Rotation due to hydrodynamic interactions between two spheres in contact

Area of Science:

• Fluid dynamics
• Particle mechanics
• Tribology

Background:

• Understanding particle interactions in fluids is crucial for various applications.
• Low Reynolds number flows simplify fluid-structure interactions.
• Contact mechanics govern particle-particle interactions.

Purpose of the Study:

• To analyze the rotational and translational motion of two close spheres in a fluid.
• To investigate the conditions leading to mechanical contact between sphere surfaces.
• To develop and validate a model for sphere motion incorporating contact interactions.

Main Methods:

• A theoretical model was developed, incorporating gravitational, hydrodynamic, and contact forces.
• Coulomb's law was used to predict transitions between rolling and slipping.
• Experimental measurements of angular and translational velocities were performed using video imaging and interferometry.
• A systematic fitting procedure was employed to match the model to experimental data.

Main Results:

• The model predicts a transition from pure rolling to rolling with slip based on the ratio of mechanical friction to load.
• The dependence of velocities on kinetic friction and surface separation was analyzed.
• Experimental data from millimeter-sized beads in viscous oil were collected and analyzed.
• Model parameters were successfully determined by fitting to experimental measurements.

Conclusions:

• The developed model accurately describes the motion of two close spheres in a fluid, including contact phenomena.
• Friction and surface separation are key factors determining the motion dynamics and contact behavior.
• The study provides a validated framework for analyzing particle-particle interactions in low Reynolds number flows.