Stokes's Law

George Gabriel Stokes was an Irish-born mathematician who spent much of his life working with fluid properties. He is most famous for his work describing the motion of a sphere through viscous fluids. This lead to the the development of Stokes's Law.  This equation shows the force needed to move a small sphere through a continuous, quiescent fluid at a certain velocity.  It is based primarily on the radius of the sphere and the viscosity of the fluid. The equation he developed is

F=6(pi)RnVc,
where R is the radius of the sphere, n is the viscosity, and Vc is the velocity through a continuous fluid. This equation can be manipulated to calculate the viscosity of the fluid. An explanation is given in the partial lab write-up linked below.

Stokes's work was further refined later to account for "wall (or edge) effects" and "end effects" by Gibson and Jacobs in 1920. These phenomena result in a slower observed velocity because the medium is not continuous. The wall effect correction accounts for the compression of the liquid against the sides of the container holding the fluid as the sphere moves through. This is based on a ratio between the sphere radius and the inner radius of the cylinder. To see a demonstration of the wall effect, click here (if you are viewing this outside the campus of Concordia College, Moorhead, the graphics may be of low resolution or may not work properly).

The end effect correction modifies Stokes law to account for the fact that the sphere does not fall indefinitely and is based on the ratio of sphere radius to the total height of the liquid. The effect of this correction is usually much smaller than the effect of the wall correction.

Stokes's law can also be used to find the viscosity of the same liquid at different temperatures. Objects move much more slowly through very cold liquids than through warm liquids. Click here to see a demonstration of the effect of temperature on viscosity (if you are viewing this outside the campus of Concordia College, Moorhead, the graphics may be of low resolution or may not work properly).


For more information on George Stokes and his work, visit the following websites:

http://sci.hkbu.edu.hk/math/stokes.html

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Stokes.html

http://www.ee.umd.edu/~taylor/frame5.htm


Go to a partial lab write-up.

Concordia College is in no way responsible for the contents of this page.

Return to the Concordia College Chemistry Deptartment Homepage.

Return to the Concordia College Homepage.

Thanks to D. J. Ulness and J. D. Koski for help in the construction of this page.