Particle Settling Velocity (Stokes)
Particle Settling Velocity (Stokes)
Fine particles settle at a terminal velocity where gravity, buoyancy and Stokes drag balance — the basis of clarifiers and sedimentation.
The settling velocity is v = (ρ_p − ρ_f)·g·d²/(18·μ). where ρ_p, ρ_f are the particle and fluid densities, d the particle diameter and μ the viscosity.
Inputs
rho_p := 2650 kg/m^3=2650 kg/m^3
rho_f := 1000 kg/m^3=1000 kg/m^3
g := 9.81 m/s^2=9.81 m/s^2
d := 0.0001 m=0.1 mm
mu := 0.001 Pa·s=1e-03 kg/m/s
Apply the Stokes settling-velocity formula.
v := (rho_p - rho_f)·g·d^2/(18·mu)=8.99e-03 m/s
Results
Settling velocity scales with the square of particle size, so coarse particles settle fast and fines stay suspended — the principle behind sizing sedimentation basins.
Assumptions & limitations
- Stokes regime (Reynolds < 1).
- Spherical particles.
- Dilute suspension.