Brownian Motion
In 1828 the Scottish botanist Robert Brown, observing pollen grains
in water, discovered the random movement of colloidal particles in a liquid.
Here we see a simple model of Brownian motion involving a large particle
(mass M) colliding with an ideal gas of small particles (mass m=M/100)
in a viscous medium (viscosity mu). The inclusion of viscosity proves
to be essential for properly describing dissipation (for a detailed treatment,
see The Feynman Lectures on Physics, Volume 1).
Einstein and Smoluchowski (1905) solved the corresponding equations
of motion and found that, after a time interval t, the large particle
has traveled an average distance r = (6kT/mu) t^(1/2) at temperature T.
We can verify this dependence by plotting log(r) vs. log(t). With increasing
equilibration time, the data are increasingly well fit by a straight line
of slope 1/2. Note that the data are plotted as cumulative averages
(as they become available) before full equilibration.
Alan Denton
e-mail: alan.denton [at] ndsu [dot] edu
Anne Denton
e-mail: anne.denton [at] ndsu [dot] edu