The effect of surface tension (Kelvin effect) on the equilibrium radius of a hygroscopic aqueous aerosol particle

Abstract

The effect of surface tension (the Kelvin effect) on the equilibrium radius of an aqueous solution drop at fractional relative humidity h less than unity is analyzed mathematically. Expressions for the lowest-order corrections to the equilibrium radius and radius ratio (relative to the volume-equivalent dry radius r dry ) due to the Kelvin effect are presented and compared with data for solution drops of ammonium sulfate and sodium chloride. To lowest order the decrease in equilibrium radius resulting from the Kelvin effect is independent of the amount of solute in the drop and is approximated to good accuracy by Δ r / nm = - ( h / 3 ) / ( 1 - h ) , with only weak dependences on solute and temperature. The importance of the Kelvin effect on drop radius is further quantified in several ways. The value of the volume-equivalent dry radius below which the Kelvin effect results in more than a 5% decrease in the equilibrium radius of a solution drop at given h is approximately r dry , 5 % / nm = 8 h / ( 1 - h ) 2 / 3 . The decrease in the hygroscopic growth factor g of an aqueous solution drop between a low relative humidity and h = 0.9 resulting from the Kelvin effect is given approximately by Δ g = - ( 3 nm ) / r dry , again with only weak dependences on solute and temperature. These approximations compare well with measurements of growth factors of ammonium sulfate solution drops for dry radius as low as 10 nm. These findings, all of which are presented for fractional relative humidity as the independent variable, allow the magnitude of the Kelvin effect and its consequences on the properties of an aqueous solution drop to be readily assessed.