190

FLUIDITY AND PLASTICITY

I:

(65)

where n and k are constants, and by derivation n = 2. The
formula is important in dealing with diffusion through porous
materials such as soils. But in this type of diffusion, it has
often been noticed that there is a separation of the components
of the diffusing substances. This subject will come up for con-
sideration later.
Brownian Movement.—Einstein (1906) has shown that the
mean square of the projections I of the displacement of the
particle in time t on the axis of displacement is
Z2 = 25t
Substituting into this equation the value of the diffusion, given
above
Z2 = RT <p±
N Zirr
This is the equation used by Perrin in his brilliant investigation
of the Brownian movement.
The Velocity of Crystallization.—As a crystal forms in a
solution, the molecules of the solute are drawn to the growing
face of the crystal. The solution bathing the face of the crystal
has therefore a lower concentration of solute than the main
body of liquid and a process of diffusion must be set up to restore
the equilibrium. The rate of crystallization must therefore
depend upon the fluidity of the solution. Even in an under-
cooled liquid, where there is no opportunity for a change in con-
centration, the viscosity of the liquid retards the proper orienta-
tion of the molecules, and crystallization does not take place
instantaneously. H. A. Wilson (1900) has demonstrated that
the velocity is directly proportional to the fluidity of the liquid
at the face of the crystal, according to the formula,
v = a(t - tQ)<p (66)
where v is the velocity of solidification in millimeters per second,
a is a constant and tQ is the temperature at which the velocity of
solidification is zero, i.e., the solidifying point, found by extrapo-
lation. This point differs somewhat from the melting-point
of the substance, being 37°C for salol instead of 42°C. This
signifies that the above relation does not hold when the amount of
undercooling, and hence the velocity of solidification, is very
small. Since, Tammann has proved that purifying a substance