How can you do process intensification of fractional crystallization cascades?
Freeze distillation or fractional crystallization is normally a slow process. But they still work even if the crystals are very small, so there’s no need for them to be slow. You could carry them out at frequencies in the neighborhood of 1 Hz using something like a phase-change regenerator. The “coolant” of the “regenerator” is probably something innocuous like brine, while the phase-change material in the “regenerator” is the material you’re actually trying to separate by partial crystallization, and it isn’t quite stationary: you pump the liquid phase in a direction parallel to the direction of the coolant, but 90° out of phase with the pumping of the coolant.
That is,
This should result in concentrating the lowest-melting solution of the phase-change mixture toward the cold reservoir, and the higher-melting parts toward the warm reservoir, while more or less maintaining the temperature gradient constant. The temperature swing may be more than you would expect, because metastable zone width increases with stirring and cooling rate, and our stirring and cooling rate here is yuuge.
If at some point the phase-change material passages are completely blocked, you can pump warm coolant past it until that’s no longer the case.
Separated phase-change material can be removed at the extremes of the apparatus, and unseparated material can be added to replace it in the middle, providing a quasi-continuous process.
This process should be sensitive enough to separate substances by even very slight differences in solubility, including difficult cases like separating erbium bromate from holmium bromate or separating heavy from normal water. It might even be capable of competing with ion-exchange chromatography. The regenerator-like configuration eliminates nearly all of the energy waste associated with traditional fractional crystallization cascades.
It’s important for the piping to be narrow enough to prevent diffusion of the liquid phase-change mixture against the concentration gradient from becoming turbulent rather than viscous, and also to prevent the diffusion of heat against the temperature gradient, since narrower passages are longer for constant volume; additionally, narrower passages mean that heat diffuses between the coolant and the phase-change material more rapidly, allowing higher frequencies. However, narrower passages require more energy applied both to pump the fluids and to restore the temperature difference between the reservoirs.
If both fluids are liquids, it may be desirable to carry out the entire process under high pressure or even to alternate between pressures (in addition to or instead of pumping coolant) to alter the equilibrium phases of the phase-change material. This may allow an escape from pernicious eutectics. Doing this with a gaseous coolant might be feasible but seems like it would be very difficult due to adiabatic heating and possible deformation of the apparatus.
Here are some possible materials, depending on the temperature range in which the material to be separated solidifies:
|-------------------+-----------------------+-------------------------------|
| temperature range | coolant | piping |
|-------------------+-----------------------+-------------------------------|
| <-200° | LN₂ | copper |
| | | brass |
| | | cryogenic stainless |
|-------------------+-----------------------+-------------------------------|
| -200°–-100° | ethane (to -182°) | cryogenic stainless |
| | R-32 (to -136°) | brass |
| | R-22 (to -175°) | copper |
| | propane (to -187°) | |
|-------------------+-----------------------+-------------------------------|
| -100°–-20° | ethanol (to -120°) | silicone |
| | propylene glycol | copper |
| | (to -59°) | brass |
| | R-134a | low-temperature stainless |
| | SF₆ (to -50°) | |
| | R-22 (below -40°) | |
|-------------------+-----------------------+-------------------------------|
| -20°–0° | brine | polyethylene |
| | ethanol | polyethylene terephthalate |
| | propylene glycol | silicone |
| | | copper |
| | | stainless |
| | | steel |
| | | brass |
| | | glass |
| | | aluminum |
| | | PTFE |
|-------------------+-----------------------+-------------------------------|
| 0°–200° | water | polyethylene |
| | mineral oil | PET |
| | propylene glycol | glass |
| | (to 188°) | silicone |
| | glycerol | polyimide |
| | ethanol | copper |
| | silicone oil | stainless |
| | | steel |
| | | brass |
| | | bronze |
| | | aluminum |
| | | PTFE |
|-------------------+-----------------------+-------------------------------|
| 200°–500° | molten nitrate salts | borosilicate glass |
| | fluorocarbons | stainless |
| | lead-tin eutectic | polyimide |
| | type metal (Sn/Pb/Sb) | copper |
| | FLiNaK | brass |
| | FLiBe | bronze |
| | NaK, Na, PbSb | |
| | tin | aluminum |
| | air | steel |
| | CO₂ | |
| | glycerol (to 290°) | |
| | steam | |
| | silicone oil | |
|-------------------+-----------------------+-------------------------------|
| 500°–1000° | molten nitrate salts | fused quartz |
| | Sn/Pb, Sn/Pb/Sb, Sn | stainless |
| | FLiNaK, FLiBe | superalloys |
| | air | fluorination may be desirable |
| | noble gases | noble metals |
| | CO₂ | |
| | nitrogen | |
|-------------------+-----------------------+-------------------------------|
| 1000°–1200° | Al, Pb, Li | stainless |
| | CO₂ | superalloys |
| | nitrogen | noble metals |
| | noble gases | fused quartz |
|-------------------+-----------------------+-------------------------------|
(All of the above is kind of a guess, not deep materials knowledge.)
Presumably the only temperature limit on the applicability of the process is being able to find piping materials that melt hotter than the materials you’re trying to separate and that won’t significantly dissolve in or react with the materials you’re separating at their melting point. (You don’t want total nonreactivity, though, because you need the crystals to nucleate, ideally on the walls.) I just don’t know what to propose above 1200°.