Circular-Rower Model of Particle Transport by Cilia Arrays in Parallel-Wall Channels

Numerous models have been developed to investigate the mechanism of metachronal wave formation and cilia dynamics but much less is known about particle transport by cilia arrays. Our simplified circular-rower model of hydrodynamically coupled cilia is well-suited to investigate particle transport by metachronal waves. Cilia are represented by spherical beads (rowers) moving on prescribed trajectories that mimic the motion of cilia tips. The rowers are placed in a parallel-wall channel to model the particle and fluid transport in a thin fluid layer. We find that trajectories of transported particles exhibit kinks, loops, and long-time non-decaying oscillations. The loops occur above the trough or crest of metachronal waves, depending on the initial particle position, channel width, and length of the metachronal wave. However, in spite of the existence of closed fluid streamlines, no stagnation regions where particles would be trapped for a long time were found. We have determined the dependence of the particle transport rate on the system parameters and investigated the dynamics and stability of metachronal waves. Our results are relevant both for understanding particle transport by cilia arrays in vivo and development of artificial microfluidic cilia systems.