Diffusion Process

The Diffusion Process

The continued growth of a cloud droplet, once condensation has started, is initially governed by the diffusion of the water vapor molecules toward the droplet. Diffusion is the process of molecules moving from regions of higher concentrations to regions of lower concentrations. At the surface of a droplet, water vapor is simultaneously condensing and evaporating. When the concentration of water vapor molecules is higher some distance from the droplet than it is at the droplet surface, the water vapor in the air diffuses toward the droplet, condenses onto the droplet, and the net effect is droplet growth. Two phenomena which influence the growth that occurs by diffusion are the curvature effect and the solution effect.

Droplets, by nature, are round. The curvature of a droplet tends to increase the concentration of vapor at the surface of the droplet. Small droplets have more curvature than larger droplets. In general, given identical atmospheric conditions, a smaller droplet will have a greater concentration of water vapor at its surface than a larger droplet. Since diffusion is the movement from higher concentrations to lower concentrations, the curvature effect tends to retard droplet growth by diffusion. As a droplet grows, its curvature decreases and becomes more like a plane surface and the influence of the curvature effect decreases as well.

In contrast with the curvature effect, the solution effect encourages growth by diffusion. Many aerosols dissolve in water. As water condenses onto them, the combination of the aerosol and water create a solution droplet. The dissolved substance displaces some of the water molecules at the surface of the droplet, and the result is a decreased concentration of water vapor at the surface. In general, the more concentrated the droplet solution is, the less concentrated the water vapor at the surface of the droplet will be. Thus, the solution effect tends to positively influence growth by diffusion. The solution effect can often encourage growth at relative humidity below 100%. As a solution droplet grows, the concentration of the droplet is diluted and the influence of the solution effect also decreases.

The curvature and solution effects work in opposition to one another on a backdrop of fluctuating atmospheric vapor pressure. A droplet that is neither growing nor decaying (i.e., getting smaller) is in equilibrium with the surrounding air. This means the concentration of water vapor at the droplet surface is equal to the concentration of water vapor a short distance away from the droplet. If the relative humidity increases for any reason, a droplet that had been in equilibrium will grow until it depletes the air of excess water vapor and reaches equilibrium once again. Conversely, if the relative humidity decreases, the droplet will evaporate until it reaches equilibrium. A droplet that manages to grow to a diameter of about 20 micrometers will start to grow by collision and coalescence.

You are encouraged to take a moment and explore the mathematics of the droplet growth process by diffusion. With this calculator, you can explore the effects of the density of the air and the liquid water mixing ratio (r_L, from thermodynamic diagrams) on the maximum radius of a droplet grown by diffusion.