Water Vapor Pressure over Complex Particles, I: Sulfuric Acid Solution Effect

ABSTRACT

The equilibrium vapor pressures of water are calculated for two different geometric configurations: a liquid cap formed on a single substrate sphere and a liquid pendular ring formed about the contact point of a pair of adhering, identical spheres. The substrate is a structureless, macroscopic (i.e., radius R > 50 nm), relatively hydrophobic sphere. For each configuration, pure water and sulfuric acid solution are used separately as the interface liquid. In addition to the available surface tension measurements of sulfuric acid solution against air, our calculations utilize the tabulated data of activity of water over the sulfuric acid solution and the solution density. The substrate's interfacial tension against air is treated as a parameter in these calculations. Then, by using Young's equation as a constraint in our calculation, we can determine the contact angle of the surface liquid residing on substrate spheres for both configurations. We apply Kelvin's equation in combination with both water activity of sulfuric acid solution and combining relations (semiquantitative relations describing molecular forces) to perform the calculations in the macroscopic picture. The calculations show, for example, that the equilibrium water vapor pressure over a pendular ring containing relatively dilute sulfuric acid solution (e.g., 0.5–10%) is always less than the equilibrium vapor pressure over the same configuration with only pure water when both sphere radii are 100 nm and contact angle is around 20°. The results also show that if all conditions are the same, except geometric configuration, the pendular ring of condensation has a lower equilibrium vapor pressure than the cap of condensation does. Even more significantly, the graph of equilibrium vapor pressure vs volume of condensed water for the pendular ring configuration indicates unconstrained condensational growth at subsaturation relative humidity. In contrast, in the cap configuration, condensational growth is usually limited for any subsaturation relative humidity.