Introduction

Once a cloud droplet is nucleated it can continue to grow by water-vapor diffusion or condensation, at first rapidly, then slowly as diameter increases, if supersaturation conditions with respect to liquid water continue to occur around the droplet or drop. Conversely, a cloud droplet or raindrop will decrease in diameter by water-vapor diffusion or evaporation, first slowly when large, then rapidly when small, as diameter decreases, assuming subsaturation conditions with respect to liquid water continue to occur around the cloud droplet or raindrop.

Condensation and evaporation are governed by the same equation, the water-vapor diffusion equation. To understand condensation and evaporation of some particle, two diffusive processes must be considered. The first of these includes water-vapor transfer to or from a particle by steady-state water-vapor diffusion. It is a result of vapor gradients that form around a particle; thus the particle is not in equilibrium with its environment. The second of these processes is conduction owing to thermal diffusion of temperature gradients around a particle that is growing or decreasing in size. Fick's law of diffusion describes these diffusion processes. In summary, consideration must be made for mass and heat flux to and away from particles. These steady-state diffusion processes are derived independently and then a net mass change is obtained iteratively, or by a direct method, by combining the equations with the help of the Clausius–Clapyeron equation.

There are several ways to solve the steady-state equations, and two will be presented. One method includes kinetic effects and one does not.