5.2.1 Brownian Motion
When observing a dilute dispersion of small particles (order of 1mm) under
the microscope, one observes—as was originally described by Brown—that
the particles display an erratic motion. If there is no convection, every
particle makes a random walk, implying that it very frequently alters
direction and speed of motion; the change in direction is completely
random, that in speed within certain bounds (cf. Section 4.3.1). This
Brownian motion is illustrated in Figure 5.12. The figure gives the projection
on a plane of the positions of a particle at regular time intervals, connected
by straight lines. The positions at 10 times shorter time intervals are also
given, and it is seen that the straight lines on the left-hand figure turn into
pathways that have an appearance like the total trajectory at left, though at
a smaller scale. The average pattern of the Brownian motion is thus
independent of the length of the time step considered, unless the latter is
extremely short. Actually, the particles may change position, say, 10^8 times
per second.
The motion of the particles is due to the heat motion of the solvent
molecules, which collide incessantly with a particle. It has become clear that
the molecules themselves follow just the same Brownian or diffusional
motion as the visible particles, albeit in still shorter time steps. On average—
FIGURE5.12 Brownian motion. Projection on a plane of the trajectory of a
gamboge particle, taking observations at constant time intervals. The right-hand side
shows the same trajectory, but the time interval is 10 times shorter than at the left-
hand side. After observations by Perrin. See text.