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(Why do bubbles in soda appear to grow in size as they move up?)
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===Why do bubbles in soda appear to grow in size as they move up? ===
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==Why do bubbles in soda appear to grow in size as they move up? ==
  
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A common misconception is that the bubbles in liquids like lager or soda water grow as they reach the surface due to a pressure difference.  While there is clearly a drop in hydrostatic pressure, it is not enough to change the bubbles the amount observed (sometimes doubling in size).  The real answer is that the bubbles actually accumulate carbon dioxide as they rise.  The surrounding liquid tends to be super saturated with carbon dioxide as it dissolves so easily in water.  As the bubble rises, it ingests some of the surrounding carbon dioxide.  In this case, the bubble itself acts as the nucleation site.  This also explains why you don’t observe the bubbles growing in beer such as Guinness; nitrogen does not dissolve as well in the liquid.  [1]
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After the bottle is opened, the partial pressure of the carbon dioxide in the liquid is greater than that of the bubble so the gas travels from the liquid to the bubble.  As the pressure difference remains approximately constant, the bubble growth can be described as:
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[[Image:Eqn5.jpg | center]]
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 +
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where Nbubble is the number of carbon dioxide molecules in the bubble and γ is the proportionality constant, and r is the radius of the bubble.  Assuming that the beer obeys the Ideal Gas Law and that both the bubble pressure and temperature are constant, you can differentiate with respect to time to find:
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[[Image:Eqn4.jpg| center]]
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Now setting this equal to the previous equation allows us to solve for the radius of the bubble: 
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[[Image:Eqn6.jpg|center]] 
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where r_o is the initial radius and v_r is the rate of increase of the bubble’s radius.  [8]
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This increase in bubble size is demonstrated in the picture of bubbles found in coca cola shown below [2]:
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[[Image:Cola.gif| center]]
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==Why do bubbles in soda water move faster than in champagne? And bubbles in champagne move faster than those in lager? ==
  
 
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Revision as of 05:52, 12 January 2009

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About me

I graduated from Duke in 2005 with degrees in Physics and Computer Science. I then moved to Rochester, MN where I worked at IBM for the last three years. I worked mainly on the Blue Gene Life Sciences Applications Team where I ported, optimized, and applied various large scale parallel codes. I just started this fall in the SEAS Applied Physics Program and am planning to work with Dr. Kaxiras.

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Fun facts on soft matter

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Final Project

I was thinking it could be fun to look into various physics about beer. I was thinking of targeting Guinness and other similar beers and the role that Nitrogen plays. I would look at things like the science behind 'the perfect pour' and an explanation for why the bubbles in the Guinness glass appear to be moving downward when conventional intuition suggests they should be rising.

Dr. Morrison, do you think this would be a good focus? I was considering expanding into either looking at other types of beer that use different gases or else looking at the larger view of nitrogen gas in foods. I've been reading about the culinary foam Ferran Adria spoke about and thought that could be interesting to look into. What do you think?

Update: Just looking into the role of bubbles in various drinks seems to offer a lot of material so I've decided to focus my paper there. I'm going to talk about the following topics:

1. Why do Guinness bubbles appear to move down?

2. Why do bubbles in soda appear to grow in size as they move up?

3. Why do bubbles in champagne move faster than bubbles in soda or lager?

4. Why does the champagne in a woman's glass go flat faster?

Explanation of Bubble Behavior in Various Beverages

Introduction

There are many interesting behaviors observed regarding bubbles in various beverages that have baffled people over the years. For instance, many scientists have argued about the direction that Guinness bubbles seem to move for years. This discussion will focus on answering this question as well as explaining other questions relating to bubbles such as: why do the bubbles in soda seem to grow? Why do bubbles accelerate? Why are they faster in soda than in lager? Finally, why does a woman’s champagne go flatter faster than a man’s? These questions are all explained through the physics of bubbles dealing with factors like buoyancy and drag forces and surfactant levels.

Why do Guinness bubbles appear to move down?

