Offering a concrete answer to your question would require some additional information, most importantly:
- the temperature of the ambient environment into which heat would be rejected
- the thermal properties of the fluid in question
- the performance requirements of your application.
That said, despite being extremely convenient in many respects, peltier devices are terribly, horribly, awfully inefficient, and generally to be avoided where feasible.
In the spirit of guesstimation, let’s assume you’re in a 20°C ambient environment, have 200 grams of material with an averaged specific heat of 4J/g°C on the trip down to Coldville from the 20°C starting point. That’s 200g75°C4J/g°C= 60kJ of thermal energy that needs to be extracted from the material of interest. Whatever is holding the sample has to get cooled down also, not to mention the structure of the system itself, so let’s double the figure, and use 120kJ as the amount of thermal energy that needs to get moved.
Getting to -55°C means a minimum 75°C temperature difference across the refrigeration engine. Figuring in the temperature rise of the heat sink over ambient, and you’re probably looking at a 90~100°C deltaT, which is beyond the reach of single-stage peltier solutions. Going to a multi-stage solution exponentiates the system inefficiencies, taking something that was bad to start with and making it really, really bad for a two-stage solution, and excruciatingly, terribly, just-this-side-of pointlessly bad for a three-stage solution. But if you need the deltaT, you need the deltaT…
Digi-key’s product listings for high-deltaT peltier modules can be found here arranged in descending order of DeltaT (max), which applies only when the device is not moving any heat from the cold to the hot side, which isn’t very useful… The Qmax figures for the high-delta multi-stage devices are in the ballpark of 10W, which only applies when the temperature difference across the device is zero, which (again) isn’t very useful… These figures represent the end points of the device’s operating curve, and in practice, the device will always be operating somewhere in between these points… So figure a Q (heat movement rate) of 5W for estimation purposes…
At this point, it’s been estimated that we need to move 120kJ (120,000 watt-seconds) of energy, and the available peltier equipment can do it at a rate of 5 watts. 120,000/5=24,000 seconds or 400 hours (!) to get the job done. A lot has been omitted in the guesstimation process, and I’d suggest that this is simply not a plausible design approach.
Something that might work better is getting a small household freezer that can make an ambient temperature of -20 tor so for you, and use a single-state peltier inside of that to drop the last 35°. The amount of heat that would need to be moved by the peltier would them be 200g4J/g°C35°C=28kJ. Figuring double that again for the stuff that has to come along for the ride, and we’re at 56kJ of total heat transfer required.
The 926-1300-ND has a Qmax rating of 153W and deltaT(max) of 72°C. We’re looking at at 35°C deltaT, which is roughly in the middle of that part’s performance curve, which would mean we’d get a heat tansfer rate of about 75W. 28,000 joules (watt-seconds)/75 watts=373 seconds, or about 6 minutes, which sounds a bit more reasonable.
…But that’s with about 250W of electric input power, which calls for a rather beefy heatsink, such as the 345-1174-ND. It’s thermal resistance is listed as 0.1°C/W with 100 CFM airflow, which would translate to a 25°C temperature rise over ambient, which added to the 35°C below ambient that we need the peltier to develop, for a total of 60°C deltaT… At that point on the peltier’s load line, the Q value would be about 25 watts, pushing the time frame for chilling stuff out toward the 20-minute mark. Which is starting to look sketchy again, but feasible. And one would probably need a fan to go with that heatsink… The 381-1068-ND looks like it could be made to fit, and could probably be run off the same low-voltage supply as the peltier. (you’d be getting condensation in the freezer, and I’m not thinking that piping 120VAC around that environment would be a good idea…)
The 382275-ND would probably make a good power supply for all that; setting the output for 28v/9A would seem about right for the peltier+fan above, and a throttling/thermostat circuit could probably be realized via that supply’s external control capability.
The freezer+peltier approach seems potentially viable, if you need a shelf stable, thermostatically-controllable solution. And if those aren’t necessary features? Just use some dry ice instead…