How passive cilia modulate tumbling of microorganisms

Many bacteria and millimeter-sized agents exhibit stochastic reorientation stages in their locomotion pattern, such as the run- and-tumble motion. This typically takes place by deployment of cilia or flagella, which in turn exert a resistive torque. It is questionable whether this feature allows free-living ciliates to modulate their tumbling motion and thus affect their reorientation in complex hydrodynamic environments. This requires the solution of a fluid-structure interaction problem at the steady Stokes regimes.

In this connection, we propose a simple two-way coupled model to describe the kinematics of a ciliated spherical microorganism subjected to a shear flow. Each cilium is modelled as a rigid slender rod connected to the body surface by a bi-cylindrical hinge, such that the kinematics of each cilium is resolved in terms of the Euler angles. The hydrodynamic torque exerted on the cilia is computed by integrating the Johnson’s slender body formulation endowed with the suited image system. This model provides meaningful insights about the effect of the ciliary torque on the kinematics of microorganisms.