Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment

Area of Science:

• Surface science and nanotechnology
• Materials science and engineering
• Colloid and interface science

Background:

• Capillary forces arise from liquid bridge formation due to vapor condensation, commonly causing powder caking and flow issues.
• Accurate prediction and control of capillary forces are essential for mitigating undesirable effects in granular materials.
• Existing models for capillary forces in sphere/plate geometry often rely on total energy or differential pressure calculations.

Purpose of the Study:

• To derive new equations for calculating capillary forces between two spheres.
• To validate the derived sphere-sphere capillary force equations through experimental measurements.
• To analyze the limitations of the Derjaguin approximation in transforming sphere/plate to sphere-sphere interactions.

Main Methods:

• Calculation of capillary force as a function of separation distance for a fixed liquid bridge volume in sphere/plate geometry.
• Derivation of equations for capillary force between two spheres based on sphere/plate geometry formulas.
• Experimental validation of derived formulas using atomic force microscopy (AFM).

Main Results:

• Theoretical formulas for capillary force between two spheres were successfully derived.
• Atomic force microscopy experiments confirmed the accuracy of the developed formulas.
• The Derjaguin approximation was found to be valid only at zero separation distance for sphere-sphere interactions.

Conclusions:

• The study provides a more accurate method for calculating capillary forces between two spheres.
• The limitations of the Derjaguin approximation at larger separation distances are explained by the changing liquid bridge area.
• The findings are crucial for controlling powder flow, preventing caking, and designing micro/nanoscale devices.