Predicting Mean Bubble Size

This falls into the area of Chemical Engineering Research sometimes done for bubble cap trays in distillation or contacting towers. I believe it might be worthwhile for you to look into using "Google Scholar" to search for such information since much of it would likely be in engineering theses, often in university libraries.

I haven't looked at this sort of research in quite a while, but much of it was done in the 1960s and 1970's. An engineering text: "Physicochemical Hydrodynamics" by V. G. Levich in the Prentiss-Hall International Series in the Physical and Chemical Engineering Sciences (1962) has some information about it. The mathematical treatment is somewhat daunting though.

That said, most engineers used physical models (with high speed cinematography to isolate bubble sizes coupled with ststistical anaylsis of scan sizes to come up with results). Then they used dimensional analysis to scale up.

I made a simple model to determine the bubble approximated diameter as function of the orifice, surface tension and pressure of incoming gas.

When the bubble grows it has a spherical form since pressures in and outside are all over the contact surface the same. The bubble has an ascending force due to the density difference and when the vertical projection of the surface tension at the orifice rim becomes less the ascending force the bubble will separate and become free.

The approximative equations are:

Ascending force Fasc≈ 4/3*Pi*R^3*( γe-γi)

Force due to the superficial tension Fσ ≈ 2*PI*r*σ*sinΦ With sinΦ=r/R

Separation will occur at R'≈ r^0.5*(1.5*σ/(γe-γi))^0.25

To obtain an R' the pressure "pi" should be greater than pe with Δp= 2*σ/R'

Surface tension depends on temperature.

Even if the model is simple it will give an order of magnitude at least and it allows a correction via some short measurements. Anyway before measurements are done it is always better to have a simple model to interpretate the results and their trends.

I hope it will help.

The gas flow rate will give the frequency of bubbles apparition.

I shall appreciate comments.

In fact I think that for many problems a simple model is sufficient and one does not need to get in complex studies. From the other point of view I consider that the role of CR4 members is not limited to indications of source books. Some times it is good to make our gray cells work. It helps to maintain a plasticity and not get too rusty!

Nick,

Good answer!

BTW, ye is the density of the media (exterior) and yi the density of the air (interior), isn´t it?

Regards

Ernesto

Yes, in fact I used "γ" the Greek letter "gamma" from the "Ω" button but the font is not very good (should be perhaps improved since "π" (Pi) looks as an "n").

I would say it is an approximation since in fact the bubble before "take off" has the form of a sphere with a conical connection to the rim. But it gives an order of magnitude and many times it is what an engineer needs.

σ is the surface tension

Dear Mr. nick name

I want to mention that the AIR BUBBLE, has different SHAPE, namely wet air- bubble, just dry bubble (not wet or not super heated) and super-heated air bubble.

This has been extensively explained in the BOOK - " THE NUCLEAR POWER ENGINEERING by Mr. ELWAKIL, published by McGRAW-HILL during 1965.

I had that book, but misplaced. If I locate it , I will try to scan and send the same.

DHAYANANDHAN.S

Thank you for the excellent information -which by the way I knew already- but the question was:

"How can I predict mean bubble size in a water air bubble column system at ambient temperature considering orifice size, liquid and air flow rates, inlet pressure, viscocity, surface tension etc.

So that the form of SUPER-HEATED air bubbles is not part of the question.

As you -I hope- noticed what I did was to give to the question an answer which even approximated is an indication of the order of magnitude.

If you can give a better explanation ( based on physics) I would appreciate to see it.