Hydrodynamics of squirmers: A review on Stokesian principles, analytical frameworks, and recent advances

Squirmer hydrodynamics forms the basis for analyzing self-propulsion in viscous environments, bridging biological and artificial microswimmers through a unified representation that relies on surface slip velocities and their induced flow fields. This review outlines detailed aspects of squirmer modeling and dynamics, highlighting the role of swimming modes and their influence on propulsion efficiency and flow topology. Analytical tools central to microhydrodynamics, such as Faxén's laws, multipole expansions, the Lorentz reciprocal theorem, the zero-force and zero-torque criteria, Stokesian dynamics, and the formulation of mobility matrices, are systematically reviewed for their application in studying swimmer–fluid interactions. The review also examines the role of confinement, addressing motion within complex geometrical environments and near solid boundaries, where hydrodynamic interactions significantly alter trajectories, stability, and collective behavior. Particular attention is given to the modification of squirmer locomotion and reorientation dynamics in proximity to walls, along with near-field lubrication effects. The review also presents recent advancements in the field, encompassing topics such as collective dynamics and pairwise swimmer interactions under various boundary and flow conditions. Overall, the analysis provides a comprehensive microhydrodynamical perspective, integrating classical theory with modern computational approaches, thereby offering a unified framework for understanding and predicting the behavior of microswimmers in complex fluidic environments.