It had been a long standing debate in bars around the world until scientists in 2004 finally solved the dilemma: do Guinness bubbles really move down? Intuition and experience with other liquids would tell us that the bubbles should have a higher buoyancy than the surrounding liquid which would cause the bubbles to move upward. Many people over the years have argued over whether or not the bubbles in Guinness actually did move up or down. For a long period, it was argued that people suggesting the bubbles moved down had simply sampled too much. Through thorough investigation, it has been proven that the bubbles we see do actually move down. In fact, the bubbles in the glass actually move both up and down. Dr. Clive Fletcher of the University of New South Wales first explained the phenomenen using computer simulations of complex fluid dynamics in 1999 and Dr. Zare of Stanford in collaboration with Dr. Andrew Alexander of Edinburgh University followed up with experimental proof that matched the simulations in 2004. [1,2]

Flow of the bubbles

Dr. Fletcher’s animations showed that to begin with, all sizes of bubbles will naturally want to rise. This is consistent with traditional theories of fluid dynamics suggesting that gas bubbles are lighter than liquid and therefore experience a buoyancy force driving them upward. However, in moving upward, the bubbles will drag some liquid with them. As the bubbles in the center of the glass (and therefore unaffected by the glass) will move to the surface at a faster rate, the liquid in the center will be dragged up at a similarly faster rate. As the liquid must eventually return to the bottom of the glass to conserve mass, a vortex of recirculating liquid is created. As the liquid moves downwards near the glass wall, the bubbles are impacted by a drag force attempted to pull them downwards as well. [1]

The buoyant force of a spherical bubble is calculated via Archimedes’ principle which states that the force is proportional to the volume of beer displaced:

Eqn1.png

In this case Vbubble is the velocity of the bubble, beer is the density of the beer, and bubble is the density of the beer. [7] Assuming that the bubble is small enough and moves slowly enough that it retains its spherical shape, this equation can be written in terms of the radius of the bubble as follows:

Eqn2.jpg


As it rises, the bubble is subjected to the drag force discussed above. This is represented by the following equation:

Eqn3.jpg

The large bubbles have enough buoyant force acting on them to overcome the drag, but the smaller bubbles, those smaller than .05 mm diameter, succumb to the drag force and are moved down. As this occurs on the outside of the glass, the bubbles moving downward are the only ones visible to the observer. This means that while the bubbles move both up and down, they appear to simply be moving in a downward manner. [1]


You can see the bubble tracks shown below:


Figure 1. Bubble tracks showing the 1mm bubbles (yellow)moving upwards but the 60 micron bubbles (red) being dragged down[2]

Dr. Zare and Dr. Alexander provide a clear step by step overview of the process:

Steps.png Pic7.gif

Step 1. Let's start at the point where you have just poured your pint of Guinness, and it is starting to settle. At the inside surface of the glass, the bubbles are touching the walls of the glass and they experience drag - just in the same way as you can feel if you slide your finger along a glass surface. At the center of the glass, the bubbles are not touching the walls, and are free to go up: this is what bubbles of gas really want to do when they are in a liquid, as we are used to seeing.

Step 2. The bubbles at the center rise rapidly until they get to the top, just below the head (the "froth"). In doing this, they have pushed and pulled the surrounding liquid with them. At the top, this liquid flowing upwards hits the surface and flows outwards towards the edges of the glass.


Step 3. The current is directed downwards by the edges of the glass. As the flow moves downwards in waves, it pushes and pulls the bubbles that are hanging around at the edges of the glass. The flow can be seen as the dark lines of liquid (no bubbles) that wave quickly down the inside of the glass.


Step 4. What goes around comes around. More bubbles flow up at the center and the circulation continues.


Step 5. Eventually the settling process comes to an end. More and more bubbles have been deposited into the head of the beer during the settling, and the cycle loses momentum.


Step 6. In summary: bubbles at the center rise up and create a circulation in the glass. The circulation causes bubbles at the edge of the glass to be pushed downwards. [2]


Other Factors

Now this work explains the overall reasoning of why Guinness bubbles appear to move in a downward direction, but it leaves many questions left unanswered. For example:


Is the glass shape important?

Does viscosity play a role?

Is the fact that Guinness bubbles are nitrogen and not carbon dioxide playing a role?


