BROWNIAN MOTION

Discovered in 1828 by the botanist Robert Brown, Brownian motion is a continuous but random motion exhibited by sufficiently small particles when suspended in a liquid. The phenomenon is due to agitation of the particles by the molecules of the liquid, and the first adequate theory was put forward by Einstein in 1905. This theory establishes a connection between the mean square distance that a Brownian particle travels in time t and the viscosity of the liquid, η, though which it travels. For a spherical particle of radius a, this relation is:

(1)

where k is Boltzmann’s constant. The quantity is thus a kind of diffusivity for the suspended particles. As a numerical example, consider particles of radius 1 μm in liquid water at 300 K (η = 1 mPas); in this case, m²/s and the RMS distance travelled in 10 s is about 2 μm.