Hydrodynamics of Confined Swimming: Persistence of Stokes Flow and Emergence of Boundary Layers.

Confinement significantly alters the hydrodynamics of swimming, yet its impact across different flow regimes remains incompletely understood. In this study, we explore how confinement influences swimming behavior, focusing primarily on the Stokes and laminar regimes. Using a minimal force model, we examine the local fluid velocity gradients to characterize the formation and thickness of the boundary layer (δ) around the swimmer. Strikingly, we find that under strong confinement, the Stokes regime persists well beyond the classical Reynolds number threshold of unity, extending into higher-Re values without the emergence of inertial effects. In this regime, δ scales linearly with the fluid gap between the swimmer and the confining walls. However, beyond a critical confinement threshold, we observe the emergence of a confinement-independent boundary layer, signaling the onset of an inertial laminar regime. While fundamentally oriented, this work lays the foundation for understanding aquatic locomotion in restricted environments, with implications ranging from natural microhabitats to the design of micro-robots navigating the human body.