The experimental work completed by Zare and Alexander addressed these points. They proved that the first two points: glass shape and viscosity actually had little effect on the bubbles. While the tulip shaped glass is ideal for locking in the aroma and hops for tasting, it actually does little to change the motion of the bubbles. The groups conducted the experiments in a variety of curved and straight glasses and found that while the patterns may change, the effect remained. As for viscosity, an initial reaction to this work is that Guinness is such a dense beer that it is likely much more viscous than other liquids and therefore the liquid will flow more slowly. This, however, is not that case. While most people view Guinness as an extremely thick and dark beer, its viscosity really is only slightly different than water. This slight difference is no where near enough to actually impact the movement of the bubbles.


The third question, the issue of the type of bubbles, is actually significant. While this effect of the circulation of the liquid throughout the glass actually can occur in any liquid, the type of bubbles used in Guinness makes it much more apparent. Unlike most soft drinks and other beers, the gas used in Guinness is nitrogen instead of carbon dioxide. The bubbles produced are much smaller. This gives Guinness its creamy texture but also means that the bubbles will be much more easily moved about by the liquid. As shown in the CFD simulations, it was only bubbles below 60 microns that were small enough to be effected by the drag force enough that they actually move downward. Another important point that will be discussed in more detail in the following sections , is that carbon dioxide bubbles tend to grow as they move up in the glass. This makes them much less likely to be affected by the drag. [2]


Aside from the size of the bubbles, the other important difference between Guinness and other liquids is the coloring. The sharp contrast in colors makes the actions of the bubbles much more apparent. The liquid is a very dark ruby due to the manner in which the malted barley is prepared. It’s roasted in a similar way to coffee beans which in turn gives the liquid its distinct dark color. The nitrogen bubbles cause the light creamy white head which makes the movement of the bubbles in the liquid much more apparent. [3] Furthermore, the nitrogen bubbles move extremely slowly at only 2 cm/s which make it much easier to observe their motion. [4] Zare and Alexander conducted further experiments to prove that these results appear in other liquids as well. The link below shows the same actions observed in Boddingtons (another draught flow beer)


http://www.chem.ed.ac.uk/guinness/movies/anim12c.mov

Still going further, they created an experiment to show the result occurring in water as well. They emulated the bubble creation placing a tube with fine whole in the bottom in the center of the glass. The bubbles were created through these holes and would then rise and exhibit the same circular flow seen in Guinness. [2]

http://www.chem.ed.ac.uk/guinness/movies/anim24a.mov


Why do bubbles in soda appear to grow in size as they move up?

A common misconception is that the bubbles in liquids like lager or soda water grow as they reach the surface due to a pressure difference. While there is clearly a drop in hydrostatic pressure, it is not enough to change the bubbles the amount observed (sometimes doubling in size). The real answer is that the bubbles actually accumulate carbon dioxide as they rise. The surrounding liquid tends to be super saturated with carbon dioxide as it dissolves so easily in water. As the bubble rises, it ingests some of the surrounding carbon dioxide. In this case, the bubble itself acts as the nucleation site. This also explains why you don’t observe the bubbles growing in beer such as Guinness; nitrogen does not dissolve as well in the liquid. [1]


After the bottle is opened, the partial pressure of the carbon dioxide in the liquid is greater than that of the bubble so the gas travels from the liquid to the bubble. As the pressure difference remains approximately constant, the bubble growth can be described as:

Eqn5.jpg


where Nbubble is the number of carbon dioxide molecules in the bubble and γ is the proportionality constant, and r is the radius of the bubble. Assuming that the beer obeys the Ideal Gas Law and that both the bubble pressure and temperature are constant, you can differentiate with respect to time to find:


Eqn4.jpg


Now setting this equal to the previous equation allows us to solve for the radius of the bubble:


Eqn6.jpg


where r_o is the initial radius and v_r is the rate of increase of the bubble’s radius. [8]

This increase in bubble size is demonstrated in the picture of bubbles found in coca cola shown below [2]:

Cola.gif


Why do bubbles in soda water move faster than in champagne? And bubbles in champagne move faster than those in lager?

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