Introduction

Optical microscopic observations of small particles dispersed in water reveal a constant state of random motion. The discovery of this phenomenon is now attributed to Robert Brown, a botanist, although other publications predate his descriptions of 1828 and 1829. While Brown correctly attributed the motion to the molecular nature of matter, controversy persisted until the experiments of Gouy in 1888 ruled out extraneous causes such as mechanical vibrations, convection currents, and illumination and focused attention on molecular agitation. As Perrin (1910) concluded, the particles seem to move independently with no effect of density or composition, although the amplitude of the motion is greater for smaller particles, with less viscous fluids, and at higher temperatures. The displacements are significant; for example, 0.2-μm spheres in water wander 10 μm from their starting point in a bit over 30 seconds. Gouy and Perrin both attributed the motion of the particle to incessant impacts of fluid molecules which impart kinetic energy equal to 3/2 kT, partitioned equally among the three translational degrees of freedom. The irregularity of the translational motion and the rapid damping of the random fluctuations by the viscous fluid, however, confounded early attempts to measure this kinetic energy by calculating the instantaneous velocity from the observed trajectory. This failure to verify directly the origin of Brownian motion led to theoretical treatments appropriate for the longer diffusion time scale.