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Enhanced Performance in Uranium Extraction by Quaternary NH4-Functionalized Amidoxime-Based Fibers.

The paper I'll discuss in this post is this one: Enhanced Performance in Uranium Extraction by Quaternary Ammonium-Functionalized Amidoxime-Based Fibers (Lu Xu,* and Hongjuan Ma*, Ind. Eng. Chem. Res. 2020, 59, 5828−5837)

I'm less alone than I used to be in my long held contention that nuclear energy is the only form of energy that is environmentally sustainable, particularly if one embraces the ethical concepts of human development goals and environmental justice. The widely held theory that so called "renewable energy" is somehow superior to nuclear energy or even that it is remotely sustainable is being experimentally tested at vast expense - on a scale of trillions of dollars of "investment" - and the results of this vast experiment are increasingly clear: So called "renewable energy" has done nothing to address climate change; is doing nothing to address climate change; and won't do anything to address climate change. In fact the rate of the accumulation of the dangerous fossil fuel waste carbon dioxide concentrations has reached the highest rate ever observed going back to the 1950's, averaging between 2.4-2.5 ppm/year in the most recently passed decade, compared to a rate of between 1.5-1.6 ppm/year averages as recently as the period between 1990 and 2000. In the 42 years between 1958 and 2000, there were 5 years in which the increases in carbon dioxide were higher than 2.0 ppm. Since 2001, there have been 17 such years in which carbon dioxide increases were greater than 2.0 ppm.

Mauna Loa CO2 annual mean growth rates

The "investment" in so called "renewable energy" is detailed here:

Frankfurt School/UNEP Global Renewable Energy Investment, 2018, Figure 3, page 14

All of the above consists of facts. Facts matter.

Although the scientific literature remains littered with new approaches to so called "renewable energy" and oodles of papers on how to store intermittent energy - not all of them as useless as so called "renewable energy" itself - one seldom sees anymore announcements accompanying them that nuclear energy in unacceptable because of that big historical (and ignorant) bugaboo, public acceptance.

One also sees a plethora of papers that state some realities about nuclear energy, that it is, in fact, essentially infinitely sustainable.

There are three potential nuclear fuel cycles that might save the world, the thorium/uranium (233) cycle, the uranium/plutonium cycle and, somewhat more speculatively, the lithium/deuterium (fusion) cycle.

It is possible that the last cycle might prove the most sustainable, but as a practical matter, it will not be available on anything like a meaningful commercial scale until at least the concentration of carbon dioxide has increased by more than 50 ppm, as it will so long as we continue to embrace ideology that hasn't worked, isn't working and won't work. After more than a decade of attending lectures at the Princeton Plasma Physics lab, many of which are on the subject of advances being made in fusion energy systems - and there have been significant advances - there are still, even if the ITER (which I strongly support) is able to show a net energy gain from fusion, huge hurdles to overcome, particularly in the areas of heat transfer and materials science.

For the two remaining cycles, both of which have been utilized on an industrial scale, I favor the one with which humanity has the overwhelmingly largest experience, the uranium/plutonium cycle, which is more or less infinitely sustainable because of the vast amounts of uranium found in seawater, recoverable because of uranium's very high energy to mass ratio, only exceeded by the extraordinary energy to mass ratio of the lithium/tritium/deuterium system which again, is not currently available. I have nothing against the thorium cycle, and can certainly think of many ways where it can provide useful synergies, but the low water solubility of thorium means that it is not infinitely sustainable. The paper under discussion is about recovering uranium from seawater.

From the paper's introduction:

The available fossil energy and resources are continuously decreasing on the planet. The exploitation of sustainable energy is of strategic significance to solve energy problems.(1) Nuclear energy is a feasible alternative to fossil energy that could be vigorously developed in the future. The main source of nuclear power is from uranium ore, which distributes unevenly in the world.(2) Evaluation of the global energy consumption rates(3) shows that the land-based uranium sources can only sustain nuclear power plants for the next 80120 years.(4) Therefore, exploiting unconventional uranium resources could be an effective guarantee for global energy need.(5)

