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# Stokes number

The Stokes number, named after Irish mathematician George Gabriel Stokes, is a dimensionless number corresponding to the behavior of particles suspended in a fluid flow. Stokes number is defined as the ratio of the stopping distance of a particle to a characteristic dimension of the obstacle, or

$Stk = \frac{\tau\,U_o}{d_c}$

where τ is the relaxation time of the particle, Uo is the fluid velocity of the flow well away from the obstacle and dc is the characteristic dimension of the obstacle. For $Stk\gg 1$, particles will continue in a straight line as the fluid turns around the obstacle therefore impacting on the obstacle. For $Stk\ll1$, particles will follow the fluid streamlines closely.