# Stokes Number

## Description

The Stokes number (Stk), named after 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 characteristic time of a particle (or droplet) to a characteristic time of the flow or of an obstacle.

Particles with low Stokes number follow fluid streamlines (perfect advection) whereas for large Stokes number, the particle’s inertia dominates so that the particle will continue along its initial trajectory.

## Variables

Stk | Stokes number (dimensionless) |

τ | relaxation time of the particle (the time constant in the exponential decay of the particle velocity due to drag) (sec) |

U_{o} | fluid velocity of the flow well away from the obstacle (m/s) |

d_{C} | characteristic dimension of the obstacle (typically its diameter) (m) |