Capillary force acting on a colloidal particle floating on a deformed interface

Area of Science:

• Colloid and Interface Science
• Soft Matter Physics
• Fluid Dynamics

Background:

• Capillary forces govern the behavior of colloids at liquid interfaces.
• Previous studies have analyzed these forces, but often neglect gravity or use approximations.
• Understanding these forces is crucial for applications in materials science and nanotechnology.

Purpose of the Study:

• To analytically determine the lateral capillary force on a spherical colloid at an arbitrarily shaped liquid interface.
• To generalize previous theoretical frameworks by incorporating the effects of gravity.
• To provide a more accurate model for capillary forces, especially for smaller colloids relative to the capillary length.

Main Methods:

• Analytical calculations considering surface tension, pressure, and gravity.
• Relating the force to the pre-deposition shape of the liquid interface.
• Generalizing a prior theoretical approach to include gravitational effects.
• Validation through exact nonlinear numerical calculations.

Main Results:

• Developed a theoretical framework for lateral capillary forces on spherical colloids at interfaces.
• Incorporated surface tension, pressure, and gravity into the force calculations.
• The results align with the Nicolson superposition approximation and Würger's curvature-dependent force.
• Extended existing models by including higher-order terms related to colloid size and capillary length.

Conclusions:

• The analytical model provides a comprehensive description of lateral capillary forces.
• The inclusion of gravity and higher-order terms enhances prediction accuracy.
• The findings are validated by numerical simulations, confirming the theoretical expressions.