Curvature driven motion of a bubble in a toroidal Hele-Shaw cell

Area of Science:

• Physics
• Materials Science
• Fluid Dynamics

Background:

• Understanding the behavior of interfaces and bubbles is crucial in various scientific and industrial applications.
• The influence of confinement geometry on interfacial energy is a key factor in phenomena like foam stability and microfluidics.

Purpose of the Study:

• To investigate the equilibrium properties of a single area-minimizing bubble confined between two parallel curved plates.
• To develop a model predicting how the bubble's surface energy is affected by the curvature of the confining plates.

Main Methods:

• Development of a theoretical model for bubble confinement between curved plates.
• Comparison of model predictions with numerical simulations using Surface Evolver.
• Analysis of bubble behavior in spherical and toroidal confinement geometries.

Main Results:

• Bubble surface energy is lower between spherical plates compared to flat plates.
• The bubble's energy is inversely related to the local Gaussian curvature of the plates: higher energy for negative curvature, lower for positive.
• Curvature acts as a geometric potential, driving bubbles from negative to positive curvature regions.

Conclusions:

• The curvature of confining plates significantly impacts the equilibrium properties and energy of trapped bubbles.
• The derived model provides a predictive tool for bubble behavior in curved geometries.
• Geometric potential arising from curvature can direct bubble migration.