What Is Stokes' Law of Viscosity?

Stokes’ law of viscosity considers forces acting upon a spherical particle suspended in liquid to derive a mathematical formula for viscosity, using the velocity at which the particle will settle at the bottom, explains Encyclopaedia Britannica. Conceptually, the friction force acting upon the sphere in a viscous liquid is directly proportional to the velocity of the sphere, the radius of the sphere and the viscosity of the fluid.

The website School Physics provides the equation, viscosity = 2gr^2(d1-d2)/9v, where g is a gravitational constant, r is the radius of the sphere, d1 is the density of the particle, d2 is the density of the liquid, and v is the terminal velocity of the particle. School Physics further explains that the velocity increases as the sphere sinks, until the frictional drag due to viscosity is balanced by gravity, at which time the velocity remains constant. Frictional drag is less for large spheres, but the terminal velocity is greater, as compared to small spheres. According to Michigan Technological University, important applications utilize Stokes’ law to manage gravitational settling of particles in a liquid. Those environmental solutions include the cleaning of particle pollutants in oceans and rivers, understanding suspended particle activity in wastewater treatment plants and the dense suspension of particles in fresh cement for construction projects.