Hydrodynamic coupling of two rotating spheres trapped in harmonic potentials

TL;DR

This paper provides a detailed theoretical analysis of the hydrodynamic coupling between two rotating colloidal spheres in harmonic traps, revealing complex eigenmodes and the significance of rotational-translation coupling beyond common approximations.

Contribution

It introduces a comprehensive theoretical framework including rotational motion, deriving correlation functions and highlighting higher-order coupling effects not captured by standard models.

Findings

Identification of collective eigenmodes based on symmetry

Derivation of auto- and cross-correlation functions including rotation

Discovery of self-coupling of translation and rotation mediated by neighboring particles

Abstract

We theoretically study in detail the hydrodynamic coupling of two equal-sized colloidal spheres at low Reynolds numbers assuming the particles to be harmonically trapped with respect to both their positions and orientations. By taking into account the rotational motion, we obtain a rich spectrum of collective eigen modes whose properties we determine on the basis of pure symmetry arguments. Extending recent investigations on translational correlations [J.-C. Meiners and S. R. Quake, Phys. Rev. Lett. 82, 2211 (1999)], we derive the complete set of auto- and cross-correlation functions emphasizing the coupling of rotation to translation which we illustrate in a few examples. An important feature of our system is the self-coupling of translation and rotation of one particle mediated by the neighboring particle that is clearly visible in the appropriate auto-correlation function. This coupling is a higher-order effect and therefore not included in the widely used Rotne-Prager approximation for the hydrodynamic mobilities.