Transport Phenomena.pdf

§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 vap
(1.5-8)
By using this empiricism and setting 8/a = 1, Eq. 1.5-7 becomes
11 = Щехр 0.408 ALZ vap
/RT) (1.5-9)
The energy of vaporization at the normal boiling point can be estimated roughly from
Trouton's rule
AL/ vap
- AH vap
- RT b
= 9ART b
With this further approximation, Eq. 1.5-9 becomes
(1.5-10)
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 2
oH 4
2.
There are, in addition, many empirical formulas available for predicting the viscosity
of liquids and liquid mixtures. For these, physical chemistry and chemical engineering
textbooks should be consulted. 4
EXAMPLE 1.5-1
Estimation of the
Viscosity of a Pure
Liquid
Estimate the viscosity of liquid benzene, QH 6
, at 20°C (293.2K).
SOLUTION
Use Eq. 1.5-11 with the following information:
V = 89.0cm 3 /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:
(6.023 X 10 23 )(6.624 X 10" 27 ) /3.8 X (273.2 + 80.1))
(89.0) ~ r V 293.2
= 4.5 X 10" 3 g/cm-s or 4.5 X 10~ 4 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 description
of such systems is, of course, quite complex, but it is often useful to replace the suspension
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).
4
See, for example, J. R. Partington, Treatise on Physical Chemistry, Longmans, Green (1949); or R. C.
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.