Page 46 - Bird R.B. Transport phenomena

§1.6 Viscosity of Suspensions and Emulsions 31

fluid and are simply related to the internal energy of vaporization at the normal boiling
point, as follows: 3
AGj « 0.408 AU (1.5-8)
vap
By using this empiricism and setting 8/a = 1, Eq. 1.5-7 becomes

11 = Щехр 0.408 ALZ /RT) (1.5-9)
vap
The energy of vaporization at the normal boiling point can be estimated roughly from
Trouton's rule

AL/ vap - AH vap - RT = 9ART b (1.5-10)
b
With this further approximation, Eq. 1.5-9 becomes

p V D (1.5-11)

Equations 1.5-9 and 11 are in agreement with the long-used and apparently successful
empiricism jx = Л ехр(В/Т). The theory, although only approximate in nature, does give
the observed decrease of viscosity with temperature, but errors of as much as 30% are
common when Eqs. 1.5-9 and 11 are used. They should not be used for very long slender
molecules, such as n-C oH 2.
2 4
There are, in addition, many empirical formulas available for predicting the viscos-
ity of liquids and liquid mixtures. For these, physical chemistry and chemical engineer-
ing textbooks should be consulted. 4

EXAMPLE 1.5-1 Estimate the viscosity of liquid benzene, QH , at 20°C (293.2K).
6
Estimation of the SOLUTION
Viscosity of a Pure
Liquid Use Eq. 1.5-11 with the following information:
3
V = 89.0cm /g-mole
T b = 80.1 °C
Since this information is given in c.g.s. units, we use the values of Avogadro's number and
Planck's constant in the same set of units. Substituting into Eq. 1.5-11 gives:

27
23
(6.023 X 10 )(6.624 X 10" ) /3.8 X (273.2 + 80.1))
r
(89.0) ~ V 293.2
3
4
= 4.5 X 10" g/cm-s or 4.5 X 10~ Pa • s or 0.45 mPa • s
§1.6 VISCOSITY OF SUSPENSIONS AND EMULSIONS
Up to this point we have been discussing fluids that consist of a single homogeneous
phase. We now turn our attention briefly to two-phase systems. The complete descrip-
tion of such systems is, of course, quite complex, but it is often useful to replace the sus-
pension or emulsion by a hypothetical one-phase system, which we then describe by

3 J. F. Kincaid, H. Eyring, and A. E. Stearn, Chem. Revs., 28, 301-365 (1941).
See, for example, J. R. Partington, Treatise on Physical Chemistry, Longmans, Green (1949); or R. C.
4
Reid, J. M. Prausnitz, and В. Е. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, 4th
edition (1987). See also P. A. Egelstaff, An Introduction to the Liquid State, Oxford University Press, 2nd
edition (1994), Chapter 13; and J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press,
London (1986), Chapter 8.