Stokes' law

In physics, a law expressing the viscous drag force F acting on a spherical object of radius r moving with velocity v through a fluid of viscosity ? as F = 6??rv; stated in 1845 by British physicist George Stokes (1819–1903). It determines the terminal velocity of small raindrops, or small bubbles in water.

In 1851, George Gabriel Stokes derived an expression for the frictional force exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid by solving the generally unsolvable Navier-Stokes equations:

where:

F is the frictional force r is the Stokes radius of the particle η is the fluid viscosity, and v is the particle's speed

If the particles are falling in the viscous fluid by their own weight, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the bouyant force exactly balance the gravitational force.