Critical Eotvos numbers for buoyancy-induced oil drop detachment based on shape analysis

Area of Science:

• Colloid and Surface Science
• Fluid Dynamics
• Interfacial Phenomena

Background:

• Understanding oil drop detachment from solid substrates in aqueous phases is crucial for various industrial processes.
• Existing models for capillary retention force show significant differences, necessitating a refined approach.
• The Eotvos number (half the Bond number) is a key dimensionless parameter governing buoyancy-induced drop detachment.

Purpose of the Study:

• To estimate critical Eotvos numbers for oil drop detachment using two distinct capillary retention force equations.
• To numerically solve the differential equation for drop shape, considering volume and contact line constraints.
• To compare numerical predictions with experimental observations and validate the models.

Main Methods:

• Utilized force balance equations from literature for capillary retention force.
• Numerically solved the differential equation governing drop shape with pinned or receding contact line constraints.
• Estimated critical Eotvos numbers for initial contact angles ranging from 20 to 90 degrees.

Main Results:

• Numerical solutions predicted equilibrium drop shapes matching experimental observations.
• Identified limits for interfacial tension and critical Eotvos numbers beyond which drop volume constraints cannot be met.
• Critical Eotvos numbers from shape analysis fall between values from the two force-balance equations.

Conclusions:

• A combination of the two capillary retention force equations is necessary for accurate detachment predictions.
• One force equation dominates at high contact angles, while the other is applicable at low contact angles.
• The study provides a more comprehensive understanding of drop detachment mechanisms influenced by interfacial forces and geometry.