The validity of the kinetic collection equation revisited – Part 3: Sol-gel transition under turbulent conditions
1Universidad Autónoma de la Ciudad de México, México City, 09790, México
2Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, México City, 04510, México
Abstract. In a coagulating system, a sol-gel transition occurs when a single giant particle (a gel) arises under certain conditions and begins to consume the mass of smaller but higher populated fraction (the sol). This single giant particle (also known as a runaway particle) is detached from the continuous spectrum. Since the kinetic collection equation (KCE) only models the evolution of the continuous size of the spectrum, as the largest particle continue to grow by accretion of smaller ones, the liquid water content predicted by the KCE will decrease.
In this paper, the sol-gel transition is proposed as the mechanism that forms the large droplets that are needed to trigger warm rain development in cumulus clouds. By using a collection kernel enhanced by turbulence and a stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. The model results show that the sol-gel transition (also called gelation) leads to the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol-gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value) reaches its maximum value. Moreover, we show that without turbulence, the sol-gel transition will not occur. In the context of theoretical cloud microphysics, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the droplet population and subsequently becomes the embryo for raindrops.