Bubbles Big and Small

Posted by jns on 24 October 2007

Bubbles seem to be on the net’s mind today. I haven’t kept all the references (here’s one: “Scientists map near-Earth space bubbles“) but it seemed that I kept reading things involving bubbles.

Now, I’ve long been fascinated by bubbles although, despite my being a scientist with a history of doing some hydrodynamics and a relatively keen interest in things dealing with buoyancy, I’ve never worked on bubbles. This is odd, because I’ve long had a question about bubbles that I’ve never answered — probably because I never spent any time thinking about it. Now, apparently, I have to give it some thought.

My question is not particularly well formed, which makes it not a terribly good scientific question.^* Nevertheless, I’ve always wondered what it is that determines the bubble size in effervescent drinks. In all classes of drinks with bubbles — soda, beer, champagne, effervescent water — there are those that have smaller bubbles and those that have larger bubbles. As a rule, I tend to prefer smaller bubbles, by the way.

The last time this question crossed my mind and there were people around who might agreeably talk about the issue, we talked about it but came to no conclusion. I think our problem was that we were imagining that it was the effect of bottle size or the shape of a bottle’s neck or some similar incidental phenomenon that determined bottle size, otherwise assuming that all carbonated beverages were otherwise equal. It now seems to me that making that assumption was rather naive and silly.

My thought today is that the bubble size is determined locally in the fluid, that is to say by the physical-chemical environment in the immediate vicinity of the bubble.^# It seems to me that there are two questions to consider on our way to the answer:

1. Why do bubbles grow?
2. Why would a bubble stop growing?

The answer to the second question, of course, might be implicit in the answer to the first.

To begin: what is a bubble? Bubbles happen in mixtures of two or more substances when little pockets of stuff-B collect inside predominantly stuff-B. That means there’s a lot more of stuff-A than stuff-A, which is to say that we usually see bubbles of stuff-B when there’s only a little bit of stuff-B mixed in with a whole bunch of stuff-A.

To be concrete, let’s talk about bubbles of carbon-dioxide () in effervescent water, say “San Benedetto” brand.^% Now, bubbles have very few features of any physical importance: their sizeis an important one, and the interface between the inside and outside of the bubble, which we might call the surface of the bubble. Some chemical properties of the stuff inside and outside the bubble might matter, too, but let’s save that for a moment.

Now, imagine that we start observing through our clear-glass bottle of San Benedetto water before we take the cap off. The water is clear and there are no bubbles. However, we are aware that there is dissolved in the water. In fact, we know that (in some sense) the is under pressure because, when we unscrew the cap, we hear a “pffft” sound. Not only that, bubbles instantly appear and float up to the surface of the water, where they explode and make little “plip plip plip” sounds.

What makes the bubbles grow? They start out as microscopically tiny things,^** gradually grow bigger, until they are big enough to float to the top of the bottle and explode.

To be more precise, bubbles of grow if it takes less energy to let a molecule into the bubble across its surface than it costs to keep it outside the bubble. (This is a physicist’s way of looking at the problem, to describe it in terms of the energy costs. A chemist might talk about it differently, but we end up describing the same things.)

What causes the bubble to float up? That’s a property called buoyancy, the name of the pseudo-force that makes things float. It’s determined by the relative density of the two substances: less dense stuff floats up, more dense stuff floats down. Notice that the use of “up” and “down” requires that we have gravity around — there is no buoyancy in orbit around the Earth, for instance.

Bubbles, then, will start to float up when they get big enough that they have enough buoyancy to overcome the forces that are holding them in place. That basically means overcoming drag produced by the water’s viscosity, which works kind of like friction on the bubble — but that’s a whole other story, too.

Are we near the answer about bubble size yet? Well, here’s one possibility: bubbles grow until they are big enough to float up to the surface and pop, so maybe they don’t get bigger because they shoot up and explode before they have the chance.

