258

FLUIDITY AND PLASTICITY

of whether it is derived from the fluidity of A or £, is obtained
from the terms of Eq. (26) containing n, and is

: -L. ^ """

and similarly the rate of flow of component B is

,
H

There will be separation of the two components only when the
thickness of the different layers is considerable or when the
passage through which the substances are forced is very small,
for in either case n will be small. If n = <» ,

(110)

and there will be no separation at all. The separation may be
calculated from the expression
Ui __ a na<pi + (n — 1)6<?2
t/2 6 (n + l)a<pi + nb<f>z
When n = 1, the component A will flow at only one-third of
the rate of J5, even though the two components have the same
fluidity and are present in equal proportion; and even if the
fluidity of B is zero, it will flow twice as rapidly as A, under
the above conditions. It follows that the flow of B is greatly
increased by making the fluidity of A large, this being the layer
in contact with the stationary boundary.
An ingenious application of the principle of superficial fluidity
was made by the Southern Pacific Railroad,1 when it was found
that the pressure required to pump certain heavy oils through
long pipe lines was inconveniently large. The problem was
to get the maximum flow of oil for a given expenditure of energy
and with a given diameter of pipe. By using a rifled pipe and
injecting about 10 per cent of water along with the oil, the
water was thrown to the outside of the pip.e by the centrifrugal
action caused by the rifling, producing a high superficial fluidity;
and thus, by a seeming paradox, the water lubricated the oil so
that the delivery became from 8 to 10 times what it would have
been had the water not been added.
One may demonstrate the effect of superficial fluidity very
^Engineering Record, 57, 676 (1908).