Bubble Oxygenation of Water

even nano bubbles will dissolve in time

I would think it would depend on quite a few factors which could be resulting in the large differences in the calculated absorbed value. Without knowing what they are it is hard to say the reason why.

Hi. I'm following thru the simple illust with the cubes but then you lose me. Its odd, with the cubes we're increasing in area as they go from 1/2 to 1/3...and at 1/3 we're already at 3X. Now if we continue to shrink the cubes and this is a linear relation, how come at 1/17 we're only at 2.5X?

Rixter's cubes are not square, as in ice cubes.

Cubed is a number times itself.

Maybe this is where you're going wrong.

I'd go with his logic, and not over-think it.

Never mind.

Rixter's example specifically motes cubes as in forms, he states it in his example noting that cubes are easier to work with.

1/3 is the linear dimension (along the edge for a cube). If you're talking constant volume, the linear dimension for 1/17 the volume would be the cube root of 1/17. In the case of spheres, the linear dimension would be radius or diameter.

Or to put it another way, it doesn't seem correct intuitively that that the radius of a bubble with only 1/17 the area would be as great as roughly 1/2 that of the big bubble

Lets say then that you learned that intuition and math do not always go together!

To put it another way, I will relate a story from 25 years ago when I first started designing Solar, etc, - a Customer had fish ponds, no grid power to them, so I sold him some Solar panels, and marine bilge pumps, appropriately sized, he had bathroom type shower style pipe and low pressure shower heads on each tank so as the sun came up they would start pumping, dropping the water 2 metres to splash into the pond, - worked great, drops would skate over the surface, But, one day he came home to find the fish in an inch or two of water, - it had been a windy day and the wind had carried the water too far sideways and much had missed the pond, so, taking eg. Rixter's figures into account, (after some trial and error, e.g. spraying just above) and my experience with 12 footer racing sail boats which had venturis to bail, - open boat, no deck, we devised a system, we took the pipe from the pump and connected it to a short larger diameter pipe, then at the fitting, it being just above the water level,pushed in all around 'sharps' - needles as in injections, which being very tiny diameter gave a very fine stream of tiny bubbles, which worked perfectly and allowed same stocking level of fish as the above water idea but no effect from the wind.

Is this the common core method?

https://www.youtube.com/watch?v=68Taeqd0ywI

common core? Ouch!

OK, diffusion per volume is proportional to Area/Volume or 1/radius of bubble.

Dividing into N bubbles of same total volume: radius = 1/cube root of N

For N bubbles: Area to volume = 1/radius = cube root of N

No, assume constant temp and time

Does the calculation consider the levels and sizes of oxygen-consuming species suspended in the water?

Thanks for that. Very interesting..And thanks to everyone who so kindly contributed. There are too many to thank individually with my arthritic figures and somewhat uncooperative smart phone. Besides, maybe the whole thread would get cumbersome. Cheers to all!

You haven't told us yet what the set-up is (if any, it might be just a thought experiment).

But if it is biological treatment, as some posters have assumed, using fine bubble diffused air, the bubbles are about 1mm dia, and as the aeration tanks are typically 4m depth the extra pressure 288Pa = 29mm water makes negligible difference. Also only about 25% of the oxygen is transferred, so the decrease in bubble dia is negligible. The liquor is already ~ saturated with nitrogen, which is not absorbed by the biomass, so the bubble nitrogen content only falls slightly (as saturation is at atmospheric pressure, but the average pressure in the bubble between release and surface is somewhat higher).

GA

I was going to ask that!

As far as I remember, that had a huge effect, but whether it was a larger one than the bubble size I do not remember.....

But I would have not had large bubbles anyway if I was designing it, I would have automatically gone for the small bubble size (I do not remember why I know this!)....maybe something like a sieve over the nozzle would help reduce bubble size. Some experimentation needed....

Don't tiny bubbles rise far slower in water if I remember correctly?......more time for absorption, less waste maybe?

Also, the depth at which the bubbles are released must play a role that nobody has mentioned yet....

In hot summer months we aerate our fishing ponds to keep oxygen levels higher.....simply blowing air under pressure into the water.

I don't think you can get all the bubbles the same size....

Cool image!

http://www.wonbrothers.com/product/airstone/airstone.htm
Sounds like a fun project.....

Yes, Hooker. Your observation is correct and supported by the best mathematical analysis in this thread. My question was qualitative--HOW MUCH better are smaller bubbles.

Sorry, I meant to say quantitative. Obviously, when one asks 'how much' one is looking for a quantitative answer.

