Longterm Influence of Inertia on the Diffusion of a Brownian Particle
  We demonstrate experimentally that a Brownian particle is subject to inertial effects at long time scales. By using a blinking optical tweezers, we extend the range of previous experiments by several orders of magnitude up to a few seconds. The measured mean square displacement of a freely diffusing Brownian particle in a liquid shows a deviation from the Einstein-Smoluchowsky theory that diverges with time. These results are consistent with a generalized theory that takes into account not only the particle inertia but also the inertia of the fluid surrounding the particle. This can lead to a bias in the estimation of the diffusion coefficient from finite-time measurements. We show that the decay of the relative error is polynomial and not exponential and, therefore, can have significant effects at time scales relevant for experiments. 
Giuseppe Pesce and Giorgio Volpe and Giovanni Volpe and Antonio Sasso
cond-mat.stat-mech cond-mat.soft