A general model to evaluate the energy barrier to nucleation in vapour system by considering real gas approaches of the equation of state

Researchers have advanced theories and models of spontaneous homogeneous nucleation which result in the so-called “classical nucleation theory” (CNT). However, the corresponding algebraic equations to calculate the classical droplet radius and nucleation rate (classical nucleation model) widely used in engineering calculations e.g. to predict condensation in nozzles and turbomachines consider assumptions regarding the ideal gas law. Due to the discussion over real gases in recent years, many works apply the CNT probably with modifications for gases like CO 2 whose working state is in many cases much closer to the critical point rather than e.g. water. However, a clear review of the modelling process might not be shown which discusses the choice of assumptions and the approaches of the equations of state (EOS). As the first step of understanding the impact of the “distance to the critical point” on nucleation processes, this work aims to model the energy barrier to nucleation Δ G ∗ , through two derivations. The first one assumes a constant liquid density and considers cubic, virial and free-energy-based approaches of EOS respectively. The second counts a free energy-based approach and a varying liquid density. Eventually, an evident deviation between the presented and several existing models is detected. For CO 2 , the isothermal compression term should be considered and a constant liquid density can be counted within a deviation of 7 %. Both cubic and virial models do not correspond to the free-energy-based one in the vicinity of the critical point. • A general model for evaluating the nucleation barrier of real gases is presented. • Quantitative differences between the previous and presented models are presented. • The impacts of real gas approaches on the nucleation model are discussed.