Global warming is becoming ever increasing concern in our society. As such the likelihood of a carbon tax in the US is becoming increasingly likely. A carbon tax will be expensive enough that coal-based power plants will either have to install carbon capture technology or close. The two front runner technologies for carbon capture are amine scrubbing, and oxyfuel combustion. The downside is that both of these technologies increase power generation cost in a new plant by about 80% and have up to a 30% parasitic load, which reduces the cycle efficiency, that is, the power production per unit fuel consumed, by the same 30%. Retrofitting existing plants by either of these technologies is even more expensive and inefficient since it requires major modifications or replacement of the existing plant in addition to the new capture technology. Sustainable Energy Solutions (SES) has developed a carbon capture technology named cryogenic carbon capture (CCC). CCC is a process by which the flue gas cools to the point that CO2 desublimates. This process is more efficient, cheaper, and has about half of the parasitic load of other technologies, approaching the theoretical minimum in CO2 separation within heat exchanger and compressor efficiencies. This thesis conceptually describes, experimentally characterizes, and theoretically models one desublimating heat exchanger as an integral part of the CCC process. A spray tower conceptually developed by SES and theoretically and experimentally explored in previous work at lab scale is developed at bench scale in this work with accompanying major modifications to the theoretical model. It sprays a cold contact liquid to cool warm gas (relative to the contact liquid) that travels up the tower. Nominal operating temperatures are around -120 to -130 °C for 90% and 99% capture, respectively. Once the flue gas cools enough, CO2 desublimates on the liquid droplet surfaces and forms a slurry with the contact liquid. This spray tower can achieve arbitrarily high CO2 capture efficiency, depending on the temperature of the exiting gas and other operational variables. The experimental data outlined here varied these operational parameters over broad ranges to achieve capture efficiencies of 55% to greater than 95%, providing a robust data set for model comparison. The operational parameters explored include liquid temperature, liquid flow rate, gas flow rate, and droplet size. These data validated a transport and design model that predicts capture for future scale-up and design of the project. The data and model indicate expected behaviors with most of these variables and a dependence on internal droplet temperature profiles that may be higher than expected. This project significantly advanced the experimental database and the model capabilities that describe the spray tower.