# How many molecules make a droplet

Hi

I am just wondering about this. How many molecules does it take before you can use the word Droplet in the atmosphere?

As an example, one H20 molecule floating around (interacting occasionally with others, but generally just floating around) would be Vapour.

If two H20 molecules combine (into a dimmer) for a while, is this a water droplet.

What about three or four molecules formed into a polymer – is this a water droplet, or is it still vapour

Say we have some vapour in the air. It raises and adiabatically cools. The molecular speed is reduced sufficiently to prevent the breaking of the hydrogen bonds in a dimmer or polymer, at what stage/number does it become liquid, as opposed to a conglomeration of vapour

Many thanks

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sophiecentaur
Gold Member
Work out the mass of a single molecule of water - easy - using the mass of a proton, for a start - then Two for the Hydrogen atoms and add the Protons and Neutrons in an oxygen atom etc.
Work out the mass of a 'drop' of water (say 1mm^3), using the density of water value that you can easily find.

Divide one by the other and get a pretty big number!

Andy Resnick
I am just wondering about this. How many molecules does it take before you can use the word Droplet in the atmosphere?
Semantics aside, the question itself involves fairly complicated physics: nucleation is a non-equilibrium process. The problem can be approximated by field theories, as an extension of mean-field theory, and a linear approximation is called 'kinetic theory'.

While the basic kinetic results are reasonably easy to understand qualitatively (there is a critical droplet radius below which the droplet evaporates, and above which the droplet continues to grow in size), the quantitative results require understanding the application of fluctuations to thermodynamic processes.

Note also that temperature is a key variable and that in the atmosphere, water droplets generally nucleate around a contaminant and the water is not in a liquid phase.

Landau and Lifgarbagez v. 10 pp 427-431 is a good place to start regarding nucleation and kinetic theory. See also:

http://aerosols.ucsd.edu/classes/sio217a/SIO217ALecture05b.pdf
http://facstaff.unca.edu/cgodfrey/courses/atms455/ppt/nucleation.pdf

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Hi Andy

Thanks for that - I will study the Köhler curve and get to the bottom of this :-)

What I am trying to (not very well at the moment) understand is how vapour changes to liquid.
I understand that in Heterogeneous nucleation (above around -40c) vapour will condense around nuclei but I just don't understand Homogeneous Nucleation. I also understand the Bergeron Process of ice over liquid (due to variations in the vapour pressures)
But (sorry about the silly questions)
At lower temperature (from 0c to -40c) do h2o molecules slow down enough to stop them re-bounding away so form hydrogen bonds.
What actually creates the liquid from vapour

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sophiecentaur
Gold Member
Work out the mass of a single molecule of water - easy - using the mass of a proton, for a start - then Two for the Hydrogen atoms and add the Protons and Neutrons in an oxygen atom etc.
Work out the mass of a 'drop' of water (say 1mm^3), using the density of water value that you can easily find.

Divide one by the other and get a pretty big number!
jeez, that was a dumb first response, wasn't it?

On a higher level - does that mean that the threshold size for a droplet to exist will vary for different pressures and temperatures and that a nucleus of a certain size must be present before one can form? Does every droplet need to have had a nucleus, initially?

that a nucleus of a certain size must be present before one can form? Does every droplet need to have had a nucleus, initially?
Not really but it depends on what you call a nucleus. The droplets can be simply bonded supercooled molecules

Does every droplet need to have had a nucleus, initially?
No, as I understand it. As a cloud rises and adiabatically cools the molecular energy is reduced (so they slow dow, to put it in my terms ;-). This allows hydrogen bonds to form and with less agitation the dimmers stay bonded, then grow into polymers and so on.

My question was, at what stage do you call a polymer a droplet. Of course some polymers will not have a curved surface so will disapate, but many will.
So assuming (just an average mass here by the way)
O = 16g/mol plus H = 1.1g/mol
So my calculator say that the average H2O
((H = 1.1g/mol X 2 = 2.2) + (O = 16g/mol) = 18.2))

With a mass of 18.2g/mol ? at what stage will a polymer (for example a (H20)2 or (H20)3 or (H20)4 etc etc) become a droplet
Does it take (H20)6 or (H20)200 or what ?

Is there (dependent on the temp and vapour pressure) a curvature minimum required ???

Oh and wikithingy is simply wrong about this so I ignored it. The page needs rewritting. Any page that states that air can "hold" # amount of water needs redoing.

