What would be the best ceiling shape for inducing condensation?
I'm guessing it would a curve ︶ or V shape, but those are just guesses. (I don't have any background on thermal physics)
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3$\begingroup$ It’s not the shape so much as the level of humidity and dew point temperature... $\endgroup$ – Solar Mike Aug 2 '18 at 11:38
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1$\begingroup$ Maximizing the surface area would yield more condensation faster. en.wikipedia.org/wiki/Romanesco_broccoli has a very high surface area for it's volume, although it might be a bit tricky to manufacture :) $\endgroup$ – user6335 Aug 2 '18 at 12:35
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$\begingroup$ @Wossname - not if it is above the dew point... $\endgroup$ – Solar Mike Aug 2 '18 at 13:55
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$\begingroup$ Any shape will induce. I think what you want is a good shape for collection (tho' to some extent if there's a prevailing breeze you might want to use that for thermal extraction) $\endgroup$ – Carl Witthoft Aug 2 '18 at 15:06
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$\begingroup$ (can't mention more than one...) thanks for your replies! (though I can't upvote because of my low karma...) Anyway, I should have added that it's a closed-system with plenty of liquid inside. $\endgroup$ – Oceanic Spoon Aug 2 '18 at 15:52
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Let's call the rate of condensation of a gas on to a surface as $r_{cond}$ in units of kg/m$^2$ s (i.e. it is a flux). The value of $r_{cond}$ in the case of heterogeneous nucleation depends on the surface temperature and the contact angle of the liquid on the surface. See these links:
The macroscopic shape of the object has no bearing on this result.
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Assuming the outside temperature is colder, then a heat sink slopped gently to drain the water droplets, installed upside down on the ceiling would work.
depending on the construction of your space, this heat sink could be some kind of finned galvanized plate that works both as a roof and ceiling. There is a wide selection on the market. The function of heat sink is to lower the temperature to get below due point.
If outside temperatures are not colder, then the same heat sink should be attached vertically to the walls, to avoid heat accumulated near ceiling by convection in the room.
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Let's imagine condensation as the process of nucleation and growth. The nucleation is a process of forming the embryos and growth will give stable condensed particles. There are two ways you could trigger nucleation events namely, homogeneous and heterogeneous.
In homogeneous nucleation, you will not have any wall/ impurities etc.
This depends on the following parameters,
- undercooling $\Delta T$
- density of condesed (liquid phase) particles $\eta_{l}$
- surface energy (tension) $\gamma_{sl}$
- frequency of molecular collision $\nu$
- probabality of the collision $\sigma$
$N_{homo}$ = $f(\Delta T, \gamma_{sl}, \nu, \sigma)$ $ ->$ a big equation (1)
Your case is heterogeneous since you have a wall to grow nucleation.
So, including the geometric parameters,
$N_{hetro}$ = $N_{homo} * g(\theta)$ $->$ another equation (2)
To answer your question,
For a given undercooling ($\Delta T$), heterogeneous nucleation will be more than the homogeneous nucleation. Also based on the $g(\theta)$ function, the $V$ shape or inverted V - ($\wedge$) will trigger more nucleation compared to the concave or convex shapes.
Please note that the cavity side of the shapes (V or $\wedge$ ) will be facing the medium containing condensing particles.
hope this helps.
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In short: What you want is to MAXIMIZE surface area and utilize a proper environment for condensation (humidity, temp, and dew point). Environment is everything and surface area will provide the most material for water vapor to condense onto.
Look into designs for common heat sinks and you'll find a solution.
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Use of something with a massive surface to volume ratio would be hugely advantageous and this is where biological designs are useful. A red blood platelet has the greatest surface area in relation to its volumetric size. Use of that shape with a thermal sink inside it would encourage condensation but humidity is a vital factor next to ambient temperatures.
