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The Stokes number , 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 to a characteristic time of the flow or of an obstacle, or
where t 0 {\displaystyle t_{0}} is the relaxation time of the particle , 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. A particle with a low Stokes number follows fluid streamlines , while a particle with a large Stokes number is dominated by its inertia and continues along its initial trajectory.
In the case of Stokes flow, which is when the particle Reynolds number is less than unity, the particle drag coefficient is inversely proportional to the Reynolds number itself. In that case, the characteristic time of the particle can be written as
where ρ p {\displaystyle \rho _{p}} is the particle density, d p {\displaystyle d_{p}} is the particle diameter and μ g {\displaystyle \mu _{g}} is the fluid dynamic viscosity.