Stokes number

A Stokes number (Stk or St) of a particle sitting in a fluid is a characterization of its tendency to flow with the fluid. It is the ratio of two characteristic times:

Stk = t0 u0 / l0

• Stk - Stokes number.
• t₀ - relaxation time of the particle (characterizing the rate at which the particle catches up to the flow).
• u₀ - fluid velocity.
• l₀ - diameter of the particle

(The latter two divide out to be the reciprocal of a time.) Particles with a low Stokes number tend to "stay with" the fluid flow, whereas with a higher stokes number take time to respond to the fluid motion, presumably more massive particles with more inertia.