Bubbles Big and Small

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.

More Undular Bores

For those who enjoyed the pictures a few days ago of undular bores — atmospheric waves visible in clouds — here are a few more treats via NASA’s Earth Observatory project.

This time the waves are in the atmosphere off the west coast of Africa, in a couple of satellite photos captured by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra and Aqua satellites on October 9, 2007. Take a few moments to read the informative text on the page, too.

(While you’re there, you might want to look at the dramatic satellite photos of the wildfires in Southern California.)

Undular Bores

Here is “Science @ NASA” again, sending me another interesting story with pretty pictures. This one — they say for shock value — is about “undular bores”. What they’re talking about is waves in the atmosphere that show up dramatically in cloud patterns.

I have a personal interest in all things waves because they were one of the things I studied in my former life as a physicist. They were waves in many forms that interested me, too, since I studied fluid motions, in which one can find physical waves, and field phenomenon, in which the waves are mathematically abstract but still represent real phenomenon.

In looking at these wave pictures coming up, it might be fun to know that in the ocean — or on any water surface — waves come in two types, call them “waves” (the big ones) and “ripples” (the little ones). Ripples are about finger sized, while waves are more body sized. Both are caused by disturbances, generally wind, but they undulate for different reasons. Ripples ripple because of the surface tension of the water; waves wave because of gravity, or buoyancy, in the water. Most water waves in the ocean, and those that break on shorelines, are generated by strong winds associated with storms that can be thousands of miles away.

Anyway, air also has buoyancy (remember: hot air rises, cool air sinks — the hot air is buoyant relative to the cool) and can sometimes show some very large scale waves, with wavelengths of about a mile. When there are clouds around they can make the waves dramatically visible. They can be caused by storms moving about as high-pressure centers collide with low-pressure centers and hot-air masses encounter cool-air masses.

Here’s Tim Coleman of the National Space Science and Technology Center (NSSTC) in Huntsville, Alabama:

“These waves were created by a cluster of thunderstorms approaching Des Moines from the west,” he explains. “At the time, a layer of cold, stable air was sitting on top of Des Moines. The approaching storms disturbed this air, creating a ripple akin to what we see when we toss a stone into a pond.”

Undular bores are a type of “gravity wave”—so called because gravity acts as the restoring force essential to wave motion. Analogy: “We’re all familiar with gravity waves caused by boats in water,” points out Coleman. “When a boat goes tearing across a lake, water in front of the boat is pushed upward. Gravity pulls the water back down again and this sets up a wave.”

[excerpt from "Giant Atmospheric Waves Over Iowa", Science @ NASA for 11 October 2007.]

There are two gorgeous visuals to see by clicking the link. The first is a video of the undular bores over Iowa. I’d suggest watching the animated gifs rather than the video because the gifs extract just the interesting parts between 9:25 and 9:45, and it keeps playing.

Then, just below that, don’t miss the radar photograph, which shows the train of waves with stunning clarity.

Now, as if that weren’t enough, I found this cool video on YouTube, intended to demonstrate “Gravity Waves” in the atmosphere, of which it is a beautiful example. But wait! Incredibly, this video also shows undular bores, over Iowa (but Tama, rather than Des Moines), as recorded by the same television station, KCCI!

Titanic Lakes

This just in from “Science @ NASA”:

Newly assembled radar images from the Cassini spacecraft are giving researchers their best-ever view of hydrocarbon lakes and seas on the north pole of Saturn’s moon Titan, while a new radar image reveals that Titan’s south pole also has lakes.

Approximately 60 percent of Titan’s north polar region (north of 60o latitude) has been mapped by Cassini’s radar. About 14 percent of the mapped region is covered by what scientists believe are lakes filled with liquid methane and ethane:

The mosaic image was created by stitching together radar images from seven Titan flybys over the last year and a half. At least one of the pictured lakes is larger than Lake Superior.

[excerpt from "New Lakes Discovered on Titan", Science @ NASA, 12 October 2007.]

Isn’t that fascinating: “hydrocarbon lakes” filled with “liquid methane and ethane”!

The photograph accompanying the press release is really quite lovely — it’s what attracted my attention in the first place. Follow the link above to see the photomosaic.

My Sputnik Childhood

I nearly let pass this notable milestone: 50 years ago today the Soviet Union^* launched the first artificial Earth-satellite, called Sputnik. It was a tiny thing — suitable I suppose to being the first baby of the birth of the space age — just 24 inches across and weighing only 184 pounds. It was made of shiny polished aluminum, so that it reflected sunlight and was easy to see from Earth. It carried two radio transmitters that emitted continuous signals that didn’t say anything, not that they had to. The message was obvious.

