Diffusion of colloidal particles in swimming suspensions

Abstract

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.