Low Reynolds number flow

Fluid motion in which viscous forces dominate inertia. It is typically smooth, and reversing the driving forces reverses the motion without changing its path.

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Reynolds number: A dimensionless ratio comparing inertial forces with viscous forces in a fluid flow. Its small value identifies when viscous effects dominate the motion.
Viscosity: A fluid property that measures resistance to deformation and internal flow. Large viscous influence is the defining physical feature of this regime.
Purcell's three-link swimmer: A theoretical swimmer made of three linked rods that moves through cyclic changes in joint angles. Its nonreciprocal shape cycle demonstrates how to swim despite time-reversible fluid mechanics.
Turbulence: Irregular fluid motion characterized by fluctuating velocities and interacting vortices across scales. It contrasts with the typically smooth, inertia-dominated behavior absent at very low Reynolds numbers.
Stokes equations: The equations describing incompressible flow when inertial terms are negligible compared with viscous terms. They govern fluid motion in the low-Reynolds-number limit.
Navier–Stokes equations: The equations governing the motion of viscous fluids through conservation of momentum and mass. Low-Reynolds-number flow emerges when their inertial terms become negligible.
Scallop theorem: A result showing that a swimmer with one reciprocal degree of freedom cannot move in a Stokes fluid by a reciprocal stroke. It sets a fundamental constraint on propulsion in this flow regime.
Inertial flow: Fluid motion in which momentum effects are significant relative to viscous stresses. It is the opposing regime where inertia cannot be neglected.
Stokes flow: A flow regime in which viscous forces dominate inertia and the Stokes equations apply. It is the standard mathematical description of this regime.
Incompressible flow: Fluid motion in which density changes are negligible, so velocity has zero divergence. Many canonical low-Reynolds-number models assume incompressibility.