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I think its a rather simple fix. A droplets requirements are for the liquid to do 2 things. Accumilate (or seperate), and then drop. The amount needed for this would differ depending on the liquid. For instance corn syrup would be more molecules then water.

Sammy8
I like simple.

So a simpler dimmer - (H20)2 - can be a droplet (or it IS a droplet) until in splits. If it doesn't agetate apart then it provides a substrate for other bond on to.

Is that right (sorry about the dim questions, just trying to understand)

sophiecentaur
Gold Member
Oh and wikithingy is simply wrong about this so I ignored it. The page needs rewritting. Any page that states that air can "hold" # amount of water needs redoing.
Didn't you know "The air is like a sponge" take it from there. :rofl:

How many molecules does it take before you can use the word Droplet in the atmosphere?
I don't believe there is any "official" number. The mean size of a cloud droplet is about 10 microns, but obviously it must grow into that size from the cloud condensation nucleus (CCN). Most of this growth is from condensation, not accretion. This is because droplets of that size have a terminal velocity of some 1 cm per second, and falling droplets tend simply to push other droplets out of the way rather than coalesce with them.

By the way, it is unlikely that more than 0.1% of all condensation involves dimers, and polymers in atmospheric water vapor are even more rare.

An excellent introduction to cloud physics is:

R. R. Rogers, M. K. Yau; A Short Course in Cloud Physics; Third Edition; Elsevier, New York, 1989.

Not dim at all. I think you got it, but I can clarify im sure. When I said accumilate it would be as the original post had mentioned atmospheric. Seperating would be a mass or majority of liquid, and some slowly overflows untill it seperates and then drops. If it cant meet those standards, then it would be a different classification.

Now the real question is, does the same amount of H2O molecules make a drop in either atmospheric or majority conditions? Assuming ofcourse that the drop off the majority doesnt have to travel down a surface to begin the droplet.

Sammy8
I like simple.

So a simpler dimmer - (H20)2 - can be a droplet (or it IS a droplet) until in splits. If it doesn't agetate apart then it provides a substrate for other bond on to.

Is that right (sorry about the dim questions, just trying to understand)

Dotini
Gold Member
Does every droplet need to have had a nucleus, initially?
I'm not sure droplets in ground fog need a nucleus. But for clouds to coalesce high in the atmosphere, nucleation is needed.

Respectfully,
Steve

I'm not sure droplets in ground fog need a nucleus. But for clouds to coalesce high in the atmosphere, nucleation is needed.
Ground fog is simply a cloud on the ground. There is no significant difference between the two populations of droplets. Both require CCN.

sophiecentaur
Gold Member
Ground fog is simply a cloud on the ground. There is no significant difference between the two populations of droplets. Both require CCN.
That has to make sense. How would a water molecule know where it was and how to behave?

cmb
How many molecules does it take before you can use the word Droplet in the atmosphere?
As your question necessarily requires, by definition, the atmosphere for the droplet to be in, then an answer could be the number of molecules in the atmosphere, which I reckon is around 1.12 x 10^44.

1) I am just wondering about this. How many molecules does it take before you can use the word Droplet in the atmosphere?

2) As an example, one H20 molecule floating around (interacting occasionally with others, but generally just floating around) would be Vapour.

3)If two H20 molecules combine (into a dimmer) for a while, is this a water droplet.What about three or four molecules formed into a polymer – is this a water droplet, or is it still vapour

4)Say we have some vapour in the air. It raises and adiabatically cools. The molecular speed is reduced sufficiently to prevent the breaking of the hydrogen bonds in a dimmer or polymer, at what stage/number does it become liquid, as opposed to a conglomeration of vapour
1) Unless there is some phenomenological difference between an agglomeration of water molecules and a droplet, the question is meaningless scientifically and therefore purely semantic.

2) At 25°C, the average water vapor molecule undergoes more than a billion inter-molecular collisions with other vapor molecules each second, at equilibrium vapor pressure. Statistical mechanics tells us that some proportion of these collisions will result in bonding. This bonding is extremely ephemeral. The next collision may result in the breaking of the first bond or may result in a second bonding.

3) It is a liquid if being a liquid is useful to your undertaking. It is a vapor if being a vapor is useful to your undertaking. Call it whatever you like. Its physical characteristics and parameters remain the same, regardless of terminology.

4) Vapor temperature measures the mean of a distribution of kinetic energies. This curve will be flatter at high temperatures and more peaked at lower temperatures. However, its range of values remains essentially the same. Some molecules will always have energies in excess of bonding values. Thus every agglomeration of molecules or droplet will be undergoing both gross condensation and gross vaporization in any giver time interval.

