Hydrodynamic correlations in three-particle colloidal systems in harmonic traps

We report on the hydrodynamic correlations between colloids immersed in a low Reynolds number fluid. We consider colloidal arrays composed of three particles; each colloid is trapped in a single harmonic potential and interacts with the other colloids only via hydrodynamic forces. We focus on the role of a third body in the two-body correlation functions. We give special attention to a collinear configuration of particles, although the salient features of an equilateral triangle configuration are outlined. The correlation functions are computed both by means of Brownian dynamics simulations, and by solving analytically and numerically the Langevin equation under the assumption of constant diffusion tensor; this approximation is validated through computer simulations. We explicitly show that the presence of a third body affects the auto-and cross-correlation functions and that their behaviour, in some specific conditions, can be different from that commonly seen in a two-particle system. In particular, we have found that the auto-correlation functions show a slower decay, while the cross-correlation ones exhibit a temporal shift and a weaker amplitude. Moreover, an unexpected behaviour related to a positive correlation and associated with the appearance of new dynamical modes is observed in the case of the collinear array of three particles. This interesting effect might be used to tune the degree of hydrodynamic correlation in few-body colloidal systems.