Stokes number
The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle (or droplet) to a characteristic time of the flow or of an obstacle, or S t k = t 0 u 0 l 0 {\displaystyle \mathrm {Stk} ={\frac {t_{0}\,u_{0}}{l_{0}}}} where t 0 {\displaystyle t_{0}} is the relaxation time of the particle (the time constant in the exponential decay of the particle velocity due to drag), u 0 {\displaystyle u_{0}} is the fluid velocity of the flow well away from the obstacle, and l 0 {\displaystyle l_{0}} is the characteristic dimension of the obstacle (typically its diameter) or a characteristic length scale in the flow (like boundary layer thickness).