Stokes's law

( Stokes's law )

• Mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium.
• The law, first set forth by the British scientist Sir George G. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a liquid column under the influence of gravity.

The force acting in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall.

The force acting downward is equal to ⁴/₃ πr³ (ρ₁ - ρ₂)g, in which ρ₁ is the density of the sphere, ρ₂ is the density of the liquid, and g is the gravitational constant.

At a constant velocity of fall the upward and downward forces are in balance.

Equating the two expressions given above and solving for v therefore yields the required velocity, expressed by Stokes's law as: v = ²/₉ (ρ₁ - ρ₂)gr²/η.