Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Powder processing Stokes number
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Stokes number

In a steady state, the particle will be carried at the velocity of the fluid, u, so the time to pass an obstacle of size D is of the order of (D/u). From the relationship between terminal velocity and acceleration, the characteristic time for velocity change is

\[{\tau _{\Delta u}} \approx \frac{{\Delta \rho {d^2}}}{{18\eta }}\]

The Stokes number (ratio of these two times) is thus given by

\[{\rm{Stk}} \approx \frac{{\Delta \rho {d^2}u}}{{18\eta D}}\]

It follows from this expression that fine particles will tend to be carried through without impact, while coarse ones will strike the obstacle (to which they may or may not adhere). This depends, however, on the velocity and viscosity of the fluid, as well as on the density difference and the obstacle size.

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