Calculations of the Equilibrium Vapor Pressure of Water over Adhering 50–200-nm Spheres

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Abstract
Treatments of condensation on aerosols generally assume the particles to be spherical implying that the condensate presents a positively curved surface to the surrounding vapor. In contrast, the region between two adhering spheres supports a pendular ring of condensation which may result in a condensate-vapor interface with negative curvature. According to the Kelvin equation, the equilibrium vapor pressure over such surfaces is depressed relative to a planar surface and therefore the substrate particle shows entirely different condensational characteristics than for an isolated sphere of similar size and composition to the adhering spheres. In this paper, literature results are utilized to develop general approaches to the calculation of the curvature of the pendular ring of condensation between two macroscopic spheres (radii > 10 nm) that may differ in size and composition. Results of calculations for specific cases are given for spheres of 50, 100, and 200 nm and for a range of condensate-substrate contact angles. Illustrative examples of critical supersaturations are calculated and dimensionless mean curvature graphs that can be used for computations of the critical supersaturations for adhering spheres of different size and composition are presented. These calculations indicate that even somewhat hydrophobic adhering spheres may be capable of activation as cloud condensation nuclei at the moderate supersaturations encountered in the atmosphere.