A simple theory based on a hard sphere model is used to calculate the self−diffusion constant and the shear viscosity of liquid carbon tetrachloride. The theory accounts for the coupling between translational and rotational motions of molecules. This feature distinguishes the hard sphere theory presented herein with that given recently by other workers. It is shown that the coupling has a large (factor of 2) effect on the diffusion constant, and thus the coupling should not be neglected even for molecules as spherical as carbon tetrachloride. The approximations that are needed to arrive at a hard sphere theory for transport coefficients are discussed in detail. This analysis reveals the strengths and limitations of such a theory.
REFERENCES
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One frequently used model of this type is the perfectly rough hard sphere. See Ref. 1 and articles cited therein for a mathematical definition. It is important to note that while this model is extreme in some sense, the properties of the model do not bound those of a real system. For example, suppose two perfectly rough spheres collided with zero impact parameter and zero relative angular velocity. Such a collision would produce no change in the angular momenta of the spheres. However, suppose two slightly aspherical hard core particles collided under the same conditions. Except for a few specific relative orientations, the collision will change the angular momenta of the particles. One may construct many classes of rough hard sphere models for which the coupling of translational and rotational motions is stronger than it is in the perfectly rough hard sphere model.
4.
This fact has been demonstrated and used in the modern equilibrium theories of liquids. For reviews, see
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Barker
and D.
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(1972
);5.
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S. Chapman and T. G. Cowling, Mathematical Theory of Non‐Uniform Gases (Cambridge University, Cambridge, England, 1970), 3rd ed.
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Equation of Ref. 1 and Eq. (2.15) of Ref. 2 provide a mathematical criterion for determining the rough hard sphere fluid closely associated with the real fluid. These equations fix the diameter for the hard spheres and the roughness (i.e., the degree of coupling between translational and rotational motions).
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14.
The following numerical procedure was used. The data on an isotherm was smoothed by a least squares fit. At the density (which is roughly the average density for the four isotherms studied by McCool and Woolf) the smoothed data on an isotherm were used to calculate According to our theory, this number is dependent on only. As a result, the number can be compared with to determine d(T).
15.
16.
M. A.
McCool
and L. A.
Woolf
, High Temp. High Pressures
4
, 85
(1972
).17.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954). In Table I‐A this text gives a Lennard‐Jones diameter of 5.9 Å, which puts the minimum of the potential at 6.6 Å.
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© 1975 American Institute of Physics.
1975
American Institute of Physics
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