Submitted by crazunggoy47 t3_y00ioa in askscience
I’m curious, is there a terminal speed of a bubble of air as it rises through the water? And how is it affected by the size of the bubble and the pressure (i.e. depth of the water)? I feel like smaller bubbles rise slower, but I don’t understand why. Surface tension?
Bubbles are ellipsoidal in shape, motion is irregular, and velocity is independent of bubble diameter (U is approx. 28 - 30 cm/sec) for bubbles having radii up to 0.75 cm. For larger bubbles their velocity tends to increase to 35 - 40 cm/sec, but they are not stable and tend to subdivide into smaller bubbles.
www.seas.ucla.edu › stenstro › Bubble
are air bubbles the most efficient mechanism for unaided traveling to the surface through water or is their some other material or form that can do so faster (eg and I'm making this up as an example: styrofoam ball, helium bubble, etc.)?
> I feel like smaller bubbles rise slower
This intuitively makes sense to me...buoyant forces of a bubble are related to volume, but the amount of water that has to move out of the way for the bubble to rise is related to cross sectional area. It takes force for water to move out of the way.... it's got inertia and viscosity after all (Hi Reynold's Number!) so bigger bubbles should rise faster.
I bet there's all sorts of neat bubble physics on exoplanets, given the variety of pressures, temperatures, gravities, and fluids present.
Good point about the square-cube discrepancy here.
And yes, there surely are bubbles nearly everywhere there is liquid. Presumably on Europa (water), Enceladus (water), and Titan (methane), just to name a few.
It seems like an evacuated container with high volume and low mass could feel greater buoyant force than air. Especially because an air bubble should reduce in volume due to the surrounding pressure, and therefore reduce its buoyancy (I think).
I’m still looking to better understand how ambient liquid pressure affects bubble velocity. It feels like on the one hand, higher pressure should impact greater force to the bubble. But on the other, higher pressure would contract the bubble and reduce its volume and buoyancy. Does that mean there is a particular optimal water depth that causes the greater bubble velocity?
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Simply put smaller the bubble smaller the gradient of buoyant forces (they act on all sides of an object and not just from below). So basically bigger bubbles accelerate faster than the smaller ones. Smaller bubbles don't rise slower they have a more uniform ascent. Now when you are thinking about a bubble's terminal velocity, it depends on friction which depends on again pressure and shape of the bubble. So now there will be a slowly depleting friction and a slowly depleting net buoyant force. Now you will need to do some calculations to find out how much these are depleting with time. Basically depending on the liquid if buoyant force depletes faster there will be a terminal velocity and if friction depletes faster then it will keep accelerating. But they both reach zero at the end simultaneously so it's about the curve.
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An educated guess would be an object with the lowest density that could hold a hydrodynamic shape and withstand the changing pressures.
Something like a torpedo, but very light for its size.
Oh this is fascinating, please expand on these! It's crazy to think they can survive that long, what's the predominant force at that scale that keeps them from collapsing or dissolving?
Also, is this a significant source of dissolved oxygen in water for fish etc?
Alot of these responses are half correct. My entire career as an engineer has been working with diffused aeration systems, so hopefully I can shed some light.
Theoretically a bubble's buoyancy is independent of all factors but volume, but that does not by any stretch mean that bubbles rise independently of size. Buoyancy here is the sole upward force that will be equivalent to the volume of water the bubble displaces (which is not constant, as the bubble will compress as it gets deeper with water pressure).
The dragging force that slows the bubbles rise is complicated and is at least partially influenced by the bubbles diameter. At the air/water boundary layer there will exist a surface charge proportionate to the surface area of the bubble and influenced by the salinity of water. That is why the smaller of a bubble you make, the more likely the bubbles will rise slowly giving the same volume of air as the surface area to volume ratio will increase.
For some context, fine bubble air is the most practical for wastewater treatment, using bubbles about 2mm in diameter. This size is ideal as the bubble rises at about 30 cm/s, gives great time in the water for oxygen transfer and still rises fast enough to mix the reactor. In contrast, we intentially use less oxygen efficient coarser air (6mm bubble size) even though the oxygen transfer is half that of finer bubbles and can rise ~10-30% faster, as the added turbulence is particularly good at mixing low solids content liquid reactors.
There are technologies already available that make use of micro and nano bubbles for a variety of applications to hyper-oxygenate the water they are put in. The theory is, the surface area to volume ratio of the air is so high, we find that the bubbles stay in suspension as the buoyant forces don't outweigh the drag forces effectively leaving the bubble in one place in the solution and allowing extremely long residence times for oxygen transfer from the bubble into the water. This technology is primarily used successfully in aquaculture.
Question for someone who knows better than me on this:
Would one reason that smaller bubbles ascend slower be that the surface area to volume ratio is much larger with a small bubble, thus the friction to buoyant force ratio is also larger? Or is friction between the water and air negligible in comparison to other forces?
What kind of applications does this bubblology have?
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Now you have me wondering how high water would need to be for the water layer to meet the vapor layer where the air is too thin?
