Transport and mixing by metachronal waves in nonreciprocal soft robotic pneumatic artificial cilia at low Reynolds numbers

Cilia are widely employed by living systems to manipulate fluid flow in various functions, such as feeding, pumping, and locomotion. Mimicking the intricate ciliary asymmetry in combination with collective metachronal beating may find wide application in fluid transport and mixing in microfluidic systems. Here, we numerically analyze the metachronal beating of pneumatic artificial cilia. We specifically address three aspects of ciliary motion: (i) pumping in the backflow region, (ii) mixing in the cilia region, and (iii) the transport-mixing transition region. Our results show that antiplectic metachrony leads to the highest mixing efficiency and transport rate in two distinct regions, i.e., below and above the ciliary surface, respectively. We find that the ciliary motion strongly enhances the diffusivity when advection is dominant at high Peclet numbers, with a factor 3 for symplectic metachrony and a factor 4 for antiplectic metachrony and synchronous beating. In addition, we find an increase with a factor 1.5 for antiplectic metachrony and a decrease with a factor 2.5 for symplectic metachrony compared with synchronous beating for fluid pumping. To investigate the higher transport rate compared to symplectic metachrony, we develop a simple two-cilia model and demonstrate that the shielding of flow between neighboring cilia is the main reason for the higher antiplectic transport rate.