Effect of viscoelasticity on the collective behavior of swimming microorganisms

Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. Using a mean-field theory and the Oldroyd-B constitutive equation, we show how linear viscoelasticity of the suspending fluid alters the hydrodynamic interactions and therefore the ability of the group to coordinate. We quantify the ability to coordinate by the initial growth rate of a small disturbance from the uniform isotropic state. For small wave numbers the response is qualitatively similar to a Newtonian fluid but the Deborah number affects an effective viscosity of the suspension. At higher wave number, the response of the fluid to small amplitude oscillatory shear flow, leads to a maximal growth rate at a particular wavelength unlike the Newtonian result.