FLUID STATICS.

Film Loop: Random walk and Brownian motion

Length: 3:50 Min., Black and White, No Sound

How does an individual atom or molecule of gas move? As we watch the path of the odd colored puck at the beginning of this film, the answer is obvious. The air molecules, like the pucks, collide with one another, rebounding in seemingly random directions at random speeds. In fact, we call this pattern random walk.

From Film-Loop 80-291 we know the distribution of speeds for the colored puck. Now we consider the length of the paths between collisions. How do the lengths of these collision free paths distribute themselves? Is the distribution of speeds Maxwellian? To follow an individual puck through our "gas", we mount a lamp on our study puck and make a time exposure of this "fire fly" in the dark. The photograph records the path of the puck while the shutter is open.

For convenience in measuring the lengths of the free paths, the photograph is enlarged and measured with a centimeter scale. Could we have constructed the puck path by using successive frames of the movie film instead of a photograph? Why do we ignore the path up to the first collision and after the last collision? Can the speed of the puck along any free path be derived from the photograph? If we had also obtained a picture of a puck of known diameter at the same scale, how could we have obtained the actual free path lengths?

In order to learn the distribution of these free paths, we construct a histogram showing the frequency of any free path length occurrence within an interval of lengths versus the free path length. The shape of the theoretical distribution is (eexp(-x/l)) where l is the mean free path. The mean free path is just the total path divided by the number of collisions less one. When a larger puck is introduced, we can compare a photograph of the path of this larger puck with the earlier pattern.

When a large disc, 22 times as massive as the small pucks, is introduced, it becomes difficult to detect the responses to individual collisions. In fact, for very large particles, the results of these collisions become lost in the acoustical modes of vibration within the particle, and the term mean free path loses most if not all of its significance. But, as the animated line indicates, the disc does respond to statistical fluctuations in the number of collisions around its edge. We give this relatively slow random movement the particular name Brownian motion after the English botanist Robert Brown who, in 1827, noted the motion of pollen particles floating in air.

The final scene in the film shows the Brownian motion of smoke particles responding to collisions with molecules in the air. The smoke particles are on the order of (10 exp 4) times as massive as the oxygen molecules and are being hit on the order of (10 exp 12) times per second so we would certainly not expect to see any random walk. What we do see, however, is the random jitter caused by local fluctuations in the number of collisions, i.e. the Brownian motion.