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 \(\tau\) is the relaxation time of the particle, \(U_o\) is the fluid velocity of the flow well away from the obstacle and \(d_c\) is the characteristic dimension of the obstacle.

In experimental fluid dynamics, the Stokes number (\(S_k\)) 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 \(S_k\gg 1\), particles will detach from a flow especially where the flow decelerates abruptly. For \(S_k\ll1\), particles follow fluid streamlines closely. If \(S_k \ll 0.1\), tracing accuracy errors are below 1%.

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:

\(c / c_0 = 1 + (u_{0} / u -1) \left(\frac{1}{1 + Stk (2 + 0.617 u / u_{0})} - 1\right)\)

where \(c\) is particle concentration, \(u\) is speed, and the subscript 0 indicates conditions far upstream of the nozzle. The characteristic distance is the diameter of the nozzle. Here the Stokes number is calculated,

\(Stk = \frac{u_{0} V_{s}}{d g}\)

where \(V_{s}\) is the particle's settling velocity, \(d\) is the sampling tubes inner diameter, and \(g\) is the acceleration of gravity.

References

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External links

• Reynolds number scaling of particle clustering in turbulent aerosols