Abstract
We demonstrate that the Lifshitz interaction energy (excluding the self-energies of the inner and outer spherical regions) for three concentric spherical dielectric media can be evaluated easily using the immense computation power in recent processors relative to those of a few decades ago. As a prototype, we compute the Lifshitz interaction energy for a spherical shell of water immersed in water vapor of infinite extent while enclosing a spherical ball of ice inside the shell, such that two concentric spherical interfaces are formed: one between solid ice and liquid water and the other between liquid water and gaseous vapor. We evaluate the Lifshitz interaction energy for the above configuration at the triple point of water when the solid, liquid, and gaseous states of water coexist, and, thus, extend the analysis of Elbaum and Schick in Phys. Rev. Lett. 66 (1991) 1713 to spherical configurations. We find that, when the Lifshitz energy contributes dominantly to the total energy of this system, which is often the case when electrostatic interactions are absent, a drop of water surrounded by vapor of infinite extent is not stable at the triple point. This instability, that is a manifestation of the quantum fluctuations in the medium, will promote formation of ice in water, which will then grow in size indefinitely. This is a consequence of the finding here that the Lifshitz energy is minimized for large (micrometer size) radius of the ice ball and small (nanometer size) thickness of the water shell surrounding the ice. These results might be relevant to the formation of hail in thunderclouds. These results are tentative in that the self-energies are omitted; surface tension and nucleation energy are not considered.
Highlights
The term Casimir effect is often used to refer to all the phenomena associated with quantum fluctuations
We demonstrate that the Lifshitz interaction energy for three concentric spherical dielectric media can be evaluated using the immense computation power in recent processors relative to those of a few decades ago
We find that when the Lifshitz energy contributes dominantly to the total energy of this system, which is often the case when electrostatic interactions are absent, a drop of water surrounded by vapor of infinite extent is not stable at the triple point
Summary
The term Casimir effect is often used to refer to all the phenomena associated with quantum fluctuations. Other closely related terminologies are quantum vacuum energy, zero point energy, Lifshitz energy, London dispersion forces, and van der Waals interactions. The ideas governing the van der Waals interactions [1] and London dispersion forces [2,3,4] originated in attempts to understand the interactions of neutral, but polarizable, molecules of gases that deviated in their characteristics from the ideal gas law. Casimir and Polder [5] later generalized these calculations to include retardation effects
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