The forces acting on an aerosol particle in still air are:
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.
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 is the gas density.
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 is the drag force on the sphere, is the drag coefficient, and V is the relative velocity between the gas and the sphere.
This equation is valid for all subsonic particle motion, from cannon balls to aerosol particles (or for instance, apples...assuming they're spherical).
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.
In the Newton's Law region, is nearly constant.