Diffusion of passive particles in active suspensions

We study how an active suspension consisting of a definite volume fraction of the microswimmer \textit{Chlamydomonas Reinhardtii} modifies the Brownian movement of small to medium size microspheres. We present measurements and simulations of trajectories of microspheres with a diameter of 20 $\mu$m in suspensions of \textit{Chlamydomonas Reinhardtii}, a so called ``puller,'' and show that the mean squared displacement of such trajectories consist of parabolic and a linear part. The linear part is due to the hydrodynamic noise of the microswimmers while the parabolic part is a consequence of directed motion events that occur randomly, when a microsphere is transported by a microswimmer on a timescale that is in higher order of magnitude than the Brownian like hydrodynamic interaction. In addition, we theoretically describe this effect with a dimensional analysis that takes the force dipole model used to describe ``puller'' like \textit{Chlamydomonas Reinhardtii} into account.