I understand, Greasy. That's why I said up front that I don't have any "bubble math", only rough observation numbers relating to plant growth.

It's not much but it seems to support the smaller bubbles are better at oxygenation argument from my perspective.

Hooker

I might be missing the point of the OP but......

I have never done the math but I have kept fish and always thought that the bubbles created by an air pump and stone did little more than move the water around at survace allowing oxygen exchange at the surface and the oxygenated water to be circulated round the tank. Not all fish tanks have air pumps now and most just use a pump to circulate the water, changing the water at surface. Bubble size is also a function of the water density, so the same air stone in a fresh water tank will produce bigger bubbles than in a salt water tank.

Bubbles are in the water for too short a time to allow any effective oxygen exchange. Big fish farms in SE Asia generally just have paddle wheels at surface to splash and move the water around for oxygen exchange.

Hi HeHound, if you look at my post, {18,} you may see that I was using very low energy, (I didn't mention it but Solar panels only 60 watts then) yet still received an excellent result by using the Venturi principle as it works on low pressure, and those needles were very tiny in diameter, so very small bubbles, hence the big result. There are for fish tanks a tube arrangement so that the bubbles bring up the water to fall through the filter, and some oxygenation there but nothing like the tiny bubbles. For pet gold fish, best not to be dependent on pumps but for fish farms different story. Paddle wheels good for dams.

Waste treatment plants in the past used mechanical agitators to oxygenate the aeration basins, and they had a tapered floating paddle wheel that flung the liquid into the air and thoroughly agitated it.

However,the edges of the aeration basins were not properly oxygenated,allowing anaerobic bacteria to thrive.

They now use bubble tubes and get very uniform oxygenation,as well as being more electrically efficient.

Here is a link you may find interesting:

http://water.epa.gov/scitech/wastetech/upload/2002_06_28_mtb_fine.pdf

Thanks for that link!!

Now thats a twist. Bubbles not effective; not in water long enough. Well I guess thats another reason for very small bubbles as they 1 rise slower and 2 circulate/mix water more. Or do they? That may depend on how forcefully they are ejected from the diffuser. But rapid ejection will also result in a shorter time in the water column. Oh boy!

It's not just bubble size, big or small, they also stir the water to spread the O2, which is just as important - perhaps more so. That's why surface paddles and sprays are effective.

Re HeHound.

The transfer of O2 to water is very rapid - our blood is mostly water and it picks up O2 very quickly in each breath (and dumps CO2) - otherwise we would die.

I don't think that the amount of time a bubble is in the water is a factor, because they are continuously generated to replace the ones that hit the surface. You have to look at the number of bubbles that exist at one time as a snapshot of the entire process, regardless of how long a particular bubble lasts. If you have a picture of a stone bubbler, you may be able to get an idea of the surface area of the bubbles compared with the area of the top surface.

As a rule of thumb and in round figures to help point you in the right direction, the O2 transfer is proportional to the surface area of exposure. That is, double the area, double the exposure.

The transfer rate is proportional to the difference in concentration of O2 in the air and the water.The obvious example is when they are in equilibrium there is no transfer of O2 at the surface.

The O2 will migrate/diffuse in both water and air at a rate depending on the inverse of the square root of density. That means the O2 will leave the air fast but move slowly in the water to a less dense volume.

For the purpose of this discussion, in terms of human perception, the transfer of O2 to the water at molecular level is instantaneous^*1, and O2 piles up at the water surface waiting for it to diffuse to less dense volumes of water.

It's like catching a train. It arrives empty with plenty of room for all the passengers, but you are stuck on the platform for ages waiting until everybody in front moves down the car.

On balance this means that large bubbles have larger areas and increase the transfer surface, lots of smaller bubbles spread throughout the water get the O2 to the less dense areas so much quicker, and are in the water for more time because they rise slower, and more O2 leaves the air.

Search for Grahams Law for more info on diffusion, and Gibbs Law for the time this transfer takes.

I hope this helps.

*1 Molecular attraction happens quickly. Have you tried dipping a brush into a pot of paint so fast that when you take it out there is no paint on the brush.

Rules of thumb aside,look at the link I provided to see the real world results of large vs small bubble oxygenation efficiency.

Small bubbles are almost twice as efficient as large bubbles.

Volume of sphere= 4/3 Pi r Cube

Area of a sphere= 4Pi r Square

Exactly as Rixter said.

