Page 255 - Bird R.B. Transport phenomena

§8.2 Rheometry and Material Functions 239

-3 - 2 - 1 0 1 Fig. 8.2-4. The material functions 17(7),
%(y)/17'(w), and TJ"(U>) for a 1.5% poly-
acrylamide solution in a 50/50 mixture
log У) of water and glycerin. The quantities 77,
с 7]'', and 17" are given in Pa • s, and ^ in
1
Pa • s . Both у and 00 are given in s" . The
2
9 Q
log 7] data are from J. D. Huppler, E. Ashare,
в
Г On в and L. Holmes, Trans. Soc. Rheol., 11,
.4 о < в °о„1 J. M. Wiest. The oscillatory normal
-< в 159-179 (1967), as replotted by
о * • в -1 stresses have also been studied ex-
о perimentally and theoretically (see
о -2 M. C. Williams and R. B. Bird, Ind.
Э
•о Eng. Chem. Fundam., 3,42-48 (1964);
в • О о
о M. C. Williams, /. Chem. Phys., 42,
2988-2989 (1965); E. B. Christiansen
217"- —*Л с
In and W. R. Leppard, Trans. Soc. Rheol.,
18, 65-86 (1974), in which the ordinate
о Steady s!tear floW of Fig. 15 should be multiplied by 39.27.
e
Small-amplitudе
sinsoidal motioi1 О
-2 1 1 \
-3 - 2 - 1 0 1
log 7 or log a)
The elongational viscosity 17 cannot be measured for all fluids, since a steady-state
elongational flow cannot always be attained. 4
The three experiments described above are only a few of the rheometric tests that
can be performed. Other tests include stress relaxation after cessation of flow, stress
growth at the inception of flow, recoil, and creep—each of which can be performed in
shear, elongation, and other types of flow. Each experiment results in the definition of
one or more material functions. These can be used for fluid characterization and also for
determining the empirical constants in the models described in §§8.3 to 8.5.
Some sample material functions are displayed in Figs. 8.2-4 to 8.2-6. Since there
is a wide range of complex fluids, as regards chemical structure and constitution,

О

4 о
о

с
8» U 8
0 ffl Fig. 8.2-5. Dependence of the second normal stress co-
"q
5b efficient on shear rate for a 2.5% solution of polyacry-
) Q
lamide in a 50/50 mixture of water and glycerin. The
1
2
-2 quantity ^ 2 is given in Pa • s , and a) is in s" . The data
of E. B. Christiansen and W. R. Leppard, Trans. Soc.
-4 -2 0 Rheol., 18,65-86 (1974), have been replotted by
logy J. M. Wiest.

C. J. S. Petrie, Elongational Flows, Pitman, London (1979); J. Meissner, Chem. Engr. Commun., 33,
4
159-180 (1985).