Mass-Conserved Density Gradient Theory Model for Nucleation Process

Abstract

Modeling droplet nucleation processes requires a molecular-scale approach to describe the interfacial tension (IFT) of spherical interfaces. Density gradient theory (DGT), also referred to as square gradient theory in some publications, has been widely used to compute the IFT of many pure and mixed systems at the molecular scale. However, the application of DGT to droplet interfaces is limited by its setup in open systems in which a stable droplet cannot be achieved. In this paper, we propose a mass-conserved DGT model in a closed system, i.e., with no-flux boundary conditions, where no mass exchange is allowed with the outside environment. As opposed to the traditional approach, this model enforces a canonical ensemble and guarantees energy dissipation. The proposed model has been successfully applied to systems with planar interfaces as well as spherical interfaces, especially for IFT calculation for droplets in the nucleation process. By extending the DGT model from open to closed systems, we demonstrate the potential of DGT as an inhomogeneous model for a wider range of academic and industrial applications.

Achieving Convergence in Multiphase Multicomponent Density Gradient Theory Calculations through Regularization

“…In addition, the presented scheme is unconditional energy stable in the sense that the discrete regularized energy is dissipated in each time step. This property can be proven analogously to Item (i) in Theorem 5, as detailed in ref 48 for the discrete setting, using the inequality from Assumption 13.…”

“…The numerical algorithm developed through is similar to ref and conserves the discrete molar amount in each component. It satisfies an energy stability estimate for a discrete approximation of the Helmholtz energy in each time step.…”

“…On the other hand, if the droplet radius is greater than the critical value, it will grow until the entire system transitions into the liquid phase. In the present work, we examine the DGT model of Mu et al, which considers domains featuring an impermeable boundary and thus allowing for the investigation of droplet nucleation in an NVT setting. The NVT framework eliminates the need for preprocessing phase equilibrium calculations and allows for the direct computation of the equilibrium density profile. ,− …”

Modeling Interfacial Properties with Spot-DGT-ePC-SAFT for Binary Mixtures Including Ionic Liquid-Based Systems

“…Sometimes, in a mixture, the intrinsic free energies of two components are close to each other, making it difficult to choose the reference substance and use the reference fluid theory. Also, for some mixtures, β ij cannot be assumed as zero. − In this case, the stabilized algorithm developed by Mu et al can be used, ,,, where neither the reference substance nor the zero β ij is required.…”

“…Also, for some mixtures, β ij cannot be assumed as zero. 42−45 In this case, the stabilized algorithm developed by Mu et al 45 can be used, 16,45,58,59 where neither the reference substance nor the zero β ij is required.…”