A general kinetic theory of liquids III. Dynamical properties

Abstract

The theory of liquids formulated in part I and applied to the equilibrium state in part II is here extended to liquids in motion. The connexion between the macroscopic and microscopic properties is revealed by the derivation of a set of generalized hydrodynamical equations, of which the fundamental equations of hydrodynamics are a special case; the more general equations describe the mean motion of clusters of molecules in the fluid. It is shown that the pressure tensor and energy-flux vector in a fluid consist of two parts, due to the thermal motion of the molecules and the intermolecular forces respectively, of which only the first is found in the kinetic theory of gases, but of which the second is dominant for the liquid state. A method is evolved for the study of those 'normal' non-uniform states which relate to actual monatomic fluids in motion. It becomes apparent, as in the case of equilibrium, that there is a region of temperature and density where analytical singularities arise, closely associated with the process of condensation. Rigorous expressions for the coefficients of viscosity and thermal conduction are then derived which apply equally to the liquid and the gas. They consist of two parts due to the thermal motion and molecular forces respectively, of which the first is dominant for the gas, and the second for the liquid. By approximating to the rigorous formula, an expression for the viscosity of liquids is obtained, comparable with certain other formulae, previously proposed on quasi-empirical grounds, and giving good agreement with experiment. An integro-differential equation is derived for the determination of the distribution functions relating to the non-uniform state. A full discussion is given of the simplest case, and the velocity distribution in non-uniform liquids and gases examined.