Maximum bubble pressure method

Abstract: A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approximation to the superficial density of molecular pairs, the Lennard‐Jones potential and the Eisenstein‐Gingrich radial distribution function, the surface tension, surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquid argon at 90°K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolman's quasi‐thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature.

Abstract: A distinction is made between the surface Helmholtz free energy F, and the surface tension γ. The surface energy is the work necessary to form unit area of surface by a process of division: the surface tension is the tangential stress (force per unit length) in the surface layer; this stress must be balanced either by external forces or by volume stresses in the body. The surface tension of a crystal face is related to the surface free energy by the relation γ=F+A(dF/dA), where A is the area of the surface. For a one-component liquid, surface free energy and tension are equal. For crystals the surface tension is not equal to the surface energy. The standard thermodynamic formulae of surface physics are reviewed, and it is found that the surface free energy appears in the expression for the equilibrium contact angle, and in the Kelvin expression for the excess vapour pressure of small drops, but that the surface tension appears in the expression for the difference in pressure between the two sides of a curved surface. The surface tensions of inert-gas and alkali-halide crystals are calculated from expressions for their surface energies and are found to be negative. The surface tensions of homopolar crystals are zero if it is possible to neglect the interaction between atoms that are not nearest neighbours.

Abstract: The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.