What equations govern the formation of droplets on a surface?

Question

When some smooth surface (like that of a steel or glass plate) is brought in contact with steam (over e.g. boiling milk) then water is usually seen to condense on that surface not uniformly but as droplets. What are the equations which govern the formation and growth of these droplets ? In particular what role does the geometry of the surface plays in it? Also it is possible to prepare experimental conditions where no droplets are formed but water condenses uniformly ?

Answer 1

It is more about properties of the material and surface roughness/texture, than geometry of the surface on the large scale. There is a nice Wikipedia article on wetting, which you may find useful. In brief, that is the difference in surface tension at liquid-solid ($\gamma_{LS}$), liquid-air ($\gamma_{LA}$), and solid-air ($\gamma_{SA}$) interfaces which define the value of contact angle $\theta=\arccos\left(\left(\gamma_{SA}-\gamma_{LS}\right)/\gamma_{LG}\right)\neq0$, and lead to droplet formation. If the angle is zero, the liquid will tend to cover the whole surface uniformly.

Answer 2

I would suggest you the following well written review articles, by Jens Eggers, who is one of the most renowed and acknowledged researchers on this field:

Drop formation – an overview

Nonlinear dynamics and breakup of free-surface flows