Page 44 - Bird R.B. Transport phenomena

§1.5 Molecular Theory of the Viscosity of Liquids 29

Eq. 1.4-15 then gives
7
7
7
(0ЛЗЗЗ)(1462)(1(Г ) (0.039)(2031)(1(Г ) , (0.828)(1754)(1(Г )
V =
^ 0.763 1.057 1.049
7
= 1714xlO" g/cm-s
12
The observed value is 1793 X 10~ 7 g/cm • s.
§1.5 MOLECULAR THEORY OF THE VISCOSITY OF LIQUIDS
A rigorous kinetic theory of the transport properties of monatomic liquids was devel-
oped by Kirkwood and со workers. 1 However this theory does not lead to easy-to-use
results. An older theory, developed by Eyring 2 and coworkers, although less well
grounded theoretically, does give a qualitative picture of the mechanism of momentum
transport in liquids and permits rough estimation of the viscosity from other physical
properties. We discuss this theory briefly.
In a pure liquid at rest the individual molecules are constantly in motion. However,
because of the close packing, the motion is largely confined to a vibration of each mole-
cule within a ''cage" formed by its nearest neighbors. This cage is represented by an en-
ergy barrier of height AGj/N, in which AGj is the molar free energy of activation for
escape from the cage in the stationary fluid (see Fig. 1.5-1). According to Eyring, a liquid
at rest continually undergoes rearrangements, in which one molecule at a time escapes
from its "cage" into an adjoining "hole," and that the molecules thus move in each of the

Vacant lattice
site or "hole"

Layer С
Layer В
Layer Л

Fig. 1.5-1 Illustration of an escape
- In fluid at rest process in the flow of a liquid.
In fluid under stress т, i/л- Molecule 1 must pass through a
"bottleneck" to reach the vacant
site.

12
F. Herning and L. Zipperer, Gas- und Wasserfach, 79,49-54, 69-73 (1936).
1
J. H. Irving and J. G. Kirkwood, /. Chem. Phys., 18, 817-823 (1950); R. J. Bearman and J. G. Kirkwood,
/. Chem. Phys, 28,136-146 (1958). For additional publications, see John Gamble Kirkwood, Collected
Works, Gordon and Breach, New York (1967). John Gamble Kirkwood (1907-1959) contributed much to
the kinetic theory of liquids, properties of polymer solutions, theory of electrolytes, and thermodynamics
of irreversible processes.
2
S. Glasstone, K. J. Laidler, and H. Eyring, Theory of Rate Processes, McGraw-Hill, New York (1941),
Chapter 9; H. Eyring, D. Henderson, B. J. Stover, and E. M. Eyring, Statistical Mechanics, Wiley, New York
(1964), Chapter 16. See also R. J. Silbey and R. A. Alberty, Physical Chemistry, Wiley, 3rd edition (2001),
§20.1; and R. S. Berry, S. A. Rice, and J. Ross, Physical Chemistry, Oxford University Press, 2nd edition
(2000), Ch. 29. Henry Eyring (1901-1981) developed theories for the transport properties based on simple
physical models; he also developed the theory of absolute reaction rates.