liquid cooling, an increase in viscosity resulted in the formation of a smooth interface whereas, under the conditions where the liquid is heated at the end of the channel section, a greater number of capillary waves were formed. This research resulted in the development of new dependencies which take into account the influence of selected thermal and flow parameters (including mass fraction) on the values of volumes specific to very viscous liquid film flows. These dependencies improve the accuracy of calculation by 8–10% and are fully applicable to the description of the performance of an apparatus with a hydraulically generated liquid film.

Dynamics and equilibria of thin viscous coating films on a rotating sphere

We examine the dynamics of a thin viscous liquid film on the outer surface of a solid sphere rotating around its vertical axis in the presence of gravity. An asymptotic model describing the evolution of the film thickness is derived in the rotating frame based on the lubrication approximation. The model includes the centrifugal and gravity forces and the stabilizing effect of surface tension. Depending on the values of the parameters, the problem admits different types of steady states: one with a uniformly positive film thickness, or those with one or two dry zones on the sphere. We prove that all steady states are energy minimizers and hence global attractors for axisymmetric states.