Stokes Paradox & Oseen Correction

Low Reynolds number flow — creeping flow, Stokes solution, Oseen's far-field correction

Stokes Flow Streamlines (Re→0)

Oseen Correction Streamlines

Drag Coefficient vs Re

Stokes Paradox & Theory

Stokes (1851): ∇²ψ² = 0
Stream fn: ψ=U sin(θ)(r − R²/r) [uniform]
Drag: F_D = 6πμRU (Stokes drag, sphere)
Stokes PARADOX (2D cylinder):
No solution at Re=0 in 2D (Whitehead 1889)
Need Oseen correction: Re·(u·∇u) ≠ 0
F_D ≈ 4πμU/[ln(2/Re)−γ] (Oseen-Lamb)
C_D ≈ 24/Re (sphere, Stokes limit)
Reynolds number
Stokes C_D
Oseen C_D
Far-field behavior