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Lulli M, Biferale L, Falcucci G, Sbragaglia M, Yang D, Shan X. Metastable and unstable hydrodynamics in multiphase lattice Boltzmann. Phys Rev E 2024; 109:045304. [PMID: 38755934 DOI: 10.1103/physreve.109.045304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 01/03/2024] [Indexed: 05/18/2024]
Abstract
Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equation of state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.
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Affiliation(s)
- Matteo Lulli
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
- Department of Physics, The Chinese University of Hong Kong, Sha Tin, Hong Kong, China
| | - Luca Biferale
- Department of Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Giacomo Falcucci
- Department of Enterprise Engineering "Mario Lucertini", University of Rome "Tor Vergata", Via del Politecnico 1, 00133 Rome, Italy
- John A. Paulson School of Engineering and Applied Physics, Harvard University, 33 Oxford Street, 02138 Cambridge, Massachusetts, USA
| | - Mauro Sbragaglia
- Department of Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Dong Yang
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Xiaowen Shan
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
- Institute of Advanced Study, BNU-HKBU United International College, Zhuhai, Guangdong 519088, China
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2
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Zhang H, Wang F, Ratke L, Nestler B. Brownian motion of droplets induced by thermal noise. Phys Rev E 2024; 109:024208. [PMID: 38491665 DOI: 10.1103/physreve.109.024208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 01/09/2024] [Indexed: 03/18/2024]
Abstract
Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at submicro scales, where intermolecular diffusion and surface tension both are significant. To address BM of microscopic droplets, we develop two stochastic multiphase-field models coupled with the full Navier-Stokes equation, namely, Allen-Cahn-Navier-Stokes and Cahn-Hilliard-Navier-Stokes. Both models are validated against capillary-wave theory; the Einstein's relation for the Brownian coefficient D^{*}∼k_{B}T/r at thermodynamic equilibrium is recovered. Moreover, by adjusting the co-action of the diffusion, Marangoni effect, and viscous friction, two nonequilibrium phenomena are observed. (I) The droplet motion transits from the Brownian to Ballistic with increasing Marangoni effect which is emanated from the energy dissipation mechanism distinct from the conventional fluctuation-dissipation theorem. (II) The deterministic droplet motion is triggered by the noise induced nonuniform velocity field which leads to a novel droplet coalescence mechanism associated with the thermal noise.
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Affiliation(s)
- Haodong Zhang
- Institute of Applied Materials-Microstructure Modelling and Simulation, Karlsruhe Institute of Technology (KIT), Strasse am Forum 7, 76131 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Fei Wang
- Institute of Applied Materials-Microstructure Modelling and Simulation, Karlsruhe Institute of Technology (KIT), Strasse am Forum 7, 76131 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Lorenz Ratke
- Institute of Materials Research, German Aerospace Center, Linder Hoehe, 51147 Cologne, Germany
| | - Britta Nestler
- Institute of Applied Materials-Microstructure Modelling and Simulation, Karlsruhe Institute of Technology (KIT), Strasse am Forum 7, 76131 Karlsruhe, Germany
- Institute of Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133 Karlsruhe, Germany
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3
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Gallo M, Magaletti F, Georgoulas A, Marengo M, De Coninck J, Casciola CM. A nanoscale view of the origin of boiling and its dynamics. Nat Commun 2023; 14:6428. [PMID: 37833270 PMCID: PMC10576093 DOI: 10.1038/s41467-023-41959-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 09/21/2023] [Indexed: 10/15/2023] Open
Abstract
In this work, we present a dynamical theory of boiling based on fluctuating hydrodynamics and the diffuse interface approach. The model is able to describe boiling from the stochastic nucleation up to the macroscopic bubble dynamics. It covers, with a modest computational cost, the mesoscale area from nano to micrometers, where most of the controversial observations related to the phenomenon originate. In particular, the role of wettability in the macroscopic observables of boiling is elucidated. In addition, by comparing the ideal case of boiling on ultra-smooth surfaces with a chemically heterogeneous wall, our results will definitively shed light on the puzzling low onset temperatures measured in experiments. Sporadic nanometric spots of hydrophobic wettability will be shown to be enough to trigger the nucleation at low superheat, significantly reducing the temperature of boiling onset, in line with experimental results. The proposed mesoscale approach constitutes the missing link between macroscopic approaches and molecular dynamics simulations and will open a breakthrough pathway toward accurate understanding and prediction.
