Theorems & Bounds
Our screen scored 14,559 two-part blends; 7,020 of them clear a climate ceiling. The cards below say what that and the screen’s other results show, and what they do not.
FluxZero owns no mathematical theorem. What it has are results from its own screen and simulations, each stated as a formula, with what that result shows, and what it does not, in plain words beside it. Every number is read from a published file, linked under each card, except where a card says its table is not published. Nothing on this page has been measured on a bench.
Figures from the home page
- 14,559Two-part blends screened by computer
Bounds & Screening Results
Enumerated
Our own enumeration and scoring of every blend in the declared component space, on five axes; on the lab's machine, the (unpublished) table regenerates byte-for-byte from one script
The buildable space, enumerated and gated
It shows the size of the search. The fuel-plus-pump space we can build from catalogue molecules is 14,559 blends, and a climate ceiling of 150 alone removes more than half of it before any performance question is asked.
Enumerated
Counted in the same run as the gate above; flammability and climate axes only. None of the candidates has a fuel without fluorine; recounted from the blend table, which is not published, the 174 split evenly between HFO-1336mzz-Z and FK-5-1-12
Our screen rates some low-carbon blends non-flammable, and all of them contain fluorine
It shows that the screen rates 174 candidates under the climate ceiling as non-flammable, a rating, not a measurement. It does not show an option without fluorine: every one of the 174 has a fluorinated fuel, half of them HFO-1336mzz-Z and half FK-5-1-12 (Novec 649), which is itself a PFAS. Nor is any of them shown to work as a dielectric coolant: of our four in-house candidates, none that is rated non-flammable has a permittivity below 6, the cut this screen uses for a fluid in direct contact with the electronics.
Checked against published data
Calibration of the thermodynamic library against literature values for four fuels (three used by the surviving blends, plus one more fluorinated fuel), the fluorinated fuels' values taken from their manufacturers' datasheets; no pump liquid is calibrated; it calibrates the library, not the molecular dynamics
Our property library, checked against published numbers
It shows the screen’s inputs are not exact. Against published values for four fluids, the property library is off by 5.2% on average in surface tension, 19.0% on HFO-1336mzz-Z (1.4% on FK-5-1-12, the other fluorinated fuel), and 0.1 °C in boiling point. The heat-flux model's band assumes one surface-tension uncertainty for every candidate, larger than the 5.2% average but smaller than the 19.0% miss on HFO-1336mzz-Z, so the bands of the HFO candidates understate that known error.
Modelled, with and without the boost
Our system model over literature properties; its bare-fluid ceiling is the textbook Zuber hydrodynamic limit and the pairing rule it applies (pump surface tension above fuel, pump boiling point at least 30 °C higher) is our own pairing rule, stated in documents we do not publish
Both figures are the two arms of one paired run on the Pentane + DMC 80:20 reference, as stated in the results record linked below; the run’s own output is not published. The model’s own median for the same blend comes from a second run of the same model.
Our model leans on an assumed surface-tension boost: set it to zero and modelled heat flux falls 40%
Our heat-flux model assumes that the surface-tension difference between the two parts adds to boiling performance. Setting the surface-tension boost alone to zero, in the same model run, lowers the reference blend's modelled heat flux to 111.5 W/cm²; that remaining figure still includes the model's other assumed boosts. That shows how much the model depends on this one assumption, not on all of them. It does not show that the effect exists: it has never been simulated with surface-tension-driven flow or measured. The boiling test on bare copper, the last of the four bench tests, is what would show it.
Simulated
Twelve molecular-dynamics runs, three seeds at each of four temperatures, fitted by weighted least squares
The sweep is of Pentane+DMF 80:20, the pair the surface-tension runs were done on. It is a different pair from the Pentane + DMC 80:20 lead.
In one simulated blend, surface tension falls as the liquid heats
In our simulation of one blend, its surface tension falls about 0.18 mN/m for every kelvin; fitted at four temperatures, that slope is too uncertain to tell apart from the range our file records for similar liquids (the file does not name that range's source), and our molecular simulations missed their own control in a separate test on this site. How the difference in surface tension between the two parts changes with temperature has not been computed. If it shrinks as the blend heats, a design margin chosen at 25 °C would be too thin at the hot end.
How these fit together, and what has been checked against other people’s measurements: the research results.
How the numbers on this page are checked
- its file were still loading in your browser,
- the question behind it had not been looked into,
- it had been looked for and not found,
- its file held no value for it,
- its file were missing or had changed,
- two files disagreed about what it describes,
- its sample were too small for the claim,
- two files gave it different values,
- its file could not be published,
- the file it is read from had last changed more than thirty days before this build,
- the question did not apply to this page or
- the program that makes it had stopped with an error; no underlined number on this page is marked.