COLLOIDAL SOLUTIONS 201
between the particles. So when two spheres come into contact,
Fig. 725, they must remain in contact for a definite period
unless the spheres are small enough to exhibit Brownian move-
ment. If the spheres were without attraction or repulsion for
each other, they would become separated as soon as their centers
have come to be in the same vertical plane.
The spheres cannot rotate as individuals during the period
of contact until the torque exceeds a certain minimum value.
The result is that during the time of contact the group of spheres
begin to rotate as a whole, and they pass out of the strata to which
they formerly belonged, Fig. 72c, and into layers of different
velocities. During this period of acceleration, the liquid will
flow around the spheres and through interstices between them.
Thus other spheres tend to collide with those already in contact
with each other, after which the combined mass tends to rotate as
a whole. When equilibrium is reached these clots will have a
certain average size, depending upon the number, size, and spe-
cific attraction of the particles.
For the present purpose, the important thing to observe
is that in the collisions of the particles we have a new source
of loss of energy, and if these clots increase in size and number
there must come a point when the clots come in contact across
the entire width of the passage. At this point viscous flow
of the material as a whole stops and plastic flow begins.
For a given substance and volume concentration, the number
of collisions will be proportional to the number of particles, which
varies inversely as the cube root of the radius. But if the
angular velocity is independent of the radius, the energy of
rotation will be proportional to the square of the radius, hence
the loss of energy, due to collisions will be inversely proportional
to the radius. This conclusion, if correct, is very important in
indicating that very finely divided particles give comparatively
viscous liquids or at higher concentrations plastic solids.
Bingham and Durham (1911) have studied suspensions of
infusorial earth, china clay and graphite suspended in water,
as well as infusorial earth suspended in alcohol as already referred
to on page 54. For each temperature, the fluidity falls off rapidly
and linearly with the concentration of solid, so that at no very high
concentration by volume the fluidity of zero would be reached, as