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Affiliation(s)
- Mirko Gallo
- Sapienza University of Rome, Rome, Italy.
- School of Architecture, Technology and Engineering, University of Brighton, Lewes Road, Brighton, UK.
| | - Francesco Magaletti
- School of Architecture, Technology and Engineering, University of Brighton, Lewes Road, Brighton, UK
| | - Anastasios Georgoulas
- School of Architecture, Technology and Engineering, University of Brighton, Lewes Road, Brighton, UK
| | - Marco Marengo
- School of Architecture, Technology and Engineering, University of Brighton, Lewes Road, Brighton, UK
- Dept. of Civil Engineering and Architecture, University of Pavia, Pavia, Italy
| | - Joel De Coninck
- School of Architecture, Technology and Engineering, University of Brighton, Lewes Road, Brighton, UK
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4
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Srivastava I, Ladiges DR, Nonaka AJ, Garcia AL, Bell JB. Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures. Phys Rev E 2023; 107:015305. [PMID: 36797914 DOI: 10.1103/physreve.107.015305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
We present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.
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Affiliation(s)
- Ishan Srivastava
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Daniel R Ladiges
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Andy J Nonaka
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Alejandro L Garcia
- Department of Physics and Astronomy, San Jose State University, 1 Washington Square, San Jose, California 95192, USA
| | - John B Bell
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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5
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Bandak D, Goldenfeld N, Mailybaev AA, Eyink G. Dissipation-range fluid turbulence and thermal noise. Phys Rev E 2022; 105:065113. [PMID: 35854607 DOI: 10.1103/physreve.105.065113] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 04/26/2022] [Indexed: 11/07/2022]
Abstract
We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equation is inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equation of Landau and Lifschitz is more appropriate. In particular, our analysis implies that both the exponentially decaying energy spectrum and the far-dissipation-range intermittency predicted by Kraichnan for deterministic Navier-Stokes will be generally replaced by Gaussian thermal equipartition at scales just below the Kolmogorov length. Stochastic shell model simulations at high Reynolds numbers verify our theoretical predictions and reveal furthermore that inertial-range intermittency can propagate deep into the dissipation range, leading to large fluctuations in the equipartition length scale. We explain the failure of previous scaling arguments for the validity of deterministic Navier-Stokes equations at any Reynolds number and we provide a mathematical interpretation and physical justification of the fluctuating Navier-Stokes equation as an "effective field theory" valid below some high-wave-number cutoff Λ, rather than as a continuum stochastic partial differential equation. At Reynolds number around a million, comparable to that in Earth's atmospheric boundary layer, the strongest turbulent excitations observed in our simulation penetrate down to a length scale of about eight microns, still two orders of magnitude greater than the mean free path of air. However, for longer observation times or for higher Reynolds numbers, more extreme turbulent events could lead to a local breakdown of fluctuating hydrodynamics.
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Affiliation(s)
- Dmytro Bandak
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Alexei A Mailybaev
- Instituto de Matemática Pura e Aplicada-IMPA, Rio de Janeiro, 22460-320, Brazil
| | - Gregory Eyink
- Department of Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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6
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Ding G, Chen J, Li Z, Cai X, Ji Y. An investigation on the bubbly flow of a
Venturi
channel based on the population balance model. CAN J CHEM ENG 2021. [DOI: 10.1002/cjce.24258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Guodong Ding
- College of Mechanical and Transportation Engineering China University of Petroleum‐Beijing Beijing China
| | - Jiaqing Chen
- College of Mechanical Engineering Beijing Institute of Petrochemical Technology Beijing China
- Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deep Water Oil & Gas Development Beijing China
| | - Zhenlin Li
- College of Mechanical and Transportation Engineering China University of Petroleum‐Beijing Beijing China
| | - Xiaolei Cai
- College of Mechanical Engineering Beijing Institute of Petrochemical Technology Beijing China
- Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deep Water Oil & Gas Development Beijing China
| | - Yipeng Ji
- College of Mechanical Engineering Beijing Institute of Petrochemical Technology Beijing China
- Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deep Water Oil & Gas Development Beijing China
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7
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Malingen SA, Hood K, Lauga E, Hosoi A, Daniel TL. Fluid flow in the sarcomere. Arch Biochem Biophys 2021; 706:108923. [PMID: 34029559 DOI: 10.1016/j.abb.2021.108923] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Revised: 04/26/2021] [Accepted: 04/30/2021] [Indexed: 12/31/2022]
Abstract
A highly organized and densely packed lattice of molecular machinery within the sarcomeres of muscle cells powers contraction. Although many of the proteins that drive contraction have been studied extensively, the mechanical impact of fluid shearing within the lattice of molecular machinery has received minimal attention. It was recently proposed that fluid flow augments substrate transport in the sarcomere, however, this analysis used analytical models of fluid flow in the molecular machinery that could not capture its full complexity. By building a finite element model of the sarcomere, we estimate the explicit flow field, and contrast it with analytical models. Our results demonstrate that viscous drag forces on sliding filaments are surprisingly small in contrast to the forces generated by single myosin molecular motors. This model also indicates that the energetic cost of fluid flow through viscous shearing with lattice proteins is likely minimal. The model also highlights a steep velocity gradient between sliding filaments and demonstrates that the maximal radial fluid velocity occurs near the tips of the filaments. To our knowledge, this is the first computational analysis of fluid flow within the highly structured sarcomere.
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Affiliation(s)
- Sage A Malingen
- Department of Biology, University of Washington, Seattle, WA 98195, United States.
| | - Kaitlyn Hood
- Department of Mathematics, Purdue University, West Lafayette, IN 47906, United States; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02138, United States
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Anette Hosoi
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02138, United States
| | - Thomas L Daniel
- Department of Biology, University of Washington, Seattle, WA 98195, United States
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8
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Kim C, Nonaka A, Bell JB, Garcia AL, Donev A. Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach. J Chem Phys 2018; 146:124110. [PMID: 28388111 DOI: 10.1063/1.4978775] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuatinghydrodynamics (FHD). For hydrodynamicsystems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poissonfluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamicfluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.
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Affiliation(s)
- Changho Kim
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Andy Nonaka
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - John B Bell
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Alejandro L Garcia
- Department of Physics and Astronomy, San Jose State University, 1 Washington Square, San Jose, California 95192, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
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9
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Oprisan A, Rice A, Oprisan SA, Giraudet C, Croccolo F. Non-equilibrium concentration fluctuations in superparamagnetic nanocolloids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:14. [PMID: 28181056 DOI: 10.1140/epje/i2017-11503-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2016] [Accepted: 01/11/2017] [Indexed: 06/06/2023]
Abstract
We investigate non-equilibrium concentration fluctuations during the free diffusion of a colloidal suspension against pure water. We investigate Fe2O3 superparamagnetic nanocolloids with sizes between 1 and 10 nm by means of a shadowgraph apparatus to determine the mixture mass diffusion coefficient and kinematic viscosity. The experiments were performed in three distinct conditions: Experiment 1 is without any magnetic field; Experiment 2 with a vertical magnetic field; Experiment 3 after turning off the magnetic field. We found no correlation between the kinematic viscosity coefficient and the external magnetic field. Conversely, we found that the mass diffusion coefficient decreases in the presence of the external magnetic field and slowly rebounds after the magnetic field was turned off.
