Questions about fusion point of water, experiments

[fluidistic]

I've been playing in the lab with distilled water and noticed that the smaller water drops are, the longer I could over cool them. In fact, even with 20 ml of distilled water, I couldn't get it to freeze when it passed by 0.0°C. Instead it would go around -3.5°C, then freeze almost instantly and the temperature would also rise almost instantly up to 0.0°C.
With small drops I could reach easily a temperature of -8 to -13 °C before they would freeze. And with very very small drops, they could reach around -15°C or so.
I'd have thought that the smaller the sample of water, the faster it would freeze but the opposite occurred.
1)Why is it so?
I've read on the Internet that an argument used to explain Mpemba's effect is that boiled water will evaporate faster than "cold water" (this is true), but then they say that this imply that it will freeze faster.
According to what I've done in the lab, less water would imply slower freeze due to a longer over cooling. 2) So are their argument flawed?
I tried to get rid of over cooling by vibrating the freezer, I could see (thanks to a camera inside the freezer) that all the surface of the drops was affected by my vibrations but it would not get rid of the over cooling...
So basically my first question is equivalent to ask why is there a greater over cooling when the water sample is smaller.
Thank you.

 

[haruspex]

Let me say straight off that I don't know the answers to your questions, but here are some thoughts.

You would indeed expect the smaller drops to freeze faster in the sense that, having made the ambient temperature low enough to freeze them, they should freeze in less time. (And that is how the offered explanation for the Mpemba effect works.) But in your experiment you are lowering the temperature very slowly and seeing what temperatures they freeze at. I see no reason to suppose the smaller drops would freeze sooner (or later) in that sense.

Surface tension:
Is it possible that surface tension opposes freezing, since the drop has to expand? A smaller drop would be more prone to such effects.
If that's the explanation then it would depend on whether these are drops on a flat surface (as I'm assuming) or in a small flask (so only a horizontal surface, plus some meniscus).

Not as cold as you think?
I don't know how you're measuring the water temperature. Are you quoting the ambient temperature and assuming the water reaches that temperature reasonably quickly? If so, is there some way heat could be creeping in, in proportion to surface area?

 

[fluidistic]

For all the drops, I lowered the ambient temperature to around 0°C or even less than this. But the drops wouldn't freeze due to that. Instead, I placed them over a horizontal aluminum plate to which I was controlling the temperature. With this configuration I had 3 thermometers (I think it was 2 thermocouples and 1 thermistor), one inside the drop, one inside the aluminum plate and one right over the drop. They would not differ by more than approximately 3°C.
I noticed that bigger drops would freeze faster because they couldn't get over cooled as low as the smaller drops.
For the 20 ml solutions the set up was different. I placed them in a freezer which was set at -20°C and lower (up to -35°C). The heat transfer in that case was with all the surrounding, especially the surface, ground and sides of the small container (I don't know the name of it but the material is glass). Such a "huge" amount of water couldn't go lower than -3.5°C. When it reached that particular temperature, it would start to freeze quite fast and the temperature would rise up to 0.0°C and was stuck there for a long time until the freezing was complete.

By the way I know the reason why the smaller drops take more time to freeze. It's because they won't freeze at 0.0°C nor anywhere close to this. They will get over cooled (I found no way to avoid this) up to much lower temperatures than bigger drops would.
I find few information of the temperature of clouds. I found a website (http://www.cas.manchester.ac.uk/resactivities/cloudphysics/background/ice/) where it states that below -39°C all drops should be frozen. Thus I'm guessing that it's common to have small drops at very low temperatures compared to 0°C.