Forces Acting on Airborne Particles
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The forces acting on an aerosol particle in still air are:
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Gravitational Force
The weight of a spherical particle of diameter d is expressed as:
where 
is the density of the particle and g is the acceleration due to gravity.
Bouyancy Force
According to Archimedes' Bouyancy Principle, the bouyant force exerted on a floating body is equal to the weight of the fluid displaced by the body. The Bouyancy Force exerted on a spherical particle is: 
where | 
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is the gas density.
Drag Force
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Sir Isaac Newton derived the general equation for the resistance force on a sphere moving through a gas while investigating the ballistics of cannon balls. Newton theorized that a sphere must push aside a volume of gas equal to the projected area of the sphere times its velocity. The general form of Newton's resistance equation is: 
where This equation is valid for all subsonic particle motion, from cannon balls to aerosol particles (or for instance, apples...assuming they're spherical). |
is the drag force on the sphere, 
is the drag coefficient, and V is the relative velocity between the gas and the sphere.
Drag Coefficient
The coefficient of drag, 
, is dependent upon Reynold's number (Re). For flow around a sphere, there are three regions for the drag coefficient: the Stoke's Law region, the Transition region, and Newton's Law region.
These relationship between drag coefficient and Reynold's number is depicted in the following figure:
******* Cd - Re figure here.
- Stokes' Law region: Re<1
- Transition region: 1<Re<1000
- Newton's Law region: 1000<Re<
In the Newton's Law region, 
is nearly constant.
