VISCOSITY AND FLUIDITY
and when n = °°, the fluidity becomes simply

87

and in this case

& = $. (28)

In a homogeneous mixture it appears, therefore, that the two
definitions lead to the same fluidity, and experimental results
lead us to believe that this is the case usually presented in liquid
mixtures, since the disk method and the capillary tube method

give the same fluidity so far as we ___>

have certain knowledge. If, however,
the number of lamellae is small, which
may well be the case in very imperfect
mixtures, or when the flow takes place
through very narrow passages, the
effective fluidity as calculated from
the volume of flow may be either
greater or less than the sum of the
partial fluidities of the components,
depending upon the order of the
arrangement of the lamellae in refer-
ence to the stationary surface. The
amount to be added or subtracted
from the effective fluidity in order to
obtain the true fluidity is represented
by the term, corresponding to the
areas A CD, etc. or AFD, etc., Fig. 33.

A combination of the cases I and II would lead to a checker-
board arrangement, but it may be shown now that such an
arrangement tends to reduce itself to the case II where fluidities
are additive.

If the arrangement considered in Fig. 32 is subjected to
continued shearing stress, the lamellae will tend to become
indefinitely elongated as indicated in Fig. 34; and unless the
surface tension intervenes, as may be'the case in immiscible
liquids, the lamellae will approach more and more nearly the
horizontal position. Thus, so far as we can determine without
going into the complicated problem of the molecular motions,
it seems certain that the fluidities will become more and more

FIG. 34.—Diagram to illus-
trate how, in incompletely
mixed but miscible fluids, flow
necessarily brings about com-
plete mixing, so that even when
the viscosities were originally
additive the fluidities finally
become additive. In immis-
cible fluids, the layers A and
B resist indefinite extension
and emulsions are the result.