Aerosol Mobility and Drift Velocity

In the development of Brownian motion up to this point, we have assumed that the only external force acting on the particle is the fluctuating Brownian force mpa. If we generalize (9.52) to include an external force Fext, we get 

As before, assuming that we are interested in times for which t t, and taking mean values, the approximate force balance is at steady state  

The ensemble mean velocity (v) is identified as the drift velocity vc rirt, where 

The drift velocity is the mean velocity experienced by the particle population due to the presence of the external force Fe . For example, in the case where the external force is simply gravity, Fe = mpg, and the drift velocity (or settling velocity) will simply be Vdriit = gt (see also (9.41)]. When the external force is electrical, the drift velocity is the electrical migration velocity [see also (9.49)]. Therefore our analysis presented in the previous sections is still valid even after the introduction of Brownian motion. 

The mobility can also be viewed as the drift velocity that would be attained by the particles under unit external force. Recall (9.50), which is the mobility in the special case of an electrical force. By definition, the electrical mobility is related to the particle mobility by Be = qB, where q is the particle charge. A particle with zero charge, has a mobility given by (9.78) and zero electrical mobility. 

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