Rotlet Modeling of Cilia: Exploring Mass Transport Dynamics

Cilia perform various functions, including sensing, locomotion, fluid flow and mass transport, all of which are important in evolutionary adaptations among organisms. We observed that the point torque (i.e., the rotlet model) accurately describes a single cilium's flow characteristics (both near- and far-field features) in a semi-infinite domain. By employing the finite-element method (FEM) and solving the advection-diffusion equation with a localized source, we investigate the mass transport induced by a single cilium represented as a point torque. Our findings reveal that the presence of the point torque enhances the flux of less diffusive particles through the domain to a larger extent as compared to highly diffusive particles. Moreover, increasing the torque magnitude, which is equivalent to augmenting the number of cilia, amplifies the flux of highly diffusive particles. To validate our approach, we employ the Langevin model governing Brownian tracers, and extend it to an array of cilia residing in confined geometries to understand mass transport.