The total amount of uranium in seawater is about 4.5 billion tons, which is 1000 times larger than that on land.(6,7) Uranium extraction from seawater was studied in the United Kingdom after the Second World War.(8) Researchers at that time prepared inorganic adsorbents and investigated promising extraction functional groups. In the early 1980s, several polymeric adsorbents were prepared and used in uranium extraction from seawater by Japan. Since the beginning of the 21st century, United States, Japan, and other countries have devoted their research on novel adsorbents and large-scale marine experiments.(9−11) At present, many methods have been used for the extraction of uranium from seawater.(12−15) Among these methods, adsorption is one of the most promising methods because of its low commercial cost, high efficiency, and ease of operation.(16−22) A large number of studies have been carried out in the field of adsorbent materials, among which amidoxime (AO) is considered to be one of the functional groups with the best coordination performance for uranium.(23−25)

Reference 4, (Review of cost estimates for uranium recovery from seawater Harry Lindner ⁎, Erich Schneider, Energy Economics 49 (2015) 922) which I happened to have in my files is rather glib in this statement: "...land-based uranium sources can only sustain nuclear power plants for the next 80-120 years..." which is obviously mistaken unless it assumes without any real justification that all nuclear reactors built over the next century will have the same operating procedures as was utilized in the 450 or so nuclear reactors successfully built and operated in the 20th century. Many of the small modular reactor designs now in development are designed to not be refueled for periods extending through several decades, the reason being that they are "breed and burn" reactors which generate and consume plutonium in situ. In this was depleted uranium long considered by people who can't think very well to be so called "nuclear waste" is transformed into useful fuel. Although many of these designs rely on the use of enriched uranium as a "starter," there is no intrinsic reason that they should. Plutonium is completely acceptable for this purpose, and, in many ways, in fact superior.

The world inventory of plutonium, excluding that released in above ground and underground nuclear weapons testing but including that currently available from used nuclear fuel, is on the order of 2,000 tons. Completely fissioned, using a recoverable energy value of 190 MeV/fission, this much plutonium contains about 160 exajoules of energy. The most recent IEA report indicates that as of 2018, humanity was consuming, for all sources of energy, oil, gas, coal, nuclear, hydroelectric and the (trivial) "renewable energy" industry, about 600 exajoules of energy per year. Thus the energy content of the plutonium already in existence is equivalent to about a three month supply of all of humanity's energy demand. However, "breed and burn" reactors operate (unlike the vast majority of nuclear reactors now in operation) on the fast neutron spectrum and are designed to contain an arrangement of depleted uranium in such a geometry as to assure that every single plutonium atom that undergoes nuclear fission converts more than exactly one atom of "depleted uranium" (U-238) into a new fissionable plutonium atom.

Some time ago, in this space, I reported on some literature concerning the critical mass of plutonium: Bare Metal Critical Masses of Commonly Available Plutonium Isotopes. Commercial plutonium - that found in power reactors - is in generally a mixture of isotopes, usually dominated by Pu-239, but also including significant quantities of Pu-240 and, depending on the amount of time it has been stored without use, Pu-241. Use MOX fuel will also contain appreciable Pu-242, and perhaps Pu-241, again dependent on the storage time, and finally in percentage terms amounting to the low single digits, Pu-238. Referring to the reported critical masses, we can crudely estimate, depending on the geometry and other components in the fuel matrix and control materials, that a reasonable critical mass (in a fast neutron spectrum) is on the order of 20 kg for commercial grade plutonium. Obtaining energy from plutonium of course, requires that a critical mass be present. Theoretically therefore, it is possible using plutonium present right now, to utilize it to start, loosely, 100,000 nuclear reactors, albeit small reactors, all fired up using plutonium.

The current inventory of depleted uranium is on the order of 1.2 million tons, already mined, and already isolated. This means, therefore, in a breed and burn setting if we shut every coal plant, every oil well, every gas mine, abandoned all fracking, all offshore oil wells, restored every wilderness area at sea and on land from the destruction associated with the construction of wind farms, set all the rivers free by dismantling dams, and used only already mined and isolated uranium, thus shutting all existing uranium mines as well - leaving the contents for future generations to use - at current levels of world energy demand, this uranium would last over 150 years. This does not count the quantities of already mined thorium, most of which is found in the tailings of lanthanide mines used to provide materials for, among other things, the so called "renewable energy" industry. The high energy to mass ratio associated with the already mined uranium and thorium makes this possible.

So much for reference 4.

As noted in the excerpt from the introduction, discussions of the recovery of seawater have been going on for over half a century, accelerating appreciably from my somewhat informal and desultory purview beginning in the 1980's. Certainly discussions of amidoxime functionalized resins has been much discussed in the literature - a rough count in my own files shows well over 100 papers and it's not like I spend a lot of time focusing on this subject. So it is reasonable to ask what's new here.

