The Hole Theory of Liquids

Abstract

RECENTLY, Furth1, in a series of papers, has developed the hole theory of the liquid state. A liquid is regarded as a continuum permeated by a large number of holes, the number of holes being comparable to the number of particles in the liquid. The motion of the holes in the material continuum is similar to that of particles in a gas, and the hole theory on this account has a formal similarity with the kinetic theory of gases. A hole has four degrees of freedom, three of translation and one corresponding to a change in its radius. The average period for radial oscillation of holes is found to be which is of a far smaller order of magnitude than the meanlife Γ of the hole, σ represents the surface tension of the liquid, ρ its density, T the temperature and k is Boltzmann's constant. The meanlife as discussed by Furth is the time for which a hole lasts before it is destroyed by evaporation of molecules into it. In determining the meanlife, Furth has neglected the effect of curvature on the rate of evaporation. When this is taken into account, the hole theory affords a simple though, because of its inherent defects, not quantitatively accurate description of the variation of viscosity of liquids with pressure. For example, for pressures smaller than p2, the internal pressure of the liquid, we have where q is the ratio of the viscosity under pressure p(kgm./cm.2) to that under atmospheric pressure, M the gram molecular weight, and R the gas constant. For most liquids pi is of the order of 103 kgm./cm.2.