86

FLUIDITY AND PLASTICITY

I 1

since, as we shall now show, by using it the viscosity is indepen-
dent of the number or arrangement of the lamellae.

Since v = Vi + v% + . . .
we obtain from Eqs. (24a) and (24b) that

or since

— ~, b =
rt,

etc.

the fluidity of the mixture is

The fluidities are, according to this definition, strictly additive
and entirely independent of the number and arrangement of
the layers. Since, however, the viscosities are usually calculated
by means of the Poiseuille formula based on the volume of flow,
it is important to determine for a given arrangement of lamellae
what correction must be made to the effective viscosity, as calcu-
lated from the volume of flow, to make it accord with the true
viscosity, as defined above and as obtained by the disk or other
similar method for the measurement of viscosity.

Reverting again to the figure, we find that

U =

If there were n pairs of alternate lamellae of the two substances
A andŁ

U = -JjfiviTi + n(n -f
R

n(n -

(26).

Since n = ,

Tl + 7*2

ui and v%, we get
U

and if & = Tr/ we obtain from Eq. (24b)

JO.

6<p2 H-------(<?i —

71

, on substituting into Eq. (26) the values of

• i , $h r

(27)