200

FLUIDITY AND PLASTICITY

which causes any cubical figure of the fluid to assume the form
of a rhombohedron, will cause the sphere to rotate, thereby
assisting the flow. The stream lines are curved on account of the
presence of the sphere, but the sphere itself moves in a linear
direction and with the velocity of the stratum of fluid which
would, if continuous, pass through the center of the sphere.
Spheres in the same stratum do not approach each other since
they all have the same velocity.

Spheres in different strata move with unequal velocity,
hence collisions must take place, depending upon the radii of
the spheres, their number per unit volume, and also upon any
attraction or repulsion which may exist between them. The

FIG. 72.—Two spheres before, during, and after collision. The initial rota-
tion of the individual spheres is lost on collision and this results in the dissipation
of energy as heat. In the place of this individual rotation there develops a
rotation of the system. It should be noted that this latter rotation causes the
centers of the spheres to move in a transverse direction, indicated by the dis-
tances from the dotted lines.
surfaces of two spheres which are approaching each other must be
moving in opposite directions, which are at right angles to the line
joining their centers, Fig. 72. The viscous resistance to this
shearing action which is set up as they approach will rapidly
dissipate as heat their energy of rotation. In other words, their
energy of rotation is converted into heat by the "collision" of
the particles.
The contact of two particles, which are large in comparison
with molecular dimensions, brings the laws of ordinary friction
into play. The spheres cannot rotate unless the torque exceeds a
certain definite value, which will become very important when
we come to consider plastic flow. This value depends upon
the pressure existing at their point of contact normal to the
surfaces and this pressure in turn depends not only on the rate
of shear but on the attraction or repulsion which may exist