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

where ${\displaystyle t_{0}}$ is the relaxation time of the particle (the time constant in the exponential decay of the particle velocity due to drag), ${\displaystyle u_{0}}$ is the fluid velocity of the flow well away from the obstacle and ${\displaystyle l_{0}}$ is the characteristic dimension of the obstacle (typically its diameter). A particle with a low Stokes number follows fluid streamlines (perfect advection), while a particle with a large Stokes number is dominated by its inertia and continues along its initial trajectory.

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