 Parallel and perpendicular drag coefficients of a slender filament

The local resistive-force theory coefficients ${\xi }_{\parallel }$ and ${\xi }_{\perp }$ describe drag along and across a filament tangent. For very slender bodies their leading logarithmic values have ratio ${\xi }_{\perp }/{\xi }_{\parallel }\simeq 2$. Geometry, ends and nonlocal fluid interactions affect the corrections. Anisotropy enables propulsion by rotating helices.