Brownian Motion

Introduction

Brownian motion is often observed as dust particles move in a shaft of sunlight even when there is no air motion to disturb them. Their displacements are usually in the millimeter range and occur over a time span of a few seconds. This animation shows the motion of a very large particle immersed in a sea of much smaller particles that is undergoing thermal motion.

Science

While some treatments of Brownian motion go into complicated statistical mathematics, I will just make the comment that the motion of our large particle is just its participation in the equipartition of energy that is normally found when two or more gases are mixed. Since the mean energy of all particles in a mixture is the same, the mean energy of the large particle is the same as that of the small particles.

$< E_{L \arg e} > = < E_{S m a l l} >$

(1.1)

Then the mean speed ratio of large to small particles is:

$\frac{< v_{L \arg e} >}{< v_{S m a l l} >} = \sqrt{\frac{m_{S m a l l}}{m_{L \arg e}}}$

(1.2)