A Differential Pressure Technique for Bubble Characterization in High-Temperature Opaque Systems
The paper I'll discuss in this post is this one: Noninvasive Differential Pressure Technique for Bubble Characterization in High-Temperature Opaque Systems (Zhuotong Sun, Brett Parkinson, Oluseye O. Agbede, and Klaus Hellgardt, Ind. Eng. Chem. Res. 2020, 59, 13, 6236-6246).
I have been thinking about bubbles for a very practical reason, at least in terms of my personal understanding, for quite some time.
Apparently I was reading papers about them almost two years ago and wrote in this space about stumbling across a beautiful old paper by a historical genius in connection with bubble dynamics: I just stumbled into a very old paper by "Lord Rayleigh" contemplating water boiling in a pot.
This is the reason that this paper caught my eye as I was scanning the recent issue of this journal, one of my favorites. It turns out that the paper doesn't address my particular interest, the behavior of gaseous fission products in liquid plutonium fuel, the old LAMPRE concept which relied on liquid nuclear fuels - in the operated experiment this was an iron/plutonium eutectic. (A ternary cobalt/cerium/plutonium eutectic was also considered but never operated experimentally.)
It turns out that the paper cited at the outset is not immediately applicable to the case of bubbles generated in situ generation of gaseous fission products - it relies on a Fourier transform of pressure changes in the outlet of a gas bubbler, it's has a nice overview of physical concepts in the behavior of bubbles and may suggest approaches to generalizing the case to bubbles arising within an opaque high temperature liquid. This paper does address two areas with surrogate systems that may be important to the nuclear case by considering bubbles in liquid tin to address metals, and a molten salt, to address the famous molten salt reactors under development by many companies in many parts of the world.
Gaseous fission products include the noble gases krypton and xenon, the former having a relatively long lived radioactive isotope Kr-85, with a half-life of about 11 years, the latter, a valuable and expensive element, has only short lived radioactive isotopes. One of these short lived isotopes, Xenon-135, has one of the highest neutron capture cross sections known, and is thus a very important isotope to consider in nuclear engineering. A severely misguided attempt to manage Xenon-135 "poisoning" led to the explosion of the Chernobyl nuclear reactor. Because of this property, among others, it is important to understand, in the conception of liquid nuclear fuels, the solubility of xenon in a liquid fuel, how it behaves when it goes out of solution - i.e. when it forms a bubble - as well as the size of the bubble and its transit time.
As I imagine nuclear fuels that will be used at higher temperatures than those experimentally utilizied in the LAMPRE case, some other elemental fission products are likely to be gaseous as well, cesium, rubidium, strontium, and barium as well as the halides bromine and iodine and bromide and iodide salts, all of which are known to be insoluble in liquid plutonium metal. (Reduction of plutonium oxides and salts to plutonium metal is generally accomplished using calcium metal, a cogener of strontium and barium, which is also insoluble in liquid and solid plutonium.) The emergence of these bubbles to the surface, notably, allows for the immediate separation of these fission products by distillation, particularly under reduced pressure, ideally a near vacuum in which the only gases are represented by the vapor pressure of the materials emerging from the bubbles.
Anyway, from the paper's introduction:
Several theoretical models and empirical correlations for the prediction of the bubble size have been reported in the literature by means of force balance during bubble formation or fitting experimental data of room-temperature aqueous systems to dimensionless numbers. However, these may not accurately predict the sizes of bubbles generated in molten systems because of the appreciable difference in the properties of liquid metals...
...Generally, bubble sizes have been measured by different methods including photographic, optical probe, electrical conductivity (resistivity) probe, acoustic, ?-ray and X-ray tomographies, magnetic resonance imaging, electrical capacitance tomography, and light-scattering techniques such as laser Doppler anemometry and particle image velocimetry.(1?31) However, optical and photographic techniques are not suitable for opaque liquids; sensitive electroresistive probes may be damaged in high-temperature or corrosive liquids while X-ray and ?-ray imaging techniques are expensive and pose danger of exposure to hazardous rays.
Of course X-ray and ?-ray are continuously generated in nuclear fuels, and any signal from them resulting from bubbles may prove difficult to discern.
In developing their approach, the authors appeal to modeling in a much cited papers on bubbles, this one: Study of Bubble Formation Under Constant Flow Conditions (M.Jamialahmadi et al., Chemical Engineering Research and Design Volume 79, Issue 5, July 2001, Pages 523-532)
A number of other models are also discussed, but this one seems to have the most bearing.
The modeling equation was developed from a neural network approach, and is thus empirical in a sense. Here it is:
The symbols correspond respectively to the dimensionless Galileo, Bond, and Froude numbers defined as follows:
The physical meaning of the symbols is quite nearly identical to this list from the Jamialahmadi paper:
d sub o here is the diameter of the orifice from which the bubble is released, d sub b the diameter of the bubble. g is the gravitational constant.
Here are signals using molten tin as the opaque fluid:
The caption:
The fast Fourier transform:
The caption:
The authors claim that this signal may be translated into the volume of the bubble, from which, with a spherical assumption, translates into a diameter.
Using this relationship they compare their "experimental" data with some of the models used to relate flow rates, orifice diameters and bubble sizes.
A representative graph:
From the Jamialahmadi paper, here is a portion of a table giving some of the equations associated with the models.
None of this means very much of course, but it all comes under the rubric of making the best of the de-socialization forced upon us by the orange nightmare's inattention to any other subject other than praising himself while he's supposed to be governing, something he has always and unambiguously unqualified to do, except in a reckless, irresponsible and often criminal fashion.
Any inconvenience, any restriction, can be made into a positive by learning something new.
I'm glad I looked at this paper, even if it didn't address the subject about which I was wondering. Poking around in the references and citations, I did find some more relevant stuff, and also managed to stumble upon a very old paper addressing some properties of liquid plutonium that I had not found previously, even though I have found out a lot about liquid plutonium, that scary stuff that I think is the only thing that can save the world, what's left to save in any case.
Find a way to enjoy the isolation with your family. May it help you to understand why and how much you love them.
