Hydrodynamic coupling of two rotating spheres trapped in harmonic potentials.

Area of Science:

• Colloid and Interface Science
• Soft Matter Physics
• Hydrodynamics

Background:

• Colloidal spheres are fundamental in soft matter.
• Understanding hydrodynamic interactions is crucial for predicting colloidal behavior.
• Existing models like Rotne-Prager approximation neglect higher-order coupling effects.

Purpose of the Study:

• To theoretically investigate the hydrodynamic coupling of two harmonically trapped colloidal spheres.
• To analyze the interplay between translational and rotational motion.
• To derive and characterize collective eigenmodes and correlation functions.

Main Methods:

• Low Reynolds number hydrodynamics.
• Symmetry arguments for determining eigenmode properties.
• Derivation of autocorrelation and cross-correlation functions.

Main Results:

• A rich spectrum of collective eigenmodes arising from rotational and translational coupling.
• Complete set of autocorrelation and cross-correlation functions derived.
• Observation of a unique self-coupling between translation and rotation mediated by a neighbor particle.

Conclusions:

• The study highlights the significance of rotational motion in colloidal hydrodynamics.
• A novel higher-order coupling effect, not present in standard approximations, has been identified.
• Results provide a more comprehensive understanding of interacting colloidal systems.