The answer to that question involves a rather clever approach to polymer design that takes into consideration the chemical speciation of uranium in seawater. In the planetary uranium cycle, water extracts uranium from crustal rocks uplifted from the mantle, both terrestrial and on the seafloor in the form of its doubly charged oxo ion, (UO2^(2+)), the uranyl ion in which uranium is in the +6 oxidation state. (The presence of oxygen in the atmosphere is necessary for this species to be observed.) In turn, however, in seawater, this oxo cation is mostly complexed with two or three carbonate ions, each of which has a charge of -2, with the result that most of the uranium is present in the form of negative ion complexes having either a charge of -2 or -4.

For this reason, the authors have chosen to incorporate positively charged quaternary ammonium complexes, this to minimize uptake by the resin of positively charged metal ions of other metals. (For example, amidoxime resins also have an affinity for seaborne vanadium.) Their experiments show a higher affinity for uranium in seawater than do other amidoxime type resins, of which many have been explored and tested.

For synthesis of their resins, they utilized ultrahigh molecular weight polyethylene to which they radiation grafted acrylonitrile, which is functionalized as an amidoxime with hydroxylamine, as well as 2-(dimethylamino)ethyl methacrylate which they abbreviate as "DMAEMA."

The following schematic from the paper shows the synthetic strategy:

The caption:

Scheme 1. Schematic Diagram of the Preparation of AO Fiber, AO-DMAEMA Fiber, AO-Q Fiber, and Q-AO Fiber The insets are structure diagrams of AO-Q fiber and Q-AO fiber, respectively.

To get a feel for the different types of absorbents represented in this scheme, it is useful to look at some excerpts of how they were synthesized:

Acrylonitrile-based UHMWPE fibers were synthesized by preirradiation-induced grafting copolymerization of AN and AAc. The UHMWPE fibers (about 2 g) were irradiated with 60Co in air at room temperature at a dose rate of 4.7 kGy/h. The absorbed dose was 80 kGy. The irradiated UHMWPE fibers were placed into a flask containing 50 vol % AN, 13 vol % AAc, and 37 vol % DMF, after purging with nitrogen for 30 min for deoxygenation.(34,36) Graft polymerization was performed at 50 C. After 5 h, the samples were washed with DMF and deionized water four times. Then, the fibers were dried in a vacuum oven at 60 C and are referred to as AN fibers. The degree of grafting (Dg) was 108% and was determined by the increase in the weight of the UHMWPE fibers after graft polymerization...

...The AN fibers were then irradiated with an electron beam at an absorbed dose of 20 kGy in air at room temperature. Then, the irradiated AN fibers were immersed in a solution consisting of 10 vol % DMAEMA, 22.5 vol % MeOH, and 67.5 vol % water after purging with nitrogen for 30 min for deoxygenation. The grafting reaction was carried out at 60 C for 5 h. The obtained fibers were washed with deionized water four times and dried to a constant weight in a vacuum oven at 60 C. The resultant fibers were referred to as AN-DMAEMA fibers...

...To modify the fibers with AO groups and quaternary ammonium groups, two synthesis approaches were investigated according to the sequence of amidoximation and quaternization (Scheme 1): Method A: amidoximation was carried out first before quaternization of the tertiary amino group, and the samples obtained were referred to as AO-Q fibers. Method B: amidoximation was carried out after quaternization of the tertiary amino group, and the synthesized samples were referred to as Q-AO fibers. AO density (D(AO)) and quaternary ammonium density (D(Q)) on the modified fibers were evaluated...

The quaternization was performed using n-bromobutane.

The IR spectra of the fibers giving a feel for their differences:

The caption:

Figure 1. FTIR spectra of UHMWPE fibers, AN fibers, AN-DMAEMA fibers, AO-DMAEMA fibers, AO-Q fibers, Q-AN fibers, and Q-AO fibers.

The relative ability of the different resins to absorb uranium on a weight basis:

The resins were tested in simulated and real seawater.

The kinetics in simulated seawater:

The caption:

Figure 7. Adsorption kinetics of the Q-AO fibers and the AO fibers in simulated seawater.

The selectivity in real seawater:

Figure 9. Adsorption capacity for metal ions by AO fibers, AO-DMAEMA fibers, and Q-AO fibers in natural seawater.

