Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell–Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier–Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell–Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.
%0 Journal Article
%1 StierleDDFT2021
%A Stierle, Rolf
%A Gross, Joachim
%D 2021
%J The Journal of Chemical Physics
%K itt jgross myown rstierle
%N 13
%P 134101
%R 10.1063/5.0060088
%T Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence
%U https://doi.org/10.1063/5.0060088
%V 155
%X Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell–Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier–Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell–Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.
@article{StierleDDFT2021,
abstract = {Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell–Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier–Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell–Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.},
added-at = {2021-10-05T17:36:31.000+0200},
author = {Stierle, Rolf and Gross, Joachim},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/241ad3e792b550d79280a48d2b40e72be/rolfstierle},
doi = {10.1063/5.0060088},
interhash = {5f5d901e894c4f7dfb3e40b7d9c7f1f4},
intrahash = {41ad3e792b550d79280a48d2b40e72be},
journal = {The Journal of Chemical Physics},
keywords = {itt jgross myown rstierle},
number = 13,
pages = 134101,
timestamp = {2023-07-28T10:19:44.000+0200},
title = {Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence},
url = {https://doi.org/10.1063/5.0060088},
volume = 155,
year = 2021
}
