Aerosol Transport – Inertia

:: Section 7

Straight-Line Particle Acceleration

I. Relaxation Time

Relaxation time characterizes the time required for a particle to adjust or "relax" its velocity to a new condition of forces. It's an indication of the particle's ability to quickly adjust to a new environment or condition. It depends on the mass and mechanical mobility of the particle, and is not affected by the external forces acting on the particle.

The relaxation time, τ, can be obtained using the following equation:

Because relaxation time is proportional to the square of particle diameter, it increases rapidly with the increase of particle size. Usually, small particles "relax" to new environments (i.e. following the flow well) in a very short time, while larger particles are more "stubborn" and tend to stick to their original path.

With the use of τ, we can easily calculate a particle's terminal settling velocity as:

Now try some particle diameters (e.g. 0.1, 1, 10 μm), and see the relaxation time they need: