Cryogenic carbon capture is a method to remove carbon dioxide from flue gas by cooling the gas mixture until the CO2 desublimates as a solid. Simulating this process is necessary to predict the rate and location of solid CO2 formation. There are three fundamental components that must be modeled to capture the desublimation dynamics: 1) the phase equilibrium, 2) the rate of phase change, and 3) the thermal effect of the phase change. These thermodynamic and transport processes are combined into a fundamental physics-based model for CO2 desublimation from flue gas. The phase-change model will be presented along with a comparison of the simulation results to experimental measurements. This model can enable better scalability of Carbon America's carbon capture technology.