Kinetics of Capillary Bridge Formation and Rupture

we first consider menisci, which are formed by capillary condensation. Condensation is limited by diffusion of vapor molecules toward the growing meniscus. Vapor molecules diffuse toward the meniscus because directly at the liquid surface the local vapor pressure is determined by the curvature via Kelvin s equation. This vapor pressure is lower than the vapor pressure far away from the surface. Kohonen, Maeda, and Christenson [571] derived an approximate expression for the change of the radius of curvature of a liquid meniscus between a sphere and a flat surface for zero contact angle. Their expression can be generalized to two spheres of different radii  

D j is the diffusion coefficient of vapor molecules in the surrounding gas in s and Mw is the molar mass of the molecules considered. Please note that P is the vapor pressure in the surrounding atmosphere far away from the meniscus. Close to the meniscus, the local vapor pressure can be different. 

We assumed that diffusion in the gap between the two particles is the same as in the bulk. This assumption is valid as long as the gap is much larger than the mean free path for collision between gas molecules. At room temperature and normal pressure, typical free path lengths are of the order of 100 nm. In some cases, the gap width can be significantly below 100 nm. Then collisions with the walls become more likely than collision with other gas molecules. This is called Knudsen flow. It can significantly slow down the process [571, 572]. 

A silica sphere of 5 pm radius is placed on a glass plate at 80% humidity. Both surfaces are perfectly wetted by water. At normal pressure and at 25 °C, the diffusion coefficient of water molecules in air is Dj = 2.4 x 10 m s and the saturation vapor pressure is Po = 3169 Pa. Thus, condensation and evaporation is described by 

To obtain a characteristic condensation or evaporation time we take dr/dt at t = 0 and extrapolate it linearly until the equilibrium value r = —Xi /]n P/Po) is reached. The linear extrapolation is described by 

---