Dynamics of thin film flows on a vertical fibre with vapor absorption

TL;DR

This study models the complex dynamics of water vapor absorption in thin silicone oil films flowing down vertical fibers, revealing how absorption influences interfacial stability and pattern formation through a coupled nonlinear PDE system.

Contribution

It introduces a novel one-sided thin-film model incorporating absorption effects, Marangoni forces, and non-mass-conserving fluxes for vapor absorption on vertical fibers.

Findings

Absorption induces irregular wave patterns and droplet coalescence.

Parameter ranges for Marangoni number and absorption flux trigger regime transitions.

Model predicts interfacial instability driven by absorption and Marangoni effects.

Abstract

Water vapor capture through free surface flows plays a crucial role in various industrial applications, such as liquid desiccant air conditioning systems, water harvesting, and dewatering. This paper studies the dynamics of a silicone liquid sorbent (also known as water-absorbing silicone oil) flowing down a vertical cylindrical fibre while absorbing water vapor. We propose a one-sided thin-film-type model for these dynamics, where the governing equations form a coupled system of nonlinear fourth-order partial differential equations for the liquid film thickness and oil concentration. The model incorporates gravity, surface tension, Marangoni effects induced by concentration gradients, and non-mass-conserving effects due to absorption flux. Interfacial instabilities, driven by the competition between mass-conserving and non-mass-conserving effects, are investigated via stability analysis. We numerically show that water absorption can lead to the formation of irregular wavy patterns and trigger droplet coalescence downstream. Systematic simulations further identify parameter ranges for the Marangoni number and absorption parameter that lead to the onset of droplet coalescence dynamics and regime transitions.