Point torque representations of ciliary flows

TL;DR

This paper introduces a point torque (rotlet) model to efficiently and accurately simulate ciliary flows near walls, extending it to confined spaces and analyzing the effects of confinement on flow fields.

Contribution

The study develops a simplified rotlet-based model for ciliary flows, extending it to bounded domains and comparing flow effects with single-wall scenarios.

Findings

Rotlet model offers high accuracy and efficiency for ciliary flow simulation.

Flow fields are minimally affected by confinement when walls are spaced at cilium length.

Flow near a single wall is similar to that in confined spaces for ciliary flows.

Abstract

Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque -- or `rotlet' -- model to capture the time-averaged ciliary flow above a planar rigid wall. We demonstrate the advantages (i.e. accuracy and computational efficiency) of using this, arguably simpler approach compared to other singularity-based models in Stokes flows. Then, in order to model ciliary flows in confined spaces, we extend the point torque solution to a bounded domain between two plane parallel no-slip walls. The flow field is resolved using the method of images and Fourier transforms, and we analyze the role of confinement by comparing the resultant fluid velocity to that of a rotlet near a single wall. Our results suggest that the flow field of a single cilium is not changed significantly by the confinement, even when the distance between the walls is commensurate with the cilium's length.