Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

• Published in: Atmospheric chemistry and physics 2016-02, Vol.16 (4), p.2083-2107
• Main Authors: Alpert, Peter A, Knopf, Daniel A
• Format: Article
• Language: English
• Subjects: Aerosol clouds; Aerosol interaction; Aerosol-cloud interactions; Aerosols; Aqueous solutions; Catalysis; Charged particles; Chemical Sciences; Cirrus clouds; Cloud chambers; Cloud formation; Cloud interaction; Cloud-climate relationships; Clouds; Computer simulation; Contact angle; Continuous flow; Cooling; Cooling rate; Diffusion chambers; Droplets; Dye dispersion; Dynamics; Energy; Environment and Society; ENVIRONMENTAL SCIENCES; Experimental data; Experimental methods; Experiments; First principles; Freezing; Humidity; Ice; Ice nucleation; Immersion; Kinetics; Laboratories; Mathematical models; Morphology; Nucleation; Parameter uncertainty; Parameters; Relative humidity; Research methodology; Simulators; Statistical analysis; Statistical methods; Stochastic models; Stochastic processes; Stochasticity; Studies; Submerging; Surface area; Surfactants; Temperature; Temperature dependence; Time dependence; Uncertainty analysis; Variability
• ISSN: 1680-7324; 1680-7316; 1680-7324
• DOI: 10.5194/acp-16-2083-2016

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of Jhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate de