1
|
Stierle R, Gross J. Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence. J Chem Phys 2021; 155:134101. [PMID: 34624998 DOI: 10.1063/5.0060088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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.
Collapse
Affiliation(s)
- Rolf Stierle
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| |
Collapse
|
2
|
Jia W, Kusaka I. Density functional study of non-isothermal hard sphere fluids. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1875077] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Wenhan Jia
- William G. Lowrie Department of Chemical and Biomolecular Engineering, Koffolt Laboratories, The Ohio State University, CBEC, Columbus, OH, USA
| | - Isamu Kusaka
- William G. Lowrie Department of Chemical and Biomolecular Engineering, Koffolt Laboratories, The Ohio State University, CBEC, Columbus, OH, USA
| |
Collapse
|
3
|
Heat, temperature and Clausius inequality in a model for active Brownian particles. Sci Rep 2017; 7:46496. [PMID: 28429787 PMCID: PMC5399351 DOI: 10.1038/srep46496] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Accepted: 03/17/2015] [Indexed: 11/20/2022] Open
Abstract
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.
Collapse
|
4
|
Löwen H. Dynamical Density Functional Theory for Brownian Dynamics of Colloidal Particles. VARIATIONAL METHODS IN MOLECULAR MODELING 2017. [DOI: 10.1007/978-981-10-2502-0_9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
|
5
|
Affiliation(s)
| | - Matteo Paoluzzi
- Department of Physics, Syracuse University, Syracuse, NY, USA
| | - Claudio Maggi
- Dipartimento di Fisica, Universita Sapienza, Rome, Italy
| |
Collapse
|
6
|
Kikkinides ES, Monson PA. Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems. J Chem Phys 2015; 142:094706. [DOI: 10.1063/1.4913636] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- E. S. Kikkinides
- Department of Mechanical Engineering, University of Western Macedonia, 50100 Kozani, Greece and Chemical Process and Energy Resources Institute (CPERI), Centre for Research and Technology Hellas (CERTH), 57001 Thermi-Thessaloniki, Greece
| | - P. A. Monson
- Department of Chemical Engineering, University of Massachusetts, 159 Goessmann Laboratory, 686 North Pleasant Street, Amherst, Massachusetts 01003-9303, USA
| |
Collapse
|
7
|
Dalton BA, Daivis PJ, Hansen JS, Todd BD. Effects of nanoscale density inhomogeneities on shearing fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052143. [PMID: 24329250 DOI: 10.1103/physreve.88.052143] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2013] [Indexed: 06/03/2023]
Abstract
It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.
Collapse
Affiliation(s)
- Benjamin A Dalton
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - Peter J Daivis
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - J S Hansen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - B D Todd
- Mathematics, Faculty of Engineering and Industrial Sciences, and Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| |
Collapse
|
8
|
Marconi UMB, Melchionna S. Weighted density Lattice Boltzmann approach to fluids under confinement. Mol Phys 2013. [DOI: 10.1080/00268976.2013.771801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
9
|
Das SP, Yoshimori A. Coarse-grained forms for equations describing the microscopic motion of particles in a fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:043008. [PMID: 24229277 DOI: 10.1103/physreve.88.043008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2013] [Revised: 06/12/2013] [Indexed: 06/02/2023]
Abstract
Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.
Collapse
Affiliation(s)
- Shankar P Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | | |
Collapse
|
10
|
Anero JG, Español P, Tarazona P. Functional thermo-dynamics: A generalization of dynamic density functional theory to non-isothermal situations. J Chem Phys 2013; 139:034106. [DOI: 10.1063/1.4811655] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
|
11
|
Hoang H, Galliero G. Local viscosity of a fluid confined in a narrow pore. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021202. [PMID: 23005753 DOI: 10.1103/physreve.86.021202] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2012] [Indexed: 06/01/2023]
Abstract
In this paper, molecular dynamics simulations of a simple Lennard-Jones fluid confined in narrow slit pores and undergoing shear have been performed. The aim is to investigate the effects of density inhomogeneities at the fluid-solid interfaces on the shear viscosity profiles. It has been found that the local viscosity was varying strongly with the distance from the solid walls for both dilute and dense fluid states with oscillations correlated to the density ones. To describe the computed viscosity profiles, we propose a scheme that uses the local average density model, combined with an adequate weight function, for the configurational viscosity and a semiempirical model for the translational viscosity. It is shown that the proposed approach is able to provide viscosity profiles in good agreement with those coming from simulations for different pore widths and for different fluid states (dilute to dense).
Collapse
Affiliation(s)
- Hai Hoang
- Laboratoire des Fluides Complexes et leurs Réservoirs, UMR-5150 with CNRS and TOTAL, Université de Pau et des Pays de l'Adour, Boîte Postale 1155, PAU Cedex 64013, France
| | | |
Collapse
|
12
|
Melchionna S, Marini Bettolo Marconi U. Stabilized lattice Boltzmann-Enskog method for compressible flows and its application to one- and two-component fluids in nanochannels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036707. [PMID: 22587209 DOI: 10.1103/physreve.85.036707] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2011] [Indexed: 05/31/2023]
Abstract
A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of nonideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. [J. Comput. Phys. 152, 642 (1999)]. Numerical tests show that, in the case of a one-component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two-component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.
Collapse
Affiliation(s)
- Simone Melchionna
- CNR-IPCF, Consiglio Nazionale delle Ricerche, Università di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
| | | |
Collapse
|
13
|
Hughes KH, Baxter SN, Bousquet D, Ramanathan P, Burghardt I. Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. II. Application to nonpolar solvation. J Chem Phys 2012; 136:014102. [DOI: 10.1063/1.3671378] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
14
|
Wittkowski R, Löwen H, Brand HR. Microscopic and macroscopic theories for the dynamics of polar liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041708. [PMID: 22181158 DOI: 10.1103/physreve.84.041708] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2011] [Indexed: 05/31/2023]
Abstract
We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as order-parameter fields. The results are critically compared with those obtained using the macroscopic approach of time-dependent Ginzburg-Landau (GL) equations for the analogous order-parameter fields. We demonstrate that, for both the microscopic DDFT and the macroscopic GL approach, the resulting dissipative dynamics can be derived from a dissipation function. We obtain microscopic expressions for all diagonal contributions and for many of the cross-coupling terms emerging from a GL approach. Thus, we establish a bridge between molecular correlations and macroscopic modeling for the dissipative dynamics of polar liquid crystals.
Collapse
Affiliation(s)
- Raphael Wittkowski
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | | | | |
Collapse
|
15
|
|
16
|
|
17
|
Mickel W, Joly L, Biben T. Transport, phase transitions, and wetting in micro/nanochannels: A phase field/DDFT approach. J Chem Phys 2011; 134:094105. [DOI: 10.1063/1.3557061] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
18
|
|
19
|
Zhao SL, Wu J. Self-consistent equations governing the dynamics of nonequilibrium colloidal systems. J Chem Phys 2011; 134:054514. [DOI: 10.1063/1.3537972] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|