Universal Approximation Formulas of Curvature Correction and Equilibrium Sizes of Hygroscopic Particles

Abstract

Theoretical analysis shows that when water activity is larger than its threshold value and the dry radius of a particle is larger than 0.005 µm, the deviation of curvature correction from unity can be accurately represented by the product of two terms, with one term strongly depending upon water activity and the other depending upon dry radius. Moreover, experimental data show that the water-activity-dependent term can be approximated by linear and one-third power functions of water activity. According to the approximation made to curvature correction, water activity is solved as analytical functions of relative humidity (RH). The analytically solved water activity is then used to compute particle equilibrium sizes using a known (observed) relationship between water activity and water uptake by unit mass of dry material. The accuracy of equilibrium sizes calculated with this method is checked with seven typical classes of aerosols. Results show that when RH ≤ 99.99%, the equilibrium radius computed with this method is accurate to within 3% (6%) if the dry radius of a particle is larger (smaller) than 0.02 µm and that when RH > 99.99%, equilibrium sizes can be estimated with an accuracy higher than 84%. Analytical approximation formulas are also derived for calculating critical equilibrium radii and critical supersaturation. The maximum relative errors of these formulas range from 3% to 15%.