(655e) Homogeneous Bubble Nucleation in Liquid Carbon Dioxide from a Hybrid of Molecular Dynamics Simulation and Density Gradient Theory

Bubble nucleation is the first stage in cavitation. This phenomenon is well known in industrial processes and generally unwanted. It may occur, if a liquid is brought into the metastable range of the vapor-liquid equilibrium. It is usually described by classical nucleation theory (CNT), which relies on extreme simplifications, e.g. assuming that the usually nanoscopic bubbles have the same properties as the saturated bulk vapor and that their surface tension is the same as that of the planar interface^1â??3. In many cases CNT fails drastically^4â??7, while in other cases, it gives fair predictions. This behavior is not fully understood, but it is argued sometimes that in nucleation different phenomena combine and sometimes errors cancel out^8,9.

Another method used for studies of nucleation in literature^10,11 is density functional theory (DFT) or simplifications thereof like the density gradient theory (DGT) first applied by Cahn and Hilliard to droplet nucleation in demixing incompressible liquids¹². DFT and DGT have the advantage of correct limiting behavior approaching both binodal and spinodal. They do also inherently consider the size dependence of surface tension. Using full DFT, however, the free energy of the heterogeneous system must be known as a functional of density, which is most often not the case. Also, both theories only give information on the thermodynamic barrier, but not on the kinetics of bubble nucleation. This is usually addressed by using expressions for the kinetic pre-factor obtained in the framework of CNT. This may be dangerous, since CNT is usually developed for describing the whole process so that using only the pre-exponential factor of CNT may lead to poor results. We propose here a different method with a clean separation between kinetics and thermodynamics.

In order to properly introduce kinetics into the DGT based nucleation model, we hybridize it with molecular simulation. As an example, CO₂ is studied. All our computations are based on the molecular model of Merker et al.¹³ of CO₂. The thermodynamic and interfacial properties of this model are used to fit the parameters of the PC-SAFT¹⁴ equation of state (EOS), as well as the influence parameter from DGT. This way, a thermodynamic link between molecular simulation and thermodynamic model is achieved, which is further confirmed by comparison to molecular simulation data in the metastable range. In a next step, the homogeneous bubble nucleation of the molecular model is simulated for two temperatures using molecular dynamics simulation following an approach first introduced by Yasuoka and Matsumoto¹⁵ for droplet nucleation and later on applied by Diemand et al.¹⁶ for bubble nucleation. The kinetic pre-factor of the proposed hybrid theory is then fit to the direct simulation data at two temperatures, where we assume an Arrhenius type dependence on temperature. This way, our hybrid method describes bubble nucleation in the whole metastable range from triple point to critical point without relying on any further assumptions. The results compare favorably to our direct simulations of the nucleation rates and to available experimental data for CO₂^17,18, while CNT shows the wrong temperature dependence and is off several orders of magnitude in terms of nucleation rates.

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