Stokes Flow & Viscosity

Creeping flow (Re≪1) around a sphere — exact Stokes solution. Visualize streamlines, velocity fields, and the drag force. Watch tracers advect in the flow field.

Viscosity η (mPa·s) 10.0

Sphere Radius R 40

Flow Speed U 1.00

Density ρ (kg/m³) 1000

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Reynolds Re

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Drag F_D (arb)

24.0

C_D = 24/Re

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Terminal v (cm/s)

Stokes drag law: F_D = 6πηRU (valid for Re = ρUR/η ≪ 1)
Velocity field (exact):
u_r = U·cos θ·(1 − 3R/(2r) + R³/(2r³))
u_θ = −U·sin θ·(1 − 3R/(4r) − R³/(4r³))

Terminal velocity (Stokes settling): v_t = 2R²(ρ_p−ρ_f)g/(9η)
Applications: sedimentation, aerosol particles, microfluidics, swimming microbes (Re ~ 10⁻⁴).