Stokes number

Physical key figure
Surname	Stokes number
Formula symbol	${\displaystyle {\mathit {St}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {St}}={\frac {t_{\mathrm {T} }}{t_{\mathrm {F} }}}}$
${\displaystyle t_{\mathrm {T} }}$ characteristic time of the particle ${\displaystyle t_{\mathrm {F} }}$ characteristic time of the fluid
Named after	George Gabriel Stokes
scope of application	Particles in currents

The Stokes number (after: George Gabriel Stokes ) is the dimensionless number that indicates the importance of the inertia of a particle (speck of dust, droplet, bubble) for its movement in a moving fluid (gas or liquid). It is defined as the ratio ${\displaystyle St}$

${\displaystyle St={\frac {t_{\mathrm {T} }}{t_{\mathrm {F} }}}}$

• the characteristic time with which the speed of the particle adapts to the speed of the surrounding fluid due to friction , ${\displaystyle t_{\mathrm {T} }}$
• at the characteristic time in which the fluid itself changes its speed due to external influences. ${\displaystyle t_{\mathrm {F} }}$

For the particle follows the local flow. ${\displaystyle {\mathit {St}}\ll 1}$

In situations where the Stokes number is used, the particles are usually so small that the frictional force between the particle and the fluid is proportional to the drift velocity ( Stokes friction ). Then is well defined as the damping time constant with which a drift speed, the cause of which suddenly disappears, decays exponentially . ${\displaystyle t_{\mathrm {T} }}$

If the fluid vibrates in a sound field , then the reciprocal of the angular frequency is : ${\displaystyle t_{\mathrm {F} }}$ ${\displaystyle \omega }$

${\displaystyle t_{\mathrm {F} }={\frac {2\cdot \pi }{\omega }}}$

If the fluid is accelerated by a nozzle (application impactor ), slowed down by a diffuser (application sampling ) or if it evades a fiber ( filtration ), then one sets

${\displaystyle t_{\mathrm {F} }={\frac {D}{u}}}$

wherein

• ${\displaystyle D}$ is the diameter of the opening or the fiber
• ${\displaystyle u}$ the flow velocity.