I think the idea has potential.
As for the mist, I do believe that it is condensation, but not in the usual form: where we would expect humidity to collect on a cold plate, the dry ice would actually create a flow of very cold air.
I was just going over the topic of condensation, while looking up insulation materials, for my house. This neat book (old but interesting) titled "The Superinsulated Home Book" by J. D. Ned Nisson & Gautam Dutt, explains condensation this way:
Quote:
...a cubic foot of air at 70 deg F can hold about 0.00118 pounds of moisture at saturation. Relative Humidity (RH) is a term used to describe the degree of saturation of an air/water vapor mixture at a certain temperature. If air at 70 deg F has a relative humidity of 40 percent, then it is holding 40 percent of the saturated amount of water vapor (i.e. 0.40 * 0.00118, or 0.00047 pounds of moisture per cubic foot of air in this case).
As air cools, it gradually loses some of its ability to hold water vapor. When 70 deg F air with 40 percent relative humidity is cooled to 50 deg F, the relative humidity goes up to 80 percent. (The amount of water vapor in the air does not change; the relative humidity is higher because the amount of water vapor that air at 50 deg F can hold is less than the amount of water vapor that 70 deg F air can hold). If it is further cooled to 43 deg F, the relative humidity reaches 100 percent, or saturation. Below that temperature, the air will not be able to hold all its moisture and the water vapor will begin to condense into liquid water. The temperature at which condensation begins to occur is called the dew point temperature.
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So for dry ice, it cools some ambient air, which drops down into the case, because it's denser, and fogs up, because it can't hold the humidity that's in the room, at that temp.
But that air will warm up fairly quickly, and should take back the humidity. If it doesn't, then you'll have an "in case" rainfall.
I don't have any advice as for chemicals or "anti-fog" products. Someone else?
As for the added cooling, the dry ice would need to contact the core, which is easiest to do around the edge of it, but you may be looking at clogging issues, as the coolant freezes. You'll have to try it and see, and gradually add thin insulation to the contact area, to prevent freezing.