Effective medium model for a suspension of active swimmers

Abstract

Several active organisms in nature tend to reside as a community in viscous fluid media. We analyze the variation of the 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 an analytical solution enable 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—which are decisive in nutrient transport and uptake or reproduction in a collective environment—as a function of the volume fraction. A stress-jump condition is also imposed across a cell to indicate the mean effective force due to nearby swimmers. For suitable values of this stress-jump coefficient, the relative increase in migration velocity and swimming efficiency is noticeably higher at an optimum occupancy. To highlight the rheological characteristics, we have analyzed the effective viscosity of the active suspension, which varies distinctively from a random suspension and alludes to self-assembly.