Stoke's Law

In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force — also called drag force — exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the generally unsolvable Navier–Stokes equations

where:
Fd is the frictional force (in N),
μ is the fluid's dynamic viscosity (in Pa s),
R is the radius of the spherical object (in m), and
V is the particle's velocity (in m/s).
If the particles are falling in the viscous fluid by their own weight due to gravity, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the buoyant force exactly balance the gravitational force. The resulting settling velocity (or terminal velocity) is given by:

where:
Vs is the particles' settling velocity (m/s) (vertically downwards if ρp > ρf, upwards if ρp < ρf ), g is the gravitational acceleration (m/s2), ρp is the mass density of the particles (kg/m3), and ρf is the mass density of the fluid (kg/m3). Note that for molecules Stokes' law is used to define their Stokes radius.