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I don‘t know about nanobubbles, but microbubbles are used in contrast enhanced ultrasound. Basically overcoming the resolution limit of conventional ultrasound systems to create an image of your microvessels for medical diagnostics.
At ambient temperature and pressure too high of an energy barrier exists for the dissolution of the bubble's contained gas. This is b/c small bubbles have a large internal pressure (scales w/ 1/r) and a high chemical potential, just like bernpfenn mentioned. Here's a cool paper showing the math behind this (doi.org/10.1021/acsomega.0c05384)
u/bernpfenn would probably know better if a more updated source exists.
High pressure alone at room temperature will only get you to supercritical fluid, which has continuous density changes with temperature and pressure. If you want liquid (which can phase change, aka boil), you need to drop the temperature below the critical temperature as well. Now, phase diagrams really only apply to pure gases because each element acts differently, and air is a mixture of elements. But, it’s mostly nitrogen and oxygen, and they behave relatively similarly, so we can sort of think about a phase diagram for it: https://www.google.com/search?q=phase+diagram+of+air&rlz=1CDGOYI_enUS990US993&hl=en-US&prmd=ivn&sxsrf=ALiCzsaO8of4T5UciV1cKC7Z__6KuT183g:1665391121805&source=lnms&tbm=isch&sa=X&ved=2ahUKEwj5rOixodX6AhVmkYkEHTU-B28Q_AUoAXoECAIQAQ&biw=375&bih=634&dpr=3#imgrc=hIjVH_jtZVTNLM
Anything below and to the right of the line is a gas. Anything to the left of the line is a liquid. Anything above the critical point is a supercritical fluid, which will totally fill its container like a gas and can no longer boil.
wonderful. Do you know some specifics? Like Temp and Salinity? Would some of the averages (spd. size) be higher / lower in the Dead Sea vs Lake Huron? Would a thermocline layer make a "bump"?
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Yes there is a terminal speed of air rising, similarly to an object falling has a terminal velocity.
With an object falling it's the the point at which acceleration due to gravity match deceleration due to air resistance.
For a bubble rising, this is the buoyancy counteracted by drag created by the liquid. So different gasses would move at different speeds though different liquids based on their viscosity.
The issue is that this drag amount is changing constantly. There will be flows and slight variations in density. The bubble will likely split well before it reaches maximum velocity.
A large bubble will deform into a more streamlined shape allowing it to rise faster, this same deformation is also what breaks it apart. The smaller the bubble the more stable it is and the more it's likely to reach terminal velocity.
In a rigid container the air pressure and thus density would not change nearly as much as an air bubble at depth. So even a rigid container filled with air should work just as well (or close enough). Something like a balloon though would shrink at lower depths and thus rise slower at the start with increasing velocity as it rises and expands.
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> Especially because an air bubble should reduce in volume due to the surrounding pressure, and therefore reduce its buoyancy (I think).
Yup. In fact, given that a lot of materials are more compressible than water, most things become less bouyant the deeper you go exactly because the water pressure compresses them. Objects that float on top of water can, at a sufficient depth, be compressed to the density of the water around them and begin to sink instead of floating!
The first.
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If you release the bubbles in the deepest parts of ocean, below 8000 m, the bubbles would have so high density that they will sink instead of rise.
This because the air compressed to more than the pressure at that depth will have a density higher than water.
But probably will the bubbles dissolve rather quick, but a baloon will definitely sink. You could fill the Marianer trench with air! Maybe.
Who are you, /u/bernpfenn 's uncle at the Thanksgiving table?
Not the person you asked, but I think 'bubblology' (thank you for that word by the way) would have relevance in micro-fluidics, which relates to lab-on-a-chip applications and microbiology and cellular biology. It may also have mechanical engineering relevance through hydro-dynamics in (micro-)pumps, injectors, and carburetors. Maybe even drug delivery systems.
Edit: and according to this link it's also very useful for water aeration, which is needed for hydroponics, hydro-culture, and general water treatment.
In general for nano: lots of surface interaction, so great if you want to a lot of chemical or physical interaction between your nano-something and whatever substance you put it in.
The math is worked out here for an object sinking in a less dense fluid, but the result is the same (in magnitude) for a bubble rising in denser fluid.
A nice fuzzy soda pop. The way the bubbles of a McDonald's Sprite tickle your 'buds.
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Russell Wilson once claimed nanobubbles protect him from concussions. He's also a complete weirdo
The weight of the air doesn't really matter, as it's much much smaller than weight of the water it displaces. The main factor is the shape of the bubble, which is the same at different depths. So the bubbles should rise essentially at the same rate regardless of pressure.
So is there a depth line where bubbles would become buoyant?
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Or how hot a given water body needs to be to sublimate to vapor directly. At sea level the answer is 100 degrees celsius.
But at La Rinconada elevation 5,100 meters water boils at 82.5 degrees Celsius or so.
