Exploring mass transport above ciliary carpets using point torque representations

Flows generated by ciliary carpets have the capacity to transport particulate and dissolved matter, as well as active particles. We observed that the flow field of a beating cilium can be accurately modelled using a point torque (singularity) in a semi-infinite Stokes flow [1]. Here, we use a superposition of these singularities to characterise the collective flows generated by a vast array of cilia. We solve the advection-diffusion equation and the Langevin equation, respectively, to understand the transport of dissolved and particulate matter by such flows. We observed that the mass transport near the ciliary carpet is affected by heterogeneity in the ciliary arrangement, the strength of a background flow, and diffusivity of the solute/particles in the fluid.

[1] Selvan S A, Duck P W, Pihler-Puzović D, Brumley D R. Point torque representations of ciliary flows. Physical Review Fluids (2023). [In press]