CHAPTER VI
FLUIDITY AND DIFFUSION

According to Stokes (1851) a sphere of radius r, impelled
through a fluid under a force F, will attain the velocity v

» = &• ^

This formula is of fundamental importance in the study of the
settling of suspensions, diffusion, Brownian movement, the rate
of crystallization of solutions, migration velocities and transfer-
ence numbers of the ions and in the conductivities of solutions.
Settling of Suspensions.—In the case of a falling sphere, the

force becomes

4.

F = g 7T#r3(p2 — pi)

where p2 and pi are the densities of the sphere and the medium
respectively, so

= -L( — V2 (63^

This formula enables one to calculate the speed of settling of
suspensions. It has been utilized in determining the viscosity
of very viscous liquids, e.g., Tammann (1898) and Ladenburg
(1907), for determining the radii of the particles in gold suspen-
sions, Pauli (1913), for measuring the charge on the electron in
air, Millikan (1910).

The Diffusion Constant.—Sutherland (1905), Einstein (1905)
and Smoluchowski (1906) have derived the relation between the
diffusion coefficient d and the fluidity,

RT v

d =

AT

where T is the absolute temperature, R is the gas constant
(83.2 X 106 c.g.s. units) and N is the number of molecules in a
gram molecule (70 X 1022). The diffusion coefficient is defined
as the quantity of solute diffusing per second through a unit
cube when the difference in concentration between the two ends
of the cube is unity. But Stokes' Law was derived for particles
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