Surfing on metachronal waves: ciliary transport by inertial coasting

Cilia are vital for many life forms, from the swimming of microorganisms to the flows that facilitate healthy human brain and lung function. Previous studies largely assume unsteady effects are negligible, despite the presence of transient unsteady effects caused by beating cilia. Using analytical theory, numerical simulations, and model experiments with a tunable transient Reynolds number, we study the flows from unsteady hydrodynamic singularities, which we call "pufflets," as a model system for inertial ciliary beating. Here, we discover "inertial coasting," where particles are transported from one cilium to the next by surfing on waves of these pufflets. Moreover, we find that incorporating unsteady effects breaks time reversibility, leading to net transport and mixing, even in spatially symmetric systems. This work helps to pave the way toward understanding ciliary flows across scales.