Effective medium model for a suspension of active swimmers

Abstract

Several active organisms in nature tend to reside as a community in a viscous fluid medium. We analyze the variation of swimming characteristics of an active swimmer present in a dilute and disperse suspension, modeled as an effective Brinkman medium. This idealized representation of a collection of active swimmers allows one to distinguish the impact of the interior domain available to an individual swimmer as well as the contribution of its neighbors. Darcy's law along with the analytical solution enables the effective resistivity to be predicted as a function of the volume fraction which is in close agreement with the well-known Carman-Kozeny equation. This facilitates the successive analysis of the propulsion speed, power dissipation, and swimming efficiency of the targeted swimmer as a function of the volume fraction which is decisive in nutrient transport and uptake or reproduction in a collective environment. A stress-jump condition is also imposed across a cell to indicate a mean effective force due to the nearby swimmers. At suitable values of this stress-jump coefficient, the relative increase of the migration velocity and swimming efficiency is noticeably higher at an optimum occupancy.