There are quite a few things which affect how fast water vapor will condense, more than the ones you mention.
It takes 540 calories per gram of water to make it turn into
vapor. The water releases this same amount when it condenses. This heat
energy has to be dissipated somewhere. If the air is still, then the
heat flow will follow the heat transfer equation, which is similar to
the diffusion equation. It depends on the thermal conductivity of the
surface and also of the air, and on the temperatures far from the
surface. Heat will flow in two directions here. You have to worry about
both the thermal conductivity of the cold surface and also that of the
layer of water that has condensed, as the heat must flow through that,
too. If the condensing water freezes (makes frost), then the thermal
conductivity of the ice must be used. The frost will also in general
not be horizontal, and this will change the surface area. If the water
layer is thick, convection will play a role and then life gets even
more complicated.
The other effect will be the rate at which water vapor can diffuse
through the air to reach the surface. This depends on pressure and
temperature.
It is probably a safe assumption that the top layer of water is in
equilibrium with the water vapor in the air layer immediately above it
(this isn't quite the case as water vapor is condensing, but if the
condensation is limited by heat transfer and diffusion, this is the way
to go). The temperature of this top layer will not be the same as that
of the cold material or of the air far away. This means solving the
diffusion and heat equations together and making the boundary
conditions match using the vapor pressure as a function of temperature.
This is not a simple calculation! Why not try some actual experiments?
Tom
(published on 10/22/2007)
