Transport Processes in Liquids

The object of the modern theory is to find the average flow of mass, momentum or energy, as observed in diffusion, viscous flow or thermal conduction, by means of the probability distribution for the co-ordinates and momenta of a representative molecule or pair of molecules. Transmission of momentum or energy in liquids, as distinct from gases, is due to the action of intermolecular forces. The probability distribution is determined by a differential equation similar to the equation of Fokker and Planck. Frequently it is sufficient to find the probability distribution in space co-ordinates only, by solving the equation of Smoluchowski. These equations are known to apply to the Brownian movement of large particles suspended in a liquid. Their validity for the movement of molecules was established only recently by combining the principles of statistics and dynamics and invoking a hypothesis of molecular chaos. The friction constants entering as parameters into the differential equations can, in principle, be derived from intermolecular forces; in practice this involves considerable difficulties. Even in its present incomplete stage the theory yields quantitative results comparing reasonably well with experiment. In addition it provides criteria for assessing the significance of viscosity formulae as put forward by previous authors.