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As a concrete example, consider boiling water. As water boils, bubbles form which rise to the surface. I know that things rise because of the Archimedes principle, however as far as I understand it, it works because water from below pushes the bubbles upwards.

My question is, (*) how did the water get below the bubble in the first place? After some thinking, I came up with the following explanation. At first, water near the bottom of the vessel heats up, releases dissolved gases and these gases expand, while in contact with the bottom of the vessel.

The bubbles continue expanding, which decreases its pressure. I am assuming that the increase in pressure due to rise in temperature is compensated because the gases expand rapidly (is this correct?). Also, I take it that (in other situations) any bubbles formed will try to expand even if the water is not being heated.

As the bubble expands, and pressure decreases, the water close to the bottom of the vessel is able to "break into" the bubble because (1) water is at a higher pressure at the bottom, so it is the first place where the water can "break into" the bubble and (2) the decrease in the pressure inside the bubble allows the surrounding water to enter it.

This way, the surrounding water gets under the bubble and then lifts the bubble to the surface.

Now, I am not sure if this is a correct explanation. The first question I have is whether (1) is valid, i.e., why can't the surrounding water enter the bubble from all sides, does the pressure difference I mention account for this?

Secondly, what happens if there is no water to enter from the sides of the bubble. To test this, I have the following experiment in mind. Consider a test tube with water and heat it uniformly from the sides and bottom. In this case, what I expect to happen is that the released gases build up at the bottom of the test tube and keep expanding until they pour the water out of the test tube (like milk boiling over).

However, I don't have the equipment to perform such an experiment and I think the experiment above might be very sensitive in that any slight asymmetry might let some water slide to the bottom of the air bubble.

To conclude, does there need to be water below the bubble to push it upwards, i.e., is (*) a valid question? If so, is the explanation above correct and what is the outcome of the experiment I have outlined above.

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Your interpretation is correct.

Single Bubble Case

We have a bubble of vapour surrounded by fluid water, with the vapour having a much lower density than the water. The average gas pressure in the bubble will be equal to the average water pressure around the bubble. But the water pressure changes with the height above the bottom surface, while the gas pressure is nearly constant (due to the density difference).

So, at the bubble top the gas pressure is higher than the water pressure, and at the bottom it's lower. This way, at the bottom water will move into the bubble and at the top, the bubble will move into the water's space. This way, water will eventually fill the space below the bubble, and the higher pressure there will lift the bubble.

Test Tube Case

Now you have a flat layer of vapour beneath the water. As long as this is undisturbed, it will stay this way.

But reality kicks in. The very nature of temperature is movement of molecules. So let's assume a tiny deviation of the vapour/water surface from being flat. Then at the lowest points of that surface, there's a higher water pressure, meaning that water will start to move downward into the vapour. This further decreases the surface flatness, accelerating the effect and soon enclosing at least some portion of vapour in water, creating a bubble.

Surface tension

The explanation so far ignored things like surface tension, cohesion and adhesion. While they are the reason that bubbles grow to a specific size before they start to rise, and that they have a roughly spherical shape, they also make real-world experiments deviate from the reasoning above.

Especially with tubes of only a few millimeters diameter, you can expect the test tube experiment to push out the water despite of the contradicting explanation given above. This will surely not happen with a tube of 10cm diameter.

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  • $\begingroup$ Thank you for this answer, I hadn't thought about it in terms of average pressures, I think that completes the explanation in (1). To summarize, water enters below the bubble from the sides and pushes it upwards and in the case of the test tube, ideally, the flat layer of bubble grows (with continued heating) and pushes the water out because the surrounding water cannot get below the bubble. $\endgroup$ – stackex33 Oct 8 '20 at 11:18
  • $\begingroup$ I think the surface tension part is important - otherwise bubbles would collapse into a shower of microbubbles. $\endgroup$ – Carl Witthoft Oct 8 '20 at 13:36
  • $\begingroup$ @CarlWitthoft Does surface tension pull water (equally in all directions) away from the center of the bubble (thus causing a spherical shape; there's the mathematical reason of energy minimization)? In the absence of surface tension, will the bubble break up into tiny bubbles which then rise to the surface because the water, in the act of breaking the bubble, gets below the microbubbles and pushes them up? $\endgroup$ – stackex33 Oct 8 '20 at 14:21
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Close. When water is heated, the water which is closest to the flame will start to vibrate rapidly such that the hydrogen bonds between the water molecules will break forming a gaseous vapour. These vapours will form bubbles. Because the density of these bubbles are much lower than the surrounding water, they will feel a buoyant force and therefore rise.

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