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Affiliation(s)
- Ana Oprisan
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA.
| | - Ashley Rice
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA
| | - Sorinel A Oprisan
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA
| | - Cédric Giraudet
- Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Erlangen, Germany
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, Anglet, France
- Centre Nationale d'Etudes Spatiales (CNES), Paris, France
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10
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Croccolo F, Ortiz de Zárate JM, Sengers JV. Non-local fluctuation phenomena in liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:125. [PMID: 27987100 DOI: 10.1140/epje/i2016-16125-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 11/18/2016] [Indexed: 06/06/2023]
Abstract
Fluids in non-equilibrium steady states exhibit long-range fluctuations which extend over the entire system. They can be described by non-equilibrium thermodynamics and fluctuating hydrodynamics that assume local equilibrium for the thermophysical properties as a function of space and time. The experimental evidence for the consistency between this assumption of local equilibrium in the equations and the non-local fluctuation phenomena observed is reviewed.
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Affiliation(s)
- F Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs, UMR 5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France.
- Centre National d'Etudes Spatiales (CNES), 2 Place Maurice Quentin, 75001, Paris, France.
| | - J M Ortiz de Zárate
- Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040, Madrid, Spain
| | - J V Sengers
- Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA
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11
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Baaske P, Bataller H, Braibanti M, Carpineti M, Cerbino R, Croccolo F, Donev A, Köhler W, Ortiz de Zárate JM, Vailati A. The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:119. [PMID: 28012143 DOI: 10.1140/epje/i2016-16119-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Accepted: 11/07/2016] [Indexed: 06/06/2023]
Abstract
Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q-4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.
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Affiliation(s)
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, F-64600, Anglet, France
| | | | - Marina Carpineti
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - Roberto Cerbino
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, 20090, Segrate (MI), Italy
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, F-64600, Anglet, France
- Centre Nationale d'Etudes Spatiales, Paris, France
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA
| | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | | | - Alberto Vailati
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy.
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12
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Pütz M, Nielaba P. Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics. Phys Rev E 2016; 94:022616. [PMID: 27627369 DOI: 10.1103/physreve.94.022616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Indexed: 11/07/2022]
Abstract
We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.
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Affiliation(s)
- Martin Pütz
- Universität Konstanz, Fachbereich für Physik, 78457 Konstanz, Germany
| | - Peter Nielaba
- Universität Konstanz, Fachbereich für Physik, 78457 Konstanz, Germany
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13
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Lei H, Baker NA, Wu L, Schenter GK, Mundy CJ, Tartakovsky AM. Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations. Phys Rev E 2016; 94:023304. [PMID: 27627409 DOI: 10.1103/physreve.94.023304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2016] [Indexed: 06/06/2023]
Abstract
Thermal fluctuations cause perturbations of fluid-fluid interfaces and highly nonlinear hydrodynamics in multiphase flows. In this work, we develop a multiphase smoothed dissipative particle dynamics (SDPD) model. This model accounts for both bulk hydrodynamics and interfacial fluctuations. Interfacial surface tension is modeled by imposing a pairwise force between SDPD particles. We show that the relationship between the model parameters and surface tension, previously derived under the assumption of zero thermal fluctuation, is accurate for fluid systems at low temperature but overestimates the surface tension for intermediate and large thermal fluctuations. To analyze the effect of thermal fluctuations on surface tension, we construct a coarse-grained Euler lattice model based on the mean field theory and derive a semianalytical formula to directly relate the surface tension to model parameters for a wide range of temperatures and model resolutions. We demonstrate that the present method correctly models dynamic processes, such as bubble coalescence and capillary spectra across the interface.
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Affiliation(s)
- Huan Lei
- Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Nathan A Baker
- Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Lei Wu
- LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
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