Predicting Particle Critical Supersaturation from Hygroscopic Growth Measurements in the Humidified TDMA. Part I: Theory and Sensitivity Studies

Abstract

A method is described to estimate the critical supersaturation of quasi-monodisperse, dry particles using measurements of hygroscopic growth at relative humidities below 100%. Köhler theory is used to derive two chemical composition?dependent parameters, with appropriate accounting for solution effects through a simplified model of the osmotic coefficient. The two unknown chemical parameters are determined by fitting the Köhler model to data obtained from humidified tandem differential mobility analyzer (HTDMA) measurements, and used to calculate the critical supersaturation for a given dry particle size. In this work the theory and methodology are presented, and sensitivity studies are performed, with respect to assumptions made and uncertainties in key input parameters to the Köhler model. Results show that for particle diameters of 40 and 100 nm, the average error between critical supersaturations derived using the proposed method and theoretical values is ?7.5% (1σ = 10%, n = 16). This error is similar to experimental uncertainties in critical supersaturations determined from laboratory studies on particles of known chemical composition (?0.6%, 1σ = 11%, n = 16).