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Thermodynamics of CO2 Snow Formation

The carbon dioxide phase diagram has 3 phases -- gaseous, liquid, and solid. The triple point (pressure 5.1 atm., temperature - 56.7C) is defined as the temperature and pressure where three phases (gas, liquid and solid) can exist simultaneously in thermodynamic equilibrium. Above the critical point (pressure 72.8 atm., temperature 31.1C) the liquid and gas phase cannot exist as separate phases. This region, known as the superfluid or supercritical phase, has properties indistinguishable from the liquid and gas phases.



Another feature is the solid-gas phase boundary. Physically, this boundary implies that the gas and solid can co-exist and transform back and forth without the presence of liquid as an intermediate phase. A solid evaporating directly into the gas is called sublimation. At normal atmospheric pressure and temperature, the stable carbon dioxide phase is gas. This means that the final product is gaseous carbon dioxide and this final state is independent of the initial phase, cleaning process, or mechanism. Any solid CO2 will just sublime. With the CO2 present as a gas, the contamination can be separated from the exhaust stream and the CO2 is available for venting outside or recovery.


The key physical property of the Carbon Dioxide system is its excellent solvent properties for many nonpolar organic compounds. Like most solvents, the solvent properties of CO2 improve as the pressure and temperature increase. In cleaning, we rely upon the liquid phase solvent properties. Please note, thermodynamically, liquid carbon dioxide is unstable at room temperature and atmospheric pressure but this thermodynamic condition only refers to equilibrium states, not non-equilibrium states.


The phase diagram tells us little regarding dry ice formation or aid in understanding organic removal process; instead, the CO2 pressure - enthalpy diagram below provides insight to the phase changes that occur during snow formation. The features include the same 3 phases along with the region of pressure and enthalpy where these phases co-exist. These regions were phase boundaries in the above figure.


In using this diagram, it is imperative to understand that the if the nozzle is designed for a true adiabatic expansion, then there are no changes in enthalpy as the pressure and temperature drops.  This means that one can use either liquid or gas CO2 feeds.  Our nozzles work with both feed sources.  Most nozzles do not maitain this condition well.  In fact, most other nozzles can not form snow with CO2 gas feed.  Therefore, as the pressure drops in an orifice, the pressure decreases vertically along a constant enthalpy line.  (Image below can be magnified)

CO2 pressure enthalpy figure

A CO2 cylinder filled with liquid CO2 at room temperature has a gas pressure of about 800 psi above the liquid. The enthalpy available to the cylinder contents are those values in the liquid-gas two phase region at about 800 psi, in the spots labeled "A" for gaseous CO2 feed and "B" for liquid CO2 feed. As the gas or liquid enters the orifice, the pressure drops from these two points with constant enthalpy values (under ideal conditions) into the two phase liquid-gas region.


With a gas fed source (starting from point A) as the pressure drops in an orifice, liquid droplets nucleate and the percentage of liquid increases. At the interface between the liquid-gas and gas-solid regions (near 80 psi.), all the liquid converts to solid - yielding about 6 % dry ice. With a liquid fed source (starting at point B) as the pressure drops in the orifice, gas bubbles form and the percentage of gas increases until the gas-solid boundary is met. Here, the remaining liquid is transformed into solid - yielding about 45% dry ice. The percentage of snow depends on the chosen feed phase and is influenced by the source pressure and temperature. This diagram gives us information on the initial and final states and the phase changes that occur during snow formation and cleaning. Actual dry ice size, velocity, and percentage formed are based upon the above considerations and also orifice and nozzle designs.


From the above, we see that snow cleaning can be done with either a liquid or gas CO2 source. Each feed has its advantages and disadvantages. Gas fed systems tend to be cleaner (easier to filter a gas than a liquid), have less heavy hydrocarbon contamination, and have less consumption per unit time. Liquid fed systems produce more snow, allow for faster cleaning, but at a higher consumption rate. If the cleaning is occasional or a "small" area, a gas feed system is recommended, while for continuous high speed cleaning or large areas, a liquid source is recommended.  One art restorer user strongly recommends CO2 gas feed.  


In our snow cleaning equipment, we chose the asymmetric Venturi nozzle design for our nozzles. This selection maintains the constant enthalpy conditions the longest, yields more snow, maximizes velocity, and a focused cleaning stream. Please note that straight tube nozzles violate the constant enthalpy condition and usually do not produce adequate snow unless the orifice diameter is larger. This is quite dramatic with gas fed sources. With liquid fed sources, it is also seen at small orifice diameters. This limitation implies an inherent inefficiency in the straight tube designs.


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