Hydrodynamic Instability of Liquid Films on Moving Fibers

Area of Science:

• Fluid dynamics
• Surface science
• Materials science

Background:

• The behavior of liquid films on solid surfaces is crucial for various industrial processes.
• Understanding film stability on moving substrates presents unique challenges compared to static ones.

Purpose of the Study:

• To investigate the stability of liquid films on moving fibers, considering both film-solid adhesion and film-gas hydrodynamic interactions.
• To identify the mechanisms and conditions that lead to film instability on moving fibers.

Main Methods:

• Linear stability analysis using the method of normal modes.
• Derivation of a general dispersion relation for coupled hydrodynamic equations of film and gas flow.
• Analysis of stability in terms of dimensionless parameters: adhesion factor, Weber number, and Reynolds number.

Main Results:

• At high fiber velocities (large Reynolds numbers), film-gas hydrodynamic interactions induce instability, overriding stabilizing adhesion forces.
• Two instability modes were identified: Kelvin-Helmholtz waves (inertia-driven) and a viscosity-driven mode at lower Reynolds numbers.
• The study provides a stability diagram, critical film thickness, and characteristic break-up times for moving fibers.

Conclusions:

• Hydrodynamic interactions with surrounding gas can destabilize liquid films on moving fibers, even when adhesion would provide static stability.
• The findings are applicable to various fiber-related technologies, including spin finishing and lubrication.
• The developed methods are general and can be applied to different liquid-solid interactions, with specific estimates for van der Waals forces.