Universität Stuttgart
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Item Open Access Development of hydrodynamic density functional theory for mixtures and application to droplet coalescence(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2021) Stierle, Rolf; Groß, Joachim (Prof. Dr.-Ing.)Predicting accurately coalescence phenomena is critical to the accurate description of the hydrodynamics of fluids and their mixtures. A promising framework for the development of models for such phenomena is dynamic density functional theory. Dynamic density functional theory enables the analysis of dynamical processes in inhomogeneous systems of pure fluids and fluid mixtures at the molecular level. In this work, a hydrodynamic density functional theory model for mixtures in conjunction with Helmholtz energy functionals based on the PC-SAFT equation of state is proposed, that obeys the first and second law of thermodynamics and simplifies to the isothermal Navier-Stokes equation for homogeneous systems. The hydrodynamic density functional theory model is derived from a variational principle and accounts for both viscous forces and diffusive molecular transport. A Maxwell-Stefan model is applied for molecular transport. This work identifies a suitable expression for the driving force for molecular diffusion of inhomogeneous systems that captures the effect of interfacial tension. The proposed hydrodynamic density functional theory is a non-local theory that requires the computation of weighted (spatial averaged) densities around each considered spatial coordinate by convolution, which is computationally expensive. This work uses Fourier-type transforms to determine the weighted densities. A pedagogical derivation is presented for the efficient computation of the convolution integrals occurring in the Helmholtz energy functionals in Cartesian, cylindrical, and spherical coordinates on equidistant grids using fast Fourier and similar transforms. The applied off-the-shelf algorithms allow to reduce dimensionality and complexity of many practical problems. Furthermore, an algorithm for a fast first-order Hankel transform is proposed, allowing fast and easy density functional theory calculations in rotationally symmetric systems. Application of the hydrodynamic density functional theory model using a well-balanced finite-volume scheme to one-dimensional droplet and bubble coalescence of pure fluids and binary mixtures is presented. The required transport coefficients, shear viscosity and Maxwell-Stefan diffusion coefficients, are obtained by applying entropy scaling to inhomogeneous fluids. The considered systems show a qualitative difference in the coalescence characteristics of droplets compared to bubbles. This constitutes a first step towards predicting the phase rupture leading to coalescence using dynamic density functional theory.Item Open Access A new dispersion contribution based on the PCP-SAFT equation of state in the framework of classical density functional theory(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2019) Sauer, Elmar; Groß, Joachim (Prof. Dr.-Ing.)This dissertation presents the development and evaluation of a dispersion contribution model of a Helmholtz energy functional in the framework of classical density functional theory. The model is based on the PCP-SAFT equation of state and was applied to fluid-liquid interfaces, confined systems, and sessile droplet systems.Item Open Access Calculation of pure substance and mixture viscosities using PCP-SAFT and entropy scaling(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2020) Lötgering-Lin, Oliver; Gross, Joachim (Prof. Dr.-Ing.)Item Open Access Optimization of transferable force fields based on reduced order and surrogate models(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2025) Fleck, Maximilian; Hansen, Niels (apl. Prof. Dr.-Ing. habil.)Classical transferable force fields are utilized to make predictions about physical properties and microscopic processes in both pure substances and mixtures. The process of developing these force fields involves optimizing the nonbonded interactions through multidimensional optimization techniques, utilizing computationally intensive Monte Carlo and molecular dynamics simulations. Due to the high correlation of force field parameters, this optimization process can be challenging. To improve efficiency, physically-based surrogate models were utilized to expedite the optimization process. In particular, new reduced order models for transport properties based on entropy scaling were developed. Now transport properties such as viscosity, thermal conductivity and self-diffusion coefficients can be represented in the optimization of force fields through surrogate models alongside static properties, which was previously not possible. Furthermore, machine-learned models for transport properties based on linear multifidelity Gaussian processes utilized in reduced residual entropy space were developed. Here, experimental data is combined with simulation results which enables to enhance predictive capabilities and optimize force fields more effectively.Item Open Access Interfacial properties using classical density functional theory : curved interfaces and surfactants(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2021) Rehner, Philipp; Groß, Joachim (Prof. Dr.-Ing.)Interfaces play an important role in natural and industrial processes. Classical density functional theory (DFT) has been established as a tool capable of predicting interfacial properties, but also of providing insight in the structure of fluids at interfaces. Compared to other statistical mechanical methods, particularly molecular simulation, an efficient implementation of DFT offers a significant reduction in computation time. This advantage comes with the cost of an increased modeling effort. In this work, the calculation of interfacial properties using DFT is discussed and applied to different aspects of interfaces. First, the properties of highly curved interfaces, as they appear in nucleation processes, are studied. This is done first by directly calculating the properties of nanodroplets using DFT in spherical coordinates and afterwards in an expansion around a flat interface. Because for some applications, the calculation time of DFT is a limiting factor, a new method to predict surface tensions from equation of state parameters is introduced. This is achieved by using a Taylor expansion of the full DFT Helmholtz energy functional around a local density. The resulting functional is identical to that used in density gradient theory except for an explicit, temperature and density dependent expression for the influence matrix. The method is subsequently used to examine in detail the parametrization of associating components, particularly water and alcohols, that pose difficulties with respect to the simultaneous description of bulk phase equilibria and interfacial properties. A multiobjective optimization approach is used to assess different models and to quantify their capabilities and limitations. The so obtained water model presents the foundation for the last segment of this work, that studies the interfacial properties of water/surfactant and water/alkane/surfactant systems. The amphiphilic surfactant molecules are modeled using a heteronuclear DFT approach that resolves the distributions of individual segments. The parameters of this group contribution method are obtained by fitting to properties of small surfactant molecules and can then be used to predict properties of larger molecules for which less or no experimental data is available. The model is used to study the adsorption and orientation of surfactant molecules at interfaces and the corresponding reduction in interfacial tension.