Stokes & Oseen Creeping Flow

Viscous flow past a sphere — streamlines, drag, and the Oseen correction
Reynolds number Re0.50
Sphere radius40
Flow speed U1.5
Streamlines10
Stokes flow (Re≪1): inertia neglected, drag F = 6πμaU. Streamlines are fore-aft symmetric.
Oseen correction accounts for weak inertia: F = 6πμaU(1 + 3Re/8). Breaks symmetry — wake develops downstream.
The stream function ψ = U·sin²θ·(r²/2 − 3ar/4 + a³/4r) gives the Stokes solution; Oseen adds a logarithmic correction term proportional to Re.
Drag coefficient: C_D = 24/Re (Stokes)C_D = 24/Re·(1+3Re/16) (Oseen)