The Oseen resistance of a particle of arbitrary shape

Let D0 be the Stokes drag on an arbitrary body moving parallel to a principal axis of resistance, with velocity U, through an unbounded fluid. The Oseen drag, D, experienced by this same body moving with equal velocity and identical orientation through the unbounded fluid is then given by the expression D/D₀ = 1 + D₀/16 π μ c U R + O(R²) where c is any characteristic particle dimension and R = cU ρ|μ is the particle Reynolds number. An analogous expression is given for the case where the motion is not parallel axis. Finally, an expression is given for the Oseen resistance of an arbitrary falling parallel to a principal axis of resistance along the axis of a cylindrical tube of finite radius.