Abstract. Heterogeneous ice nucleation remains one of the outstanding problems in cloud physics and atmospheric science. Experimental challenges in properly simulating particle-induced freezing processes under atmospherically relevant conditions have largely contributed to the absence of a well-established parameterization of immersion freezing properties. Here, we formulate an ice active, surface-site-based stochastic model of heterogeneous freezing with the unique feature of invoking a continuum assumption on the ice nucleating activity (contact angle) of an aerosol particle's surface that requires no assumptions about the size or number of active sites. The result is a particle-specific property g that defines a distribution of local ice nucleation rates. Upon integration, this yields a full freezing probability function for an ice nucleating particle. Current cold plate droplet freezing measurements provide a valuable and inexpensive resource for studying the freezing properties of many atmospheric aerosol systems. We apply our g framework to explain the observed dependence of the freezing temperature of droplets in a cold plate on the concentration of the particle species investigated. Normalizing to the total particle mass or surface area present to derive the commonly used ice nuclei active surface (INAS) density (ns) often cannot account for the effects of particle concentration, yet concentration is typically varied to span a wider measurable freezing temperature range. A method based on determining what is denoted an ice nucleating species' specific critical surface area is presented and explains the concentration dependence as a result of increasing the variability in ice nucleating active sites between droplets. By applying this method to experimental droplet freezing data from four different systems, we demonstrate its ability to interpret immersion freezing temperature spectra of droplets containing variable particle concentrations. It is shown that general active site density functions, such as the popular ns parameterization, cannot be reliably extrapolated below this critical surface area threshold to describe freezing curves for lower particle surface area concentrations. Freezing curves obtained below this threshold translate to higher ns values, while the ns values are essentially the same from curves obtained above the critical area threshold; ns should remain the same for a system as concentration is varied. However, we can successfully predict the lower concentration freezing curves, which are more atmospherically relevant, through a process of random sampling from g distributions obtained from high particle concentration data. Our analysis is applied to cold plate freezing measurements of droplets containing variable concentrations of particles from NX illite minerals, MCC cellulose, and commercial Snomax bacterial particles. Parameterizations that can predict the temporal evolution of the frozen fraction of cloud droplets in larger atmospheric models are also derived from this new framework.
Pulmonary response to intratracheal instillation of ultrafine versus fine titanium dioxide: role of particle surface area
