Equilibrium Shapes and Their Stability for Liquid Films in Fast Flows

Area of Science:

• Fluid Dynamics
• Rheology
• Nonlinear Dynamics

Background:

• Understanding the behavior of liquid films under external flow is crucial for various industrial processes.
• The transition from a stable film to bubble formation involves complex fluid dynamics and instabilities.

Purpose of the Study:

• To experimentally and theoretically investigate the deformation of suspended liquid films by external flow.
• To identify stable equilibrium shapes and the conditions leading to bubble formation.
• To develop a model that captures the nonlinear deformations and forces involved.

Main Methods:

• Experimental observation of liquid film deformation under controlled flow conditions.
• Development of a mathematical model to simulate the film's behavior and forces.
• Analysis of the model's solution diagram to identify bifurcations and stability limits.

Main Results:

• A family of non-minimal but stable equilibrium shapes for the liquid film was identified.
• A critical flow speed was determined, beyond which the film undergoes unstable inflation.
• The model accurately reproduced the observed nonlinear deformations and forces.

Conclusions:

• Bubble formation is linked to a loss of equilibrium at high flow speeds.
• At lower speeds, bubble formation results from the loss of stability in overly inflated shapes.
• The study reveals a saddle-node or fold bifurcation governing the transition to bubble formation.