To grasp the meaning of the data in the table that follows, it is useful to take a look at two equations for the variables described therein and the associated text (as a graphics object):

Q sub M here is a weight ratio essentially obtained by digesting the resin in a microwave in the presence of acid (which oxidizes it) and determining via inductively coupled plasma mass spectrometry (ICP/MS) the weight of the uranium in the resin.

Table 2 showing the values of K(M), K(U) and the selectivity β.

The authors' conclusions:

Quaternary ammonium-functionalized AO fibers were prepared by radiation-induced grafting polymerization of AN and DMAEMA onto the UHMWPE fibers, where the tertiary ammonium groups (N(CH3)2) of PDMAEMA were then converted into quaternary ammonium groups by 1-bromobutane. The optimized preparation process was investigated. The results suggest that the different sequences of amidoximation and quaternization could lead to a significant difference in the distribution of functional groups in the inner and outer layers of the fibers and finally result in a different adsorption performance for metal ions. For the Q-AO fibers, most of the quaternary ammonium groups distributed in the inner layer of the fibers, while AO groups distributed in the outer layer of the fibers. The resultant Q-AO fibers with D(AO) of 0.70 mmol/g and D(Q) of 0.56 mmol/g were considered to be an excellent adsorbent in screening adsorption experiments. Compared with traditional amidoxime-based adsorbents, enhanced adsorption capacity and adsorption kinetics of Q-AO fibers were obtained, suggesting that the cooperative adsorption between the Coulombic interaction and the coordination interaction strengthened the affinity for uranyl carbonate. Additionally, the adsorption capacity for uranium by the Q-AO fibers increased seven-fold to 0.210 mg/g in comparison with the AO fibers in natural seawater...

As I indicated above, these resins are not likely to be necessary to maintain access to uranium to power nuclear reactors for sustainable energy for many centuries, assuming we use our existing isolated uranium more wisely in "breed and burn" scenarios. (Wise use of nuclear resources would involve also utilizing the other actinides, specifically neptunium, americium, and curium as well as uranium and plutonium. I also note that valuable radioactive and nonradioactive fission products should also be recovered and put to use.)

We thus have many centuries to develop superior technologies not only for the recovery of elements (and fresh water) from seawater, but which may include getting past the goal line with respect to fusion power. A more immediate use would be to remove chemotoxic uranium from drinking or agricultural water where it may exist as a result of natural geologic or anthropogenic activities.

I hope, in spite of the immediate threat of Covid-19, that you are enjoying the great privilege of being alive as well as is possible in these circumstances. Here in New Jersey, it's a beautiful spring day.

Yet Another New Weekly Reading Record Established at the Mauna Loa Carbon Dioxide Observatory.

Over the next few weeks, through some week in May I'll be recycling text related to this topic of setting new weekly records for the concentration of the dangerous fossil fuel waste carbon dioxide concentrations in the planetary atmosphere, just changing the numbers to accommodate the numbers associated with the records.

Recycling is good, no? So I've heard.


Somewhat obsessively I keep a spreadsheet of the weekly data at the Mauna Loa Carbon Dioxide Observatory, which I use to do calculations to record the dying of our atmosphere, a triumph of fear, dogma and ignorance that did not have to be, but nonetheless is.

I had the naive wishful thinking notion that restrictions on automobile traffic with all of the worldwide lock downs would lead to a slowing of carbon dioxide accumulations. Something quite different has been observed with the most recent weekly data.

The data from the Mauna Loa Carbon Dioxide Observatory:

Up-to-date weekly average CO2 at Mauna Loa

Week beginning on March 29, 2020: 415.74 ppm
Weekly value from 1 year ago: 412.39 ppm
Weekly value from 10 years ago: 391.47 ppm
Last updated: April 5, 202

This week's reading, 415.75 ppm is the highest weekly average ever recorded at Mauna Loa, surpassing the record set last week, which was 415.53 ppm.

As I often note in this space the readings are sinusoidal, superimposed on a steadily rising slightly less than linear axis, as this graphic, which I often reproduce, from the Mauna Loa website shows:

Every year, like clockwork, a new all time record is set in May.

Last year's (then) highest ever recorded value, recorded on May 9, 2019, was 415.39 ppm

The increase in this week's reading over the same week 1 year ago is 3.35 ppm.

As of this writing, there have been 2,303 such data points, readings, at Mauna Loa. This week's reading is "only" the 100th largest.

Of the top 50 such readings, 29 have taken place in the last five years, 36 in the last ten years, and 40 in the twenty-first century.

