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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
Contents
where
In the case of Stokes flow, which is when the particle (or droplet) Reynolds number is less than unity. Then the particle drag coefficient is inversely proportional to the Reynolds number itself, the characteristic time of the particle can be defined as
where
In experimental fluid dynamics, the Stokes number is a measure of flow tracer fidelity in particle image velocimetry (PIV) experiments where very small particles are entrained in turbulent flows and optically observed to determine the speed and direction of fluid movement (also known as the velocity field of the fluid). For acceptable tracing accuracy, the particle response time should be faster than the smallest time scale of the flow. Smaller Stokes numbers represent better tracing accuracy; for
Non-Stokesian drag regime
The preceding analysis will not be accurate in the ultra-Stokesian regime. i.e. if the particle Reynolds number is much greater than unity. Assuming a Mach number much less than unity. A generalized form of the Stokes number was demonstrated by Israel & Rosner.
Where
An additional function
It follows that this function is defined by,
Considering the limiting particle free-stream Reynolds numbers, as
Where the constant
Application to anisokinetic sampling of particles
For example, the selective capture of particles by an aligned, thin-walled circular nozzle is given by Belyaev and Levin as:
where
where