Radiation-induced condensational growth and cooling of cloud-sized mist droplets

A laboratory-experimental and theoretical-modeling investigation was conducted of isobaric, radiative cooling of cloud-like water mists to a remote heat sink, similar to what can happen at the tops of clouds. For mist initially at 208C cooled by a radiative sink at 2208C, the mean (D₄₃) mist droplet diameter grew from 5.5 to 8.4 mm and the mist temperature decreased from 208 to 38C in just 80 s. Modeling showed that conventional assumptions were able to predict the measured temperature decrease reasonably well but not droplet size changes, suggesting that bulk radiative cooling was being reasonably well modeled but not detailed, droplet-size-dependent behavior. In a theoretical analysis, Lewis-number near unity was exploited to obtain an analytic expression for quasi-steady supersaturation that agrees with what Davies reported in 1985 but is simpler and is a function of only droplet size distribution, surface tension, and solute parameters and not radiative transfer. A simpler expression for the corresponding time constant was also found that is a function of only the binary diffusion coefficient and D₃₁ moment of the droplet diameter distribution. The time constant was found to be in milliseconds and not seconds. Simply modifying quasi-steady supersaturation (i.e., applying droplet cooling effects uniformly to all droplet sizes) was shown not to be an acceptable substitute for including droplet-specific radiation terms in the droplet growth equation. These results confirm that radiative cooling at cloud top can have a significant effect on droplet size evolution and temperature change and provide data and analytical simplifications for use in further needed investigations of radiation modeling assumptions and parameterizations.