Fluid Dynamics of Squirmers and Ciliated Microorganisms

The fluid dynamics of microswimmers has received attention from the fields of microbiology, microrobotics, and active matter. Microorganisms have evolved organelles termed cilia for propulsion through liquids. Each cilium periodically performs effective and recovery strokes, creating a metachronal wave as a whole and developing a propulsive force. One well-established mathematical model of ciliary swimming is the squirmer model, which focuses on surface squirming velocities. This model is also useful when studying active colloids and droplets. The squirmer model has been recently used to investigate the behaviors of microswimmers in complex environments, their collective dynamics, and the characteristics of active fluids. Efforts have also been made to broaden the range of applications beyond the assortment permitted by the squirmer model, which was established to specifically represent ciliary flow and incorporate biological features. The stress swimmer model imposes stresses above the cell body surface that enforce the no-slip condition. The ciliated swimmer model precisely reproduces the behaviors of each cilium that engages in mutual hydrodynamic interactions. Mathematical models have improved our understanding of various microbial phenomena, including cell-cell and cell-wall interactions and energetics. Here, I review recent advances in the hydrodynamics of ciliary swimming and then discuss future challenges.