One germ is too small to see but if you have a whole tablespoon full of germs can you see them.

It would have something to do with water's surface tension, I imagine, but I don't actually know the answer. (I thought "polymer" refers to something covalently bonded, not something with temporary hydrogen bonds. Again though, I don't actually know.)

It would have something to do with water's surface tension, I imagine, but I don't actually know the answer. (I thought "polymer" refers to something covalently bonded, not something with temporary hydrogen bonds. Again though, I don't actually know.)
Since surface tension is a product of the hydrogen bonding force, one might assume that it is present in even a very small number of bonded water molecules.

You are correct as to the definition of polymer. Properly used, the term polymer refers to molecules that are covalently bonded, often in a replicated chain. However, I have noticed in my readings in water science that the term is occasionally used to refer to structured assemblies of water molecules bound only by hydrogen bonds. I don't like this usage, myself, but it is fairly common.

cmb
Since surface tension is a product of the hydrogen bonding force...
Could you please explain what you mean?

Water is a polar molecule. Charge all over. Why is 'hydrogen' the sole key to the 'bonding force', then?

cmb
Properly used, the term polymer refers to molecules that are covalently bonded, often in a replicated chain.
I wasn't aware that there were any polymers that weren't chains of replicating links. Which polymers aren't a chain of repeating monomers?

Could you please explain what you mean?

Water is a polar molecule. Charge all over. Why is 'hydrogen' the sole key to the 'bonding force', then?
Yes water is a polar molecule. It has two positive charges (or one bimodal positive charge) at the end with the hydrogen atoms; and it has two negative charges (or one bimodal negative charge) at the end with the two "lone pairs" of electrons.

Surface tension is usually viewed as a tessellated network of water molecules each of which is bonded to four other surface water molecules. Two molecules are bonded at the positive end and two are bonded at the negative end. In surface tension, these four bonded molecules are also seen as being bonded to the two adjacent molecules of the four perimeter molecules. These bonds are not saturated, hence the tessellation.

These bonds are described in the literature as "hydrogen bonds". The usage goes back to Moore and Winmill in 1912.

In a water droplet, these bonds are extremely ephemeral. The average surface molecule on a water droplet is replaced some ninety billion times each second.

I wasn't aware that there were any polymers that weren't chains of replicating links. Which polymers aren't a chain of repeating monomers?
You are absolutely right. Polymers are not my field, therefore my error on the part of vagueness.

I wasn't aware that there were any polymers that weren't chains of replicating links. Which polymers aren't a chain of repeating monomers?
Well proteins are meant to be polymers and the amino acids aren't all the same and don't repeat. A similar story with DNA. Of course that depends if they stictly are polymers.
Since surface tension is a product of the hydrogen bonding force, one might assume that it is present in even a very small number of bonded water molecules.
2 molecules don't make a surface, though. I'd say something could only be said to have surface tension if it has a surface, which means there has to be molecules in the centre which aren't part of the surface. Furthermore, the H-bonds would have to line up on this surface to make a "surface tension". Only then, I think, it would be OK to call it a droplet. However, I don't actually know, I am just speculating.

1) Unless there is some phenomenological difference between an agglomeration of water molecules and a droplet, the question is meaningless scientifically and therefore purely semantic.

2) At 25°C, the average water vapor molecule undergoes more than a billion inter-molecular collisions with other vapor molecules each second, at equilibrium vapor pressure. Statistical mechanics tells us that some proportion of these collisions will result in bonding. This bonding is extremely ephemeral. The next collision may result in the breaking of the first bond or may result in a second bonding.
And this has to do with the question - how ?

3) It is a liquid if being a liquid is useful to your undertaking. It is a vapor if being a vapor is useful to your undertaking. Call it whatever you like. Its physical characteristics and parameters remain the same, regardless of terminology.
No, the physical characteristics and parameters are different.

4) Vapor temperature measures the mean of a distribution of kinetic energies. This curve will be flatter at high temperatures and more peaked at lower temperatures. However, its range of values remains essentially the same. Some molecules will always have energies in excess of bonding values. Thus every agglomeration of molecules or droplet will be undergoing both gross condensation and gross vaporization in any giver time interval.
You obviously don't understand cloud dynamics. Or, maybe you do? I can’t tell from your answer. Surely a “droplet” (as per the original question) would be the result of a longer term condensation sequence

I asked, what I thought was a perfectly good question. OK it may have been slightly lower down the grand scale of questions - but it was a question all the same.