Detachment force of particles from fluid droplets.

Area of Science:

• Soft matter physics
• Interfacial phenomena
• Fluid dynamics

Background:

• Understanding droplet deformation is crucial in various scientific fields.
• Particle interactions at fluid interfaces influence droplet behavior.
• Existing models for de Gennes-Hooke constant have limitations for realistic particle sizes.

Purpose of the Study:

• To calculate the deformation of a spherical droplet under opposing forces applied to embedded particles.
• To derive accurate force-distance curves and analyze the de Gennes-Hooke constant for realistic particle-to-droplet size ratios.
• To investigate energy dissipation and the influence of line tension during particle detachment.

Main Methods:

• Free-energy analysis to determine force-distance relationships.
• Calculation of the de Gennes-Hooke constant, incorporating corrections for realistic particle sizes.
• Investigation of energy dissipation and deviation from linear force-displacement behavior near detachment.
• Analysis of the impact of line tension on detachment forces and contact angle.

Main Results:

• Derived a new expression for the restoring force constant: 2πγ[0.5 - ln(ν/2)](-1), showing excellent agreement with numerical analysis.
• Identified significant O(1) constant terms that correct previously reported logarithmic dependencies for realistic particle-to-droplet size ratios (ν = 0.001 to 0.01).
• Observed that dissipated energy becomes a dominant factor in work done during detachment as particle size decreases, indicating a higher energy barrier.
• Demonstrated that line tension alters the contact angle with particle displacement, deviating from a constant value.

Conclusions:

• The study provides a more accurate model for droplet deformation and particle detachment forces, especially for experimentally relevant particle sizes.
• The findings highlight the importance of considering higher-order corrections and dissipated energy for small particles, impacting understanding of desorption energy barriers.
• The influence of line tension on interfacial mechanics, specifically contact angle dynamics, is quantified, offering new insights into wetting phenomena.