Aerosol Transport – Inertia

:: Section 7

Straight-Line Particle Acceleration

III. Stopping Distance

To determine the maximum distance a particle with an initial velocity V₀ will travel in the still air without any external forces (i.e. only drag force is acting on the particle), stopping distance is introduced. Similar to relaxation time, stopping distance indicates the ability of a particle to respond to a new condition.

For particles with an initial velocity V₀, we can get its velocity equation via similar derivations of the velocity equation with zero final velocity (i.e. stopped):

If we integrate the above equation with regard to t, we can get the travel distance as:

Taking the condition that at t = ∞, we can get the formula for the stopping distance:

where S is the total distance traveled -- the stopping distance, or inertial range.

The table below lists the stopping distance (S) for various d_p:

*For initial velocity (V₀) of 1000 cm/s.

Does a larger or a smaller particle stop faster?