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The upwards force from buoyancy is proportional to volume and the difference in density, drag is complicated but largely proportional to cross sectional area and shape. The best thing would be a light, long and narrow, streamlined torpedo shape.
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Wow, I plugged in a pressure of 16000 PSI into this calculator and you're right! It exceeds the density of water. That's weird.
It looks like it. See my comment to TexasPop. Air matches the density of water at a water depth of around 5.3 miles.
That's interesting. Why aren't they deleterious to the ultrasound resolution due to the constant refraction from the medium shift? Does that refraction change act like dithering in astronomical images?
>I’m still looking to better understand how ambient liquid pressure affects bubble velocity.
In a stable volume the pressure wouldn't affect the rate at which it 'fell' in this case falling is negative. But in the case of a bubble, it's pressure is equal to the liquid at the level it is in. But as the bubble ascends through the liquid column, the bubble diameter will increase to maintain pressure.
Now if we take Stokes law and the fact that pressure will vary linearly through the column, but velocity will vary by the square, and terminal velocity will vary by the cube, Id venture to say that the optimal water depth is farthest away from the point where the bubble was created, as R would be the greatest (until structure is no longer supported).
Immediate benefits of nano-bubble aeration
Saturates water with up to 79,000x more oxygen than traditional aeration
Can remain within the water column for 2-3 months
Sustains the rapid growth of beneficial bacteria and desirable microbes
Prevents accumulation of anaerobic bottom muck and sediments
Helps reduce the impact of nutrients responsible for fueling weeds and algae
Provides cyanotoxin control as demonstrated in laboratory settings
Gas bubbles having such a small diameter shrink in water due to ions existing at the interface between gas and liquid, which in turn increases the ion concentration at the interface and raises the inner pressure and temperature of the bubbles, causing various phenomena to occur.
We think that taking advantage of these phenomena will provide many different possibilities.
In recent years, it was revealed that the micro-nano bubbles have a lot of useful properties. These include the following capabilities:
Sterilization capability:The agglomeration and collapse process of the micro-nano bubbles converts oxygen in the air into active oxygen, creating bactericidal molecules including OH and O3.
Cleaning capability: Ions existing at the gas-liquid interface of the micro-nano bubbles decompose and adsorb oil and fat contamination, which allows removal of the contamination without the need for cleaning agents.
Bio-activation capability: It has been proven that the micro-nano bubbles penetrate deep into biological cells and enhance the immunity of the cells. This has allowed elimination of the need for antibiotics or reduction of the amount of antibiotic usage.
Growth promotion capability: It has been verified that using the micro-nano bubbles allows fish, crustacea and plants to be grown 20 to 30 percent larger than those grown in an ordinary manner.
Cell protection capability: It has been found that oysters grown with the micro-nano bubbles remain alive even if they are frozen to minus 20°C. This is likely because the micro-nano bubbles protect oysters’ cells against damage due to freezing.
Heat transfer capability: The micro-nano bubbles can be used to raise or lower the temperature of a liquid rapidly and effectively.
Vaporization promotion capability: It has been proven that the micro-nano bubbles contained in a liquid promote vaporization of the liquid. Applications based on this effect include highly efficient water-cooled cooling towers and evaporation based desalination systems.
Environmental purification capability: The micro-nano bubbles help restore the biological balance in lakes, rivers or seas and remove odors and toxic substances produced by anaerobic bacteria. This effect stays for a long time even in a large water body such as oceans and seas.
>oi.org/10.1021/acsomega.0c05384
That was a nice dive into the theory.
In essence, to dissolve gas into liquids, smaller bubbles have a longer time in contact with the liquid due to the mentioned stability and surface in contact with the liquid multiplied with the time.
Size, there are nanobubble generators with 1000 GPM water flow. These generators require 100 psi gas pressure and 3.3 m3 gas per hour.
yes, Moleaer is THE leading company developing nano bubble generators for industrial volumes. I use a 200 GPM unit for removing algae from a 75,000 m3 lake. It is quite a spectacular transformation to see clear, transparent water in a tropical lake. The fish loved it. Oxygen levels rose to 8 mg/L.
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Larger size correlates with more speed since the resistance is probably related to radius squared, but volume is related to radius cubed. However, since large air bubbles are unstable, something like a submarine should be able to rise faster since it is larger.
Correct link: http://www.seas.ucla.edu/stenstro/Bubble
The source says that this only applies to bubbles >0.1 cm radius.
The source appears to be class notes, and does not cite sources itself. The idea that ascent rate is independent of bubble radius is counterintuitive to me given how Rayleigh drag works (normally appropriate at high Reynolds number). A quick search I did failed to find anything to confirm this. So, I'm leery of accepting this claim uncritically, and I'd like to see a better source here and explanation of the physics.
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plasma_phys t1_irpc0n0 wrote
I don't know about water specifically, except that two-phase flow is a very heavily studied phenomenon for water cooled power plants, but the amusingly titled Physics Today article Through a Beer Glass Darkly walks through a simple physics model of bubble-in-liquid physics for the case of dissolved CO2 in beer - with experimental data!