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Miles, John Richard Newmarch (1965) Molecular distribution functions and the calculation of optical and transport properties of non-uniform liquids. Doctoral thesis, Sir John Cass College.
The Kirkwood theory of transport processes in liquids contains two main assumptions. The establishment of the Fokker-Planck equation requires that the total force on a molecule should lose correlation in a time during which the momentum changes by only a small amount, and the Smoluchowski equation governs the distribution of molecular pairs only if the momentum loses correlation quickly enough for the mean pair force to be considered constant during the process. This thesis examines these assumptions and their bearing on the calculation of viscosity and flow anisotropy.
The condition that the fluctuating force X(E)-⟨X(E)ₜ⟩ on a molecule loses correlation much faster than the momentum (shown by Suddaby and Gray (ref. 16) to be necessary for the identification of Kirkwood’s friction constant with that of Brownian movement theory) is shown also to ensure that the higher terms in Kirkwood’s expansion of the frictional force ⟨X(E)ₜ⟩ are negligible.
Suddaby's expansion of the Fokker-Planck equation is solved numerically to determine a second approximation to the radial distortion for carbon tetrachloride, using two empirical mean potentials.
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