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Xue X, Biferale L, Sbragaglia M, Toschi F. A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:142. [PMID: 34821992 PMCID: PMC8616863 DOI: 10.1140/epje/s10189-021-00144-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 10/30/2021] [Indexed: 06/13/2023]
Abstract
We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in the absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean settling velocity is quantitatively assessed, especially in comparison with unconfined situations. Results show that the expected effects of confinement are very well captured by the numerical simulations, wherein the confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the proposed methodology in highlighting the effects of confinement on the motion of particles in the presence of thermal fluctuations.
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Affiliation(s)
- Xiao Xue
- Department of Physics and J.M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Department of Physics & INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- Department of Mechanics and Maritime Sciences, Division of Fluid Dynamics, Chalmers University of Technology, 41296 Göteborg, Sweden
| | - Luca Biferale
- Department of Physics & INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Mauro Sbragaglia
- Department of Physics & INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Federico Toschi
- Departments of Physics and of Mathematics and Computer Science and J.M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy
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Parsa MR, Kim C, Wagner AJ. Nonuniqueness of fluctuating momentum in coarse-grained systems. Phys Rev E 2021; 104:015304. [PMID: 34412354 DOI: 10.1103/physreve.104.015304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 06/07/2021] [Indexed: 11/07/2022]
Abstract
Coarse-grained descriptions of microscopic systems often require a mesoscopic definition of momentum. The question arises as to the uniqueness of such a momentum definition at a particular coarse-graining scale. We show here that particularly the fluctuating properties of common definitions of momentum in coarse-grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we derive analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.
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Affiliation(s)
- M Reza Parsa
- Department of Applied Mathematics, University of California, Merced, California 95343, USA
| | - Changho Kim
- Department of Applied Mathematics, University of California, Merced, California 95343, USA
| | - Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
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Parsa MR, Wagner AJ. Large Fluctuations in Nonideal Coarse-Grained Systems. PHYSICAL REVIEW LETTERS 2020; 124:234501. [PMID: 32603140 DOI: 10.1103/physrevlett.124.234501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Revised: 03/12/2020] [Accepted: 05/15/2020] [Indexed: 06/11/2023]
Abstract
Using the recently introduced molecular dynamics lattice gas approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a nonideal equation of state. The molecular dynamics lattice gas method gives a guidance to the exact nature of the fluctuation in such systems.
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Affiliation(s)
- M Reza Parsa
- Department of Applied Mathematics, University of California, Merced, California 95343, USA
| | - Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
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Shan X. Central-moment-based Galilean-invariant multiple-relaxation-time collision model. Phys Rev E 2019; 100:043308. [PMID: 31771023 DOI: 10.1103/physreve.100.043308] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Indexed: 11/07/2022]
Abstract
Aiming at systematically correcting the non-Galilean-invariant thermal diffusivity in the previous multiple-relaxation-time Boltzmann equation collision model [Shan and Chen, Int. J. Mod. Phys. C 18, 635 (2007)IJMPEO0129-183110.1142/S0129183107010887], we show that by separately relaxing the central moments of the distribution function, Chapman-Enskog calculation leads to the correct hydrodynamic equations with mutually independent and Galilean invariant viscosity and thermal diffusivity, provided the velocity-space discretization preserves moments up to the fourth order. By transforming the central moments back to the absolute reference frame and evaluating using fixed discrete velocities, the efficient and accurate streaming-collision time-stepping algorithm is preserved. The lattice Boltzmann model is found to have excellent numerical stability in high-Reynolds-number simulations.
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Affiliation(s)
- Xiaowen Shan
- Shenzhen Key Laboratory of Complex Aerospace Flows, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
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Belardinelli D, Sbragaglia M, Benzi R, Ciliberto S. Lattice Boltzmann simulations of nonequilibrium fluctuations in a nonideal binary mixture. Phys Rev E 2019; 99:063302. [PMID: 31330737 DOI: 10.1103/physreve.99.063302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2018] [Indexed: 06/10/2023]
Abstract
In recent years the lattice Boltzmann (LB) methodology has been fruitfully extended to include the effects of thermal fluctuations. So far, all studied cases pertain to equilibrium fluctuations, i.e., fluctuations with respect to an equilibrium background state. In this paper we take a step further and present results of fluctuating LB simulations of a binary mixture confined between two parallel walls in the presence of a constant concentration gradient in the wall-to-wall direction. This is a paradigmatic setup for the study of nonequilibrium (NE) fluctuations, i.e., fluctuations with respect to a nonequilibrium state. We analyze the dependence of the structure factors for the hydrodynamical fields on the wave vector q in both the directions parallel and perpendicular to the walls, highlighting the long-range (∼|q|^{-4}) nature of correlations in the NE framework. Results at the small scales (high wave numbers) quantitatively agree with the predictions of fluctuating hydrodynamics without fitting parameters. At larger scales (low wave numbers), however, results show finite-size effects induced by confinement and call for further studies aimed at controlling boundary conditions in the fluctuating LB framework as well as compressibility effects. Moreover, in the presence of a nonideal equation of state of the mixture, we also observe that the (spatially homogeneous) average pressure changes, due to a genuinely new contribution triggered by NE fluctuations. These NE pressure effects are studied at changing the system size and the concentration gradient. Taken all together, we argue that the results of this article are useful and instrumental to boost the applicability of the fluctuating LB methodology in the framework of NE fluctuations, possibly in conjunction with experiments.
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Affiliation(s)
- Daniele Belardinelli
- Department of Physics & INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Mauro Sbragaglia
- Department of Physics & INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Roberto Benzi
- Department of Physics & INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Sergio Ciliberto
- Laboratoire de Physique de Ecole Normale Superieure de Lyon (CNRS UMR5672), 46 Allée d'Italie, 69364, Lyon, France
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Blommel T, Wagner AJ. Integer lattice gas with Monte Carlo collision operator recovers the lattice Boltzmann method with Poisson-distributed fluctuations. Phys Rev E 2018; 97:023310. [PMID: 29548240 DOI: 10.1103/physreve.97.023310] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2017] [Indexed: 06/08/2023]
Abstract
We examine a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, which we call a Monte Carlo lattice gas, has interesting properties that shed light on the origin of the multirelaxation time collision operator, and it derives the equilibrium distribution for an entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.
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Affiliation(s)
- Thomas Blommel
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
| | - Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
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Wagner AJ, Strand K. Fluctuating lattice Boltzmann method for the diffusion equation. Phys Rev E 2016; 94:033302. [PMID: 27739715 DOI: 10.1103/physreve.94.033302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Indexed: 06/06/2023]
Abstract
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.
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Affiliation(s)
- Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
| | - Kyle Strand
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
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Affiliation(s)
- Anthony J.C. Ladd
- Chemical Engineering Department, University of Florida , Gainesville, USA
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Belardinelli D, Sbragaglia M, Biferale L, Gross M, Varnik F. Fluctuating multicomponent lattice Boltzmann model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023313. [PMID: 25768641 DOI: 10.1103/physreve.91.023313] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2014] [Indexed: 06/04/2023]
Abstract
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
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Affiliation(s)
- D Belardinelli
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Sbragaglia
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - L Biferale
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Gross
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - F Varnik
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
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