Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring

We use a continuous acquisition, high-speed camera with integrated centroid tracking to simultaneously measure the positions of a ring of micron-sized particles held in holographic optical tweezers. Hydrodynamic coupling between the particles gives a set of eigenmodes, each one independently relaxing with a characteristic decay rate (eigenvalue) that can be measured using our positional data. Despite the finite particle size, we find an excellent agreement between the measured eigenvalues and those numerically predicted by Oseen theory applied to the two-dimensional (2D) ring geometry. Particle motions are also analyzed in terms of the alternative eigenmode set obtained by wrapping onto the ring the eigenmodes of a 1D periodic chain. We identify the modes for which the periodic chain is a good approximation to the ring and those for which it is not.