Abstract
We determine the regularized van der Waals contribution to pressure within a spherical cavity of vapor in a homogeneous, isotropic, infinite medium. The spherical Hamaker function, , has been defined, for the first time, in contrast to the conventional Hamaker function for planar surfaces, . For the materials under consideration, the pressure inside the cavity varies as , where a is the radius of the cavity. For radii below a transition radius, the surface energy (or surface tension) becomes size dependent and could have important implications for homogeneous nucleation of nanosized bubbles in liquids, as well as cavitation of bubbles. image
Highlights
Dispersion forces, such as van der Waals force and Casimir force, arise due to the modification in the fluctuations of the electromagnetic field by the presence of boundaries
Current understanding of van der Waals force between macroscopic objects is based on Lifshitz theory
Though a vapor cavity in an infinite medium has only one interface, the corresponding problem in the planar multilayer configuration is that of a layer of vapor contained between two half-spaces of liquid, i.e., the configuration studied by Lifshitz
Summary
Dispersion forces, such as van der Waals force and Casimir force, arise due to the modification in the fluctuations of the electromagnetic field by the presence of boundaries. We find the van der Waals contribution to pressure within a cavity of vapor, the electromagnetic properties of which is assumed to be identical with that of vacuum, in a homogeneous, isotropic, infinite liquid (see Fig. 1). In parallel to the works mentioned above, Belosludov and Nabutovskii, motivated by applications to homogeneous nucleation in superheated liquids, computed the van der Waals pressure in a spherical cavity within a homogeneous, infinite, isotropic medium [21]. Though a vapor cavity in an infinite medium has only one interface, the corresponding problem in the planar multilayer configuration is that of a layer of vapor contained between two half-spaces of liquid, i.e., the configuration studied by Lifshitz. We are adding to the main results of Belosludov and Nabutovskii by (1) identifying a relation between the spherical and planar Hamaker coefficients, (2) giving results for liquids other than water, and (3) presenting results in a more useful form
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