Modelling ciliary flows in confined geometries*

Ciliary flows are typically studied in-vitro using microfluidics. Existing theoretical studies capture the flow generated by collective ciliary motion (including Ramirez-San Juan et al. 2020), but fail to resolve the flow generated by individual cilia, which play a crucial role in mixing and nutrient exchange. We propose a new model based on a point torque (i.e., a rotlet) to capture such flows between two parallel plates. The flow field correction due to the bounded domain is resolved using the method of images and Fourier transforms. We observe that a rotlet captures both near- and far-field features of the flow field generated by the individual cilia as opposed to a point force (i.e., stokeslet). The flow generated by an array of cilia is modelled using a superposition of point torques, a framework which enables us to quantify the effects of hydrodynamics confinement, and is employed to study micromixing and nutrient exchange at the ciliary surface.

[1] G. R. Ramirez-San Juan et al., Nature Physics 16(9), 958-964 (2020).