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Accelerating a micron size particle in an air stream

  1. Apr 17, 2014 #1
    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. jcsd
  3. Apr 17, 2014 #2
    the particle velocity can be approximated by:
    [itex]\frac{du_p}{dt}=\frac{1}{\tau_p}(u-u_p)[/itex],
    with u the air velocity and characteristic relaxation timescale is given by Stokes drag law:
    [itex]\tau_p = \frac{\rho d_p^2}{18\mu}[/itex]

    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.
     
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