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A basal body is the centriole-derived structure at the base of a cilium or a eukaryotic flagellum. It anchors and organizes the microtubules of the projecting structure. A typical basal body contains nine peripheral microtubule triplets; farther along the cilium, the corresponding outer elements usually continue as doublets. The central pair found in many motile cilia is not a pair of central microtubules running through the basal body.^[ref]

In a cell bearing a primary cilium, a mature centriole can dock at the cell membrane and act as its basal body. The same underlying organelle therefore has different roles depending on its position and associated structures: a centriole within a centrosome helps organize an intracellular microtubule system, whereas a basal body organizes a projection from the surface. The ninefold arrangement is connected to assembly of SAS-6 into a central cartwheel scaffold.^[ref]

Biological fluid dynamics studies fluid flows generated by and acting on organisms, biological cells, tissues and biological transport networks. Examples include blood flow through microcirculation, cytoplasmic streaming within a biological cell, flagellum propulsion and bioconvection in swimming suspensions.

The Reynolds number $\mathrm{Re}=\rho UL/\mu$ compares inertia with viscous forces, using density $\rho$, dynamic viscosity $\mu$, speed $U$ and length $L$. A microscopic swimmer can operate in Stokes flow, where viscous forces dominate and motion responds to the instantaneous force balance. Larger swimming animals can instead transfer appreciable momentum to the surrounding fluid, as modeled by Lighthill elongated-body theory. ^[ref]

Transport introduces another comparison: the Péclet number $\mathrm{Pe}=UL/D$ measures advection against diffusion with diffusion coefficient $D$. Thus the same flow can move slowly enough to have negligible inertia, yet carry a slowly diffusing substance effectively. Choosing the appropriate dimensionless quantities connects biological scale to the governing mechanical and transport models.

An appendage used for movement or other functions. Bacterial flagella are driven by a bacterial flagellar motor; their construction differs from eukaryotic motile cilia.

A bacterial filament rotates as part of a motor-driven propeller, whereas a typical eukaryotic flagellum bends through microtubule-associated motor activity. The shared functional name therefore does not imply identical architecture or a single evolutionary origin for every appendage called a flagellum. ^[ref]

K. E. Summers is the first author, with I. R. Gibbons, of a 1971 experiment demonstrating ATP-induced sliding within treated axonemes. Brief trypsin digestion left the recognizable nine-doublet arrangement but changed the response to added ATP: outer microtubule groups separated by active relative movement.^[ref]

Observing the time course mattered. A final disassembled specimen alone could suggest passive damage, whereas the moving structures revealed a coordinated process. The nucleotide and ion requirements also resembled those of flagellum movement, linking the altered preparation to the operation of the original mechanical system.^[ref]

Resistive-force theory approximates the local viscous force on a moving slender elastic filament by separate drag coefficients along and across its tangent. Let $\mathbf{t}$ be the unit tangent and $\mathbf{v}$ the material velocity relative to the ambient fluid. The force per unit length on the elastic filament isThe positive parallel and perpendicular drag coefficients of a slender filament are defined per unit length; for a sufficiently slender isolated body, their leading logarithmic ratio is ${\xi }_{\perp }/{\xi }_{\parallel }\simeq 2$.

The directional difference can generate propulsion. For example, take a straight element with $\mathbf{t}=(\cos \theta ,\sin \theta )$ and impose transverse velocity $\mathbf{v}=V{\mathbf{e}}_y$. Direct substitution givesA transverse motion of a tilted element therefore has an axial force component. In a propagating flagellum deformation, the correlation of tilt and transverse velocity can produce nonzero mean thrust. For a freely swimming body, the unknown translation and rotation follow by imposing zero total external force and torque, including the resistance of the head if present.

This is a local Stokes flow approximation. It neglects the nonlocal hydrodynamic interactions retained by slender-body theory, so nearby boundary conditions, tightly spaced elastic filaments and detailed end effects can require a more complete model.