Refer to this link for other shapes:

http://math2.org/math/geometry/areasvols.htm

Excellent additional dimension to the discussion, Horace. However, have we not established that smaller bubbles have more than twice the surface area as per Rixter's early excellent calculations?

Greasy. Careful here. A small bubble cannot have more surface area than a larger one.

It is only when you have a lot of smaller bubbles does the total surface area increase, where for the same total volume of O2 as the large bubble, Rixter has shown the maths for this.

That makes small bubbles better to transfer O2 to the water to start with, but also better because they spread out to carry the O2 direct and quicker (than diffusion alone) to a larger volume of water as well. Much more efficient.

At STP water will only take up a certain amount of O2, there are charts of saturated oxygen concentration at various temperatures. Once reached, no more will dissolve.

Thus with smaller bubble sizes, you reach equilibrium faster, but can not exceed it. Excess O2 is forced out as the water freezes or as it reached a boil. At boil the remanent O2 is steam distilled out of the water.

That is how they make clear ice cubes - boil the water in a vacuum until all the air is steam distilled out.

And that is why aerated water contains air inclusions as it freeses.

Those charts should be at various temperatures and pressures. At smaller bubble sizes, the higher pressure inside the bubble raises the saturation point at the surface of the bubble.

I'm going to quibble with most of these answers, and what is CR4 like without a good quibble?

Your question says that the document says that "many small bubbles allows a much higher percentage of that oxygen to dissolve." The discussion so far has been focused on the RATE of dissolution, not on the PERCENTAGE that dissolves. There is a big difference.

The rate of dissolution and the percentage that dissolve both depend on the pressure of the gas at the surface of the bubble. The smaller the bubble, the more surface tension will try to contract the bubble, raising the air pressure inside the bubble. So even though the rate of dissolution goes up as a result of surface area, it goes up even more as a result of higher internal pressure. The bubbles have to be pretty small for the pressure to rise significantly though. Another factor is that the deeper the bubble below the surface the higher the water pressure will be, but in a small tank or jar, this won't be much of a factor.

In addition, since the air pressure in the bubble is higher, the equilibrium percentage at the surface of the bubble is higher. Even more interesting, as the gases in the bubble dissolve, the bubbles get smaller, resulting in even higher internal pressure, so the equilibrium percentage goes up even more. This should continue, with the bubbles shrinking, the pressure rising, the equilibrium percentage rising, until the bubble disappears entirely.

As a result the AMOUNT of oxygen that is absorbed from small bubbles is much higher than that absorbed from large bubbles or from the surface.

You forgot to allow for the expansion of the bubble and the reduced pressure as it

rises,the temperature change as it travels through the differing micro-thermoclines,

the decreasing ability of oxygen to dissolve in warmer water,whether the bubble is

following directly behind another bubble,which will tend to accelerate the 2nd

bubble's rate of rise,and possible merger with the bubble above.

Also,as oxygen is depleted,the nitrogen that is now left in the bubble is more

concentrated,and expands less,per degree of temperature,than oxygen.

And many other variables that I have omitted.

There are a lot of dynamics involved,but the "proof of the pudding" as they say, is in the link I provided above.(#28).

Real world results.Simplified,not much math involved.

Thanks for expanding on those points. If you look at any system, the real world always complicates it if you look closely enough. Whether any of those processes affect the original question I will leave to your greater knowledge.

My main point was to distinguish between the rate of dissolution and the percentage of dissolution, as stated in the original question.

Are the bubbles oxygen or atmospheric air?

Is this just a theoretical question, or do you want to oxygenate some water or liquor in eg a biological treatment process? If it's the latter, answering your question won't help much, as you're unlikely to know the number or dia of the bubbles. Using air, with fine bubble diffusers (porous discs) a typical transfer efficiency into clean water is 5% (of the oxygen in the air) per m disc submergence. Coarse bubble eg teeter plate or pipes with small holes efficiency about 2-3% per m. But there are other things to take into account, transfer is usually lower into dirty water or mixed liquor, and the effect is greater with fine bubble.

Temperature makes little difference in practice as transfer is increased by 1.024^T-20, but decreased due to lower oxygen solubility (from air) at higher temperature, given by 468/(31.6 + T) (where T is in °C) and the 2 effects pretty much balance.

This would goes to the ratio of volume and surface area or dimensionless number k = (constant)(volume)^1/3 / (surface area)^1/2 of a bubble, solution(Le Chatelier's Principle) and a geometric problem.

Pretty interesting to see in the lab, but probably i bet there are studies on this.