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I am looking for an expression for the velocity of a micron sized (1 - 10 micron diameter) sized particles under accelerating forces.

I have aerosols in mind.

This is what I have in mind The resisting force acting on the particle is

$F_D = 3 \pi \mu Vd$ so its (mechanical) mobility is $\frac{V}{F_D} = \frac{1}{3 \pi \mu d}$

This expresses velocity of a particle per unit force. Does that mean that if the same force acts on a bunch of different sized particles, the smaller particles should move faster due to their smaller size and the dependance is $\frac{1}{d}$? Is this problem perhaps more complicated than this (full F=ma treatment)

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Looking through wikipedia's entry on mobility, it looks like the mobility gives the velocity at which the force you apply equals the drag from the material the particle is passing through. At that velocity, the net F is zero, so no you don't really need F=ma and I would guess that your interpretation is valid. Looks like your equation is a version of Stokes Drag given at en.wikipedia.org/wiki/Drag_(physics) half way down the page. –  Jason A May 7 '13 at 11:31
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