Abstract
In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.
Highlights
Homogeneous nucleation of droplets plays an important role in processes in the atmosphere, since it describes forming of the secondary aerosols, and in many technological processes such as nucleation in the crude nature gas during the gas cleaning, nucleation in steam turbine, etc.Despite many attempts that resolved partial subproblems of the nucleation, there is no complete theory which would give quantitatively correct predictions.Studying the nucleation has its roots in the work of Gibbs and Volmer and Farkas; it was mainly developed by Bercker end Doring
We used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the Statistical Associating Fluid Theory (SAFT) EoS developed by Gross and Sadowski [1]
We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions
Summary
Homogeneous nucleation of droplets plays an important role in processes in the atmosphere, since it describes forming of the secondary aerosols, and in many technological processes such as nucleation in the crude nature gas during the gas cleaning, nucleation in steam turbine, etc. It is more realistic to consider a smoother change of the interface This approach was developed by Cahn and Hilliard [4, 5] the main ideas were given already by van der Waals [6] (English translation by Rowlinson [7]). Main idea of their theory ( known as DGT) was to extend the Helmholtz free energy of the system containing the droplet by the term of gradient of the particle density. A recent study of the gradient theory with comparison to molecular simulations was given by Baidakov et al. In this work, we continue in our approach [3] to concentrate on the nucleation of one component using the DGT, which mathematically leads to the problem how to solve the boundary value problem for the ordinary differential equation of the first order. We encountered a systematic temperature drift of both nucleation theories to the experimental data which is not explained by present theories
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