# Accelerating a micron size particle in an air stream

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1. Apr 17, 2014

### furrygerbil

Hi,

I have a 1m long, 10mm ID vertical tube attached to a vacuum system. I have a known flow rate of the air down the tube which is used to calculate the air velocity.

My question is if I then add micrometre sized particles (initially at rest) to the air stream what is their velocity at the end of the tube?

I know that eventually the particles will reach the same velocity as the air stream they are suspended in but is the tube long enough to achieve this?

I have spent a long time googling various ideas about this and have drawn a blank on a simple solution and it might not even be possible (simply), so I hand the question over to the collective wisdom of Physics Forums :)

Kind Regards

Craig

2. Apr 17, 2014

### bigfooted

the particle velocity can be approximated by:
$\frac{du_p}{dt}=\frac{1}{\tau_p}(u-u_p)$,
with u the air velocity and characteristic relaxation timescale is given by Stokes drag law:
$\tau_p = \frac{\rho d_p^2}{18\mu}$

if you have a 1 micron particle. the relaxation time is 3 microseconds, so you expect the particle to reach the air velocity in approximately this time.