I don’t like that answer for a few reasons. We began by observing that different brand products had different size bubbles, meaning different size bubbles exploding at the surface, so something is going on besides the simple matter of dissolved in water, or else they would all have the same size bubbles. You can look at the bubbles floating up from the bottom and see that they are different sizes in different products to begin with and they don’t change size much on the way up. Thus: bubbles grow very quickly to their final size and their size does not seem limited by how it takes them to float up. Another reason: sometimes bubbles get stuck to the sides of the bottle, but they don’t sit there and grow to arbitrary sizes; instead, they tend to look much like the freely floating bubbles in size.

There could be a chemical difference, with different substances in the drink limiting the size of the bubbles for some chemical reason. Certainly that’s a possibility, but it’s not what I’m interested in here because I want to explain how there can be bubbles of such obviously different sizes in different brands of what is pretty basically water with insignificant chemical differences in their impurities.

That seems to leave us with one option: the energy balance between the inside and outside of the bubble. Whatever it was that caused it to be favorable for dissolved to rush into the bubble at first has some limit. There is some reason that once the bubble reaches a particular size, the energy balance no longer favors crossing preferentially from water to bubble interior and the bubble stops growing.

Now we can look at the “energy balance” matter a little more closely. There are two forces at work. One is osmotic pressure. Osmosis describes how stuff-A moves relative to stuff-B across a barrier (in this case the surface of the bubble); osmotic pressure is the apparent force that causes one substance to move relative to the other across the interface.

The forces at work keeping the bubble in shape are two. One is osmotic pressure inside the bubble, where there is a significantly higher concentration of than in the fluid outside, so it creates an outward pressure at the bubble’s surface. The other is the pressure of the water on the surface of the bubble, trying to keep it from expanding.

So, it looks like the size of the bubbles are determined by a balance between water pressure –determined by the water’s density and gravity — and osmotic pressure inside the bubble, which is caused by the relative concentrations of inside and outside the bubble.

It would seem, then, that bubbles grow in size until the water pressure on the bubble, which is trying to squeeze it smaller, matches the osmotic pressure of the inside the bubble, which is trying to expand the bubble.

This works for me, because I know that the osmotic pressure of the is going to depend on how much was dissolved in the water to begin with. My conclusion, roughly speaking: drinks with bigger bubbles had more carbon-dioxide dissolved in them to start with than drinks with smaller bubbles. At least, that’s my working hypothesis for now, disregarding lots of other possible effects in bubbles. I’ll have to do some experiments to see whether it holds up.

This is just my answer for the moment, my provisional and incomplete understanding. It’s not a subject you can just look up on Wikipedia and be done with. (The articles at about.com that discussed bubbles in sodas I didn’t find credible.) I found several references (one, two, three) that, in journalistic fashion, touted the research of University of Reims’ Gerard Liger-Belair as “Unlocking the Secrets of Champagne Bubbles”, but in fact it was a contribution to nucleation and had nothing to offer about bubble size. The third reference, by the way, has a glaring error in the second sentence, and the rest of the text suggests that the author of the story had little understanding of what was being talked about.

Here, in fact, is a piece about bubbles by Liger-Belair (mentioned in the last paragraph), called “Effervescence in a glass of champagne: A bubble story“. It’s a nice read but it skirts ever so gracefully past the question of bubble size.

As we say in the biz: more research is indicated.
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^* My usual contention being that most of the work of finding the answer lies in asking a good question.

^# What might “immediate vicinity” mean, you ask? In physicist fashion, I’m going to suggest that length-scales in the problem will be roughly determined by the size of the bubbles, so let’s take “immediate vicinity” to mean anything within 1, or 2, or maybe 3 bubble radii. (On closer examination we’d have to consider thermal diffusivity and mass-species diffusivity and such things, but that’s for a more sophisticated analysis.)

^%“San Benedetto” is the brand of effervescent water that we prefer here at Björnslottet, in case you were wondering.

^**But why! Bubbles first start (“nucleate”) either around small impurities or bits of dust in the fluid, or just from fluctuations in the local concentration of bubble stuff. Let’s leave that as an interesting question for another time and just assume they get started somehow.