Surfing on metachronal waves: ciliary transport by inertial coasting

TL;DR

This paper investigates how inertia influences ciliary fluid transport by introducing Pufflets, inertial flow models, and demonstrates that particles can efficiently surf on metachronal waves due to inertial effects, unlike in purely viscous flows.

Contribution

It introduces Pufflets as a new model for inertial ciliary flows and shows how inertial effects enable net particle transport and surfing on metachronal waves, advancing understanding of rapid flow dynamics.

Findings

Pufflets accurately model inertial flows generated by rapid impulses.

Pairs of Pufflets can break time reversal symmetry to induce net particle displacement.

Particles can surf on metachronal waves due to inertial coasting, enhancing transport efficiency.

Abstract

Motile cilia drive biological fluid transport through whip-like beating motions that synchronize into metachronal waves. The lengths of these cilia span three orders of magnitude, from microns in human airways to millimeters in ctenophores. While recent studies have considered ciliary flows at intermediate Reynolds numbers, the effect of inertia on coordinated particle transport remains unexplored. Here, we address this gap using "Pufflets," the inertial counterparts of Stokeslets. These Pufflets describe rapidly accelerating flows generated by short-lived impulses, encoded by spatiotemporally singular momentum injections. To produce such rapid impulses experimentally, we designed an Atwood machine that generates long-lived Pufflet flows, which we capture with high-speed PIV measurements that agree well with analytical theory and simulations. Moreover, we find that pairs of equal and opposite Pufflets can drive net particle displacements and mixing due to time reversal symmetry breaking, which would be impossible in Stokes flow. Finally, we consider metachronal waves of Pufflets. Remarkably, we discover that particles can surf on these waves by coasting inertially from one cilium to the next, leading to highly efficient particle transport. This work paves the way toward understanding rapidly accelerating flows and collective transport driven by biological and artificial cilia.