Non-Dimensional Analysis of Droplet Size Distributions in a Convection Cloud Chamber

In a laboratory convection cloud chamber, supersaturation is produced by turbulent mixing of air from the saturated warm bottom and cool top surfaces. A model simplification of supersaturation is using a stochastic differential equation (SDE). Under a constant rate of injection of CCN, a steady-state droplet size distribution (DSD) can be achieved. A better understanding of the equilibrium DSD is critical for understanding chamber and cloud physics. A general solution for the equilibrium DSD for cloud chamber conditions (such as those in the Pi Chamber at Michigan Tech University) has evaded the scientific community. Previous research suggested solutions for the case of an equilibrium DSD without aerosol effects (i.e., without curvature and solute effects in the droplet growth equation), without supersaturation fluctuations, or with supersaturation fluctuations on the DSD modeled (in the equation for the PDF of droplet radius squared) as a diffusivity that is linearly proportional to the supersaturation variance and the Lagrangian autocorrelation time scale of the supersaturation fluctuations. Non-dimensional analysis is a powerful tool to simplify the domain of initial conditions. Using this, we can investigate the solution of the non-aerosol case, with application to the aerosol case. Contrary to the diffusion domain, my results suggest using a term proportional to the supersaturation standard deviation times the squared Lagrangian autocorrelation time scale instead of diffusivity.