Dynamics of a microorganism in a sheared viscoelastic liquid

In this paper, we investigate the dynamics of a model spherical microorganism, called squirmer, suspended in a viscoelastic fluid undergoing unconfined shear flow. The effect of the interplay of shear flow, fluid viscoelasticity, and self-propulsion on the orientational dynamics is addressed. In the limit of weak viscoelasticity, quantified by the Deborah number, an analytical expression for the squirmer angular velocity is derived by means of the generalized reciprocity theorem. Direct finite element simulations are carried out to study the squirmer dynamics at larger Deborah numbers. Our results show that the orientational dynamics of active microorganisms in a sheared viscoelastic fluid greatly differs from that observed in Newtonian suspensions. Fluid viscoelasticity leads to a drift of the particle orientation vector towards the vorticity axis or the flow-gradient plane depending on the Deborah number, the relative weight between the self-propulsion velocity and the flow characteristic velocity, and the type of swimming. Generally, pullers and pushers show an opposite equilibrium orientation. The results reported in the present paper could be helpful in designing devices where separation of microorganisms, based on their self-propulsion mechanism, is obtained.