If the fact that this reading is 24.27 ppm higher than it was ten years ago bothers you, don't worry, be happy. Just repeat over and over and over and over, until it becomes a modern day Gregorian chant - "Renewable energy is great! Renewable Energy is Great! Renewable energy is great! Renewable energy is great!" Talk about Elon Musk and his cobalt laced electric cars.

Maybe you'll feel better.

I won't.

My impression that I've been hearing all about how rapidly renewable energy has been growing since I began writing here in 2002, when the reading on April 14, 2002 was 375.14 ppm should not disturb you, since it is better to think everything is fine rather than focus on reality.

In this century, the solar, wind, geothermal, and tidal energy on which people so cheerfully have bet the entire planetary atmosphere, stealing the future from all future generations, grew by 9.76 exajoules to 12.27 exajoules. World energy demand in 2018 was 599.34 exajoules. Unquestionably it will be higher in 2019 and in 2020.

10.63 exajoules is slightly over 2% of the world energy demand.

2018 Edition of the World Energy Outlook Table 1.1 Page 38 (I have converted MTOE in the original table to the SI unit exajoules in this text.)

According to this report, the fastest growing source of energy on the planet in the 21st century over all was coal, which grew from 2000 to 2018 by 63.22 exajoules to 159.98 exajoules.

If you think that unlike you, I am worrying and not being happy, you can always chant stuff about how "by 2050" or "by 2075" or "by 2100" we'll all live in a so called "renewable energy" nirvana powered by the sun and tooling around in Tesla electric cars.

I may be too jaded to be comforted, having heard this stuff my whole adult life - and I'm not young - but you could try. It's not results that count, but good intentions.

After the last Covid-19 patient on the planet has recovered, the much larger problem of climate change will still be with us.

History will not forgive us, nor should it.

Got a "locked in" project to do something you always wanted to do but didn't?

Here's mine:

My French is lousy; my German worse.

Last summer, at my mother-in-law's funeral, while giving my eulogy, I quoted a passage from Hesse's Demian that I'd translated into English, prefacing it with "Taking some small liberties with the translation from the German to get at what I think it means, Hesse wrote..."

A number of people came up to me after the eulogy and told me how much they liked what I had to say. A few people asked if I would send them a copy of it, with one or two praising the translation.

I recall some centuries ago, when I was young, I recall reading a translator's note on some book I was reading, admittedly sexist remark that has nevertheless stayed in my mind - I don't think it would be written today - that said, "A translation is like a woman, to the extent she is true, she is not beautiful." (Ok, the remark sucks, but it does express an idea.)

I've decided that to improve - better put to restore - my French, I'm going to work on translating Camus' La Peste into English. Every translation takes something away and perhaps puts too much in, but it seems like a project to undertake that I would never undertake if not confined. The thing is, that when you do a translation, you have to think about the structure of the language you're translating and of course, you need to expand your vocabulary, so it's definitely a constructive exercise.

OK, this will be memorable.

One of my sisters-in-law lives alone, in New York of all places, ground zero.

My wife just announced that we're going to have Easter Dinner with her on Zoom.

She's going to make the same thing we make, we'll set the computer at the end of the table and eat by zoom.

Strange world; a memorable one too.

Well, on the bright side, my son was able to find a way to graduate early from college.

My son entered college with 30 accepted AP credits, meaning technically, if not practically, he was a sophomore the day he was admitted.

Unfortunately, because of the arrangement of prerequisites and required courses for his major, he was going to be forced to stay four years. This had unfortunate economic consequences meaning a higher debt load.

As an outgrowth of this crisis though, he was able to wriggle out the opportunity from the department to take that last required course concomitantly with the prerequisite as independent study, and fill his schedule with some graduate courses.

It means he gets out six months earlier with his degree.

Moreover, if he keeps his GPA up where it's been through all of this, he gets a free year for a 30 credit masters, so he can stay around the campus with his girlfriend.

I don't think this would have happened were it not for this tragedy; a small consolation, but personally, a consolation nonetheless. This of course, doesn't negate the tragedy, but for him, some little good comes out of it.