Launching a satellite, in principle, is a simple thing. Point it in the right direction, accelerate it to a speed of something like 11 km/s (or about 7&miles/s)^# and it goes into orbit around the Earth. In practice this is not so easy. It takes a lot of rocket fuel to accelerate even 184 pounds to a speed near 7 miles/second, and that fuel takes more fuel to accelerate it, and that fuel takes more fuel to accelerate it, and so on.^& After you figure all that out, you end up with a very tall, multi-stage rocket that is very impressive when it takes off, even for the smallest payloads.^**

Then there’s all that goes into getting all the stuff to the launch-pad so it can take off. There’s a remarkable amount of engineering, mission planning, fabrication, transportation, and organization that goes into one of these events, and they only got bigger as the missions got more sophisticated. A modern space-shuttle launch comes at the end of years of planning and months of preparing the payloads; the launch itself involves hundreds of people at locations scattered around the world.

And it all started with that tiny little Sputnik. I was not quite two years old at the time, so I don’t remember its happening. I didn’t have any memorable artificial-satellite experiences until I went outside one night to see a transit of an Echo communications satellite some years later.

It surely affected my life, though. Sputnik was so alarming to the powers in Washington — perhaps to the average American, too — that we, the entire country, suddenly developed a keen, new interest in science and engineering, and in science, engineering, and mathematics education, and I was undoubtedly a product of that. When people today wring their hands about a shortage of scientists and engineers — which hasn’t been true for decades — I imagine it’s an echo from that time.

People looking to justify our commitment to sending a man to the moon thought of all sorts of alleged “spin-offs” from the space program, and proclaimed the marvels of Tang, Teflon, and Velcro, none of which were invented by NASA, nor invented for NASA. Computer systems and microelectronics got some boost, but the average computer user today would be shocked to see the primitive computer hardware that got Neil Armstrong to the moon.

One of the things that was touted as an accomplishment of NASA, a spin-off of the moon program, was project management. I think that may be a real contribution. My experience from doing a couple of space-shuttle missions is that the planning process is not fast nor particularly efficient, but it accomplishes its goals with deliberation and thoroughness. That care and deliberation has suffered some in recent years, perhaps a result of political and management hubris that believed we must know how to cut corners by now.

As a product of the Sputnik age, I take the growth of modern technology and America’s leading role in developing it rather for granted, but it’s far from established that we shall always be the leader. I believe that our remarkable achievements from the 80s and 90s in developing the personal computer, for instance, resulted from the investment our country made in science and technology education in the 60s, coupled with national interest, motivation, and pride.

Those emotions and commitments take nurturing; they musn’t be taken for granted or they whither. I fear that that’s been happening in recent years, and that our complacency will catch up with us if we do nothing about it. The renewal won’t be fast, because it takes new generations to grow into it, although current generations can do the plowing and fertilizing.

That’s part of the reason that I started Ars Hermeneutica, Limited in 2004, and that’s the big motivation behind our vision of a scientifically literate America.

I didn’t set out to write this as a justification or a motivational piece or an advertisement — or even as a fund-raising appeal^## — but I guess these all have one thing in common: that I care deeply about them.
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^*Which, one notes in passing, no longer exists. Things change, and even countries don’t last on forever.

^#The speeds are near the escape velocity from Earth, which is a bit more speed than is needed to establish an orbit, but it gives an idea of the speeds involved.

^&It’s not an infinite sum — the sequence does converge, and it has an exponential form, for roughly the same reason that the equation for compound interest has an exponential form. If you want details, Google “rocket equation”.

^**Note, however, that there are big differences in actual acceleration depending on the payload and the rocket chosen to launch it. Those of us accustomed to the Saturn V rockets launching an Apollo mission, or the rockets for shuttle launches, imagine a stately launch in which the heavy payloads seem like they’re never going to move, then they finally stroll off into the wild blue yonder. With that in mind, seeing once the launch of a sounding rocket, which doesn’t even attain orbit, was a surprise: it jumped off its launch-pad like a startled rabbit.

^## Although, it bears repeating that Ars Hermeneutica is a 501(c)(3) tax-exempt corporation, and contributions are tax deductible. Click to see how to Support Ars Hermeneutica.