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:

Direct-contact bubble columns are employed in high-temperature metallurgical processes such as steelmaking, degassing of aluminum, de-oxidation of copper, and high-temperature heat storage and chemical conversion in molten salts. The size and residence time of bubbles generated affect the chemical and physical interactions between gas constituents and the molten media, influencing the overall performance of direct-contact systems.(1) The bubble size influences bubble rise velocity, which consequently determines the residence time of the bubble in the molten metal, while the bubble surface area between the gas and liquid phases dictates the performance of interfacial transport and mixing processes.(1) Accurate information about bubble size is essential in order to characterize, control, and enhance the performance of processes based on high-temperature molten media.
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, γ-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 γ-ray imaging techniques are expensive and pose danger of exposure to hazardous rays.

Of course X-ray and γ-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:

Figure 3. Typical signal graph of pressure pulses generated during bubble release in molten tin at 600 C.

The fast Fourier transform:

The caption:

Figure 4. Typical frequency domain output of the single-sided spectrum of the absolute signal amplitude of the time series data.

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:

Figure 7. Comparison of helium bubble sizes obtained using the DPT from a 1 mm i.d. injector in glycerol at 25 C with literature correlations.

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.

Nelson Mandela was roughly the same age as Joe Biden when he took on saving his country...

...from decades of incompetent, ignorant and vicious leadership. He was born in 1918 and served as President of South Africa from 1994-1999, five years of magnificent leadership.

He was 76 when he became President of South Africa, and his warm and forgiving personality saved his country from decades of disgrace.

Joe Biden has to save a country savaged by malicious, corrupt, and ignorant leadership for a period of only four years.

The years of experience that Biden will bring to the job will come into play in a big way. Joe can do it.

That is all.

Some luminescent language castigating several cultures in a history book.

My hobby is reading history books, but I rarely read them cover to cover but rather excerpt them, reading sections of interest in detail and skimming other sections loosely.

In lock down, I find myself reading books cover to cover.

Right now I'm reading Parshall and Tully's Shattered Sword from cover to cover, with many pleasant surprises in the section on the background culture of Japan as it moved in the direction of war with the United States.

It covers the cultural resentment that the Japanese exhibited toward the White colonization of Asia which Japan itself had only narrowly resisted prior to the Meiji Restoration in 1868, the year that Japan was "opened" by the United States, Parshall and Tully compare the word "opened" and "raped."

It has this really luminescent phrase describing the reality how Japan envisioned itself as "liberating" it's Asian neighbors from "White Imperialism:"

The militarists concept of "liberation" ultimately proved to be little more than the shoving aside of the white powers so that the Japanese might themselves swill at the trough of economic exploitation. However, that apparently did little to sully the underlying purity of this grand vision in their eyes. Neither did Japanese resentment of racist inequality from the West stop it from foisting an equally virulent form of oppression on its own Asian neighbors.

"...swill at the trough..."

It sums up the dishonesty of both sides well, does it not?

They also describe how despite public exhaustion with a long war in China, which they call "the Chinese tar baby" how...

"The Japanese public felt powerless and detached from their own domestic politics, viewing the machinations of the Army and Navy, the assassination of government officials by members of the armed forces and other unsavory political acts of their own military with a jaundiced eye. That the prospect of fighting an additional war against the most powerful economy of earth, with the British and Dutch Empires thrown in for good measure, could bring a sense of elation to the Japanese public demonstrates the depth of its resentment against white imperialism in general and America in particular."

This forceful language to my eye evokes the history in a powerful way. It's cruelly fair.

I'm glad I'm able to use this time to read more deeply.

Tabular Lancet Infectious Disease Fatality Comparisons by Age: SARS, Covid-19, Influena.

All Covid related scientific papers are open sourced. The table here comes from this paper, a comment in Lancet Infectious Diseases: Likelihood of survival of coronavirus disease 2019 (Ruan, Lancet Infectious Diseases, March 31, 2020.)

An excerpt of the text:

Comparisons of case fatality ratios for SARS, COVID-19, and seasonal influenza in different age groups are shown in the figure. Even though the fatality rate is low for younger people, it is very clear that any suggestion of COVID-19 being just like influenza is false: even for those aged 2029 years, once infected with SARS-CoV-2, the mortality rate is 33 times higher than that from seasonal influenza. For people aged 60 years and older, the chance of survival following SARS-CoV-2 infection is approximately 95% in the absence of comorbid conditions. However, the chance of survival will be considerably decreased if the patient has underlying health conditions, and continues to decrease with age beyond 60 years.5, 6

I added the bold.

The table:

The caption:

FigureComparison of case fatality ratios for SARS,1, 8 COVID-19,7 and seasonal influenza9

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