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Wang H, Zhang X, Che J, Zhang Y. Lattice Boltzmann simulation for phase separation with chemical reaction controlled by thermal diffusion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:126. [PMID: 34633556 DOI: 10.1140/epje/s10189-021-00130-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
This study investigates phase separation behavior and pattern formation in a binary fluid with chemical reaction controlled by thermal diffusion. By incorporating the Arrhenius equation into the lattice Boltzmann method (LBM), the coupling effects of the pre-exponential factor K, viscosity [Formula: see text], and thermal diffusion D on phase separation were successfully evaluated. The effect of the competition between thermal diffusion and concentration on the phase separation morphology and dynamics of binary mixtures under a chemically reacting controlled by slow cooling is assessed based on the extended LBM. The calculations indicated that increases in viscosity and thermal diffusion can obtain interconnected structures (ISs) and lamellar structures (LSs) for cases with small K. However, concentric phase-separated structures (CSs) were observed in cases with large K. The increase in the degree and efficiency of phase separation were significantly greater in cases with decreased viscosity and increased thermal diffusion.
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Affiliation(s)
- Heping Wang
- Nanchang Key Laboratory of Photoelectric Conversion and Energy Storage Materials, Key Laboratory of Optoelectronic Materials and New Energy Technology, School of Sciences, Nanchang Institute of Technology, Nanchang, 330099, People's Republic of China.
| | - Xiaohang Zhang
- Nanchang Key Laboratory of Photoelectric Conversion and Energy Storage Materials, Key Laboratory of Optoelectronic Materials and New Energy Technology, School of Sciences, Nanchang Institute of Technology, Nanchang, 330099, People's Republic of China
| | - Jinxing Che
- Nanchang Key Laboratory of Photoelectric Conversion and Energy Storage Materials, Key Laboratory of Optoelectronic Materials and New Energy Technology, School of Sciences, Nanchang Institute of Technology, Nanchang, 330099, People's Republic of China
| | - Yuhua Zhang
- Nanchang Key Laboratory of Photoelectric Conversion and Energy Storage Materials, Key Laboratory of Optoelectronic Materials and New Energy Technology, School of Sciences, Nanchang Institute of Technology, Nanchang, 330099, People's Republic of China
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Schaefer C, Paquay S, McLeish TCB. Morphology formation in binary mixtures upon gradual destabilisation. SOFT MATTER 2019; 15:8450-8458. [PMID: 31490530 DOI: 10.1039/c9sm01344j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation is strongly affected by critical thermal fluctuations. We propose a mechanism of pretransitional structuring of a mixture that approaches the miscibility gap and predict scaling relations that describe how the characteristic feature size of the emerging morphology decreases with an increasing quench rate. These predictions quantitatively agree with our kinetic Monte Carlo and molecular dynamics simulations of a phase-separating binary mixture, as well as with previously reported experimental observations. We discuss how these predictions are affected by non-conserved order parameters (e.g., due to chemical reactions or alignment of liquid-crystalline molecules), hydrodynamics and active transport.
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Affiliation(s)
- Charley Schaefer
- Department of Physics, University of York, Heslington, York, YO10 5DD, UK.
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Lin C, Luo KH, Fei L, Succi S. A multi-component discrete Boltzmann model for nonequilibrium reactive flows. Sci Rep 2017; 7:14580. [PMID: 29109453 PMCID: PMC5673997 DOI: 10.1038/s41598-017-14824-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2017] [Accepted: 10/16/2017] [Indexed: 11/09/2022] Open
Abstract
We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field. Compared to standard lattice Boltzmann models, the DBM presents not only more accurate hydrodynamic quantities, but also detailed nonequilibrium effects that are essential yet long-neglected by traditional fluid dynamics. Apart from nonequilibrium terms (viscous stress and heat flux) in conventional models, specific hydrodynamic and thermodynamic nonequilibrium quantities (high order kinetic moments and their departure from equilibrium) are dynamically obtained from the DBM in a straightforward way. Due to its generality, the developed methodology is applicable to a wide range of phenomena across many energy technologies, emissions reduction, environmental protection, mining accident prevention, chemical and process industry.
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Affiliation(s)
- Chuandong Lin
- Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China.
| | - Kai Hong Luo
- Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China. .,Department of Mechanical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK.
| | - Linlin Fei
- Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China
| | - Sauro Succi
- Istituto Applicazioni Calcolo, CNR, Via dei Taurini 19, 00185, Rome, Italy
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Lamorgese A, Mauri R. Spinodal decomposition of chemically reactive binary mixtures. Phys Rev E 2016; 94:022605. [PMID: 27627358 DOI: 10.1103/physreve.94.022605] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Indexed: 06/06/2023]
Abstract
We simulate the influence of a reversible isomerization reaction on the phase segregation process occurring after spinodal decomposition of a deeply quenched regular binary mixture, restricting attention to systems wherein material transport occurs solely by diffusion. Our theoretical approach follows a diffuse-interface model of partially miscible binary mixtures wherein the coupling between reaction and diffusion is addressed within the frame of nonequilibrium thermodynamics, leading to a linear dependence of the reaction rate on the chemical affinity. Ultimately, the rate for an elementary reaction depends on the local part of the chemical potential difference since reaction is an inherently local phenomenon. Based on two-dimensional simulation results, we express the competition between segregation and reaction as a function of the Damköhler number. For a phase-separating mixture with components having different physical properties, a skewed phase diagram leads, at large times, to a system converging to a single-phase equilibrium state, corresponding to the absolute minimum of the Gibbs free energy. This conclusion continues to hold for the critical phase separation of an ideally perfectly symmetric binary mixture, where the choice of final equilibrium state at large times depends on the initial mean concentration being slightly larger or less than the critical concentration.
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Affiliation(s)
- A Lamorgese
- Department of Civil and Industrial Engineering, University of Pisa, Largo Lazzarino 1, 56122 Pisa, Italy
| | - R Mauri
- Department of Civil and Industrial Engineering, University of Pisa, Largo Lazzarino 1, 56122 Pisa, Italy
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Krishnan R, Puri S. Molecular dynamics study of phase separation in fluids with chemical reactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052316. [PMID: 26651704 DOI: 10.1103/physreve.92.052316] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Indexed: 06/05/2023]
Abstract
We present results from the first d=3 molecular dynamics (MD) study of phase-separating fluid mixtures (AB) with simple chemical reactions (A⇌B). We focus on the case where the rates of forward and backward reactions are equal. The chemical reactions compete with segregation, and the coarsening system settles into a steady-state mesoscale morphology. However, hydrodynamic effects destroy the lamellar morphology which characterizes the diffusive case. This has important consequences for the phase-separating structure, which we study in detail. In particular, the equilibrium length scale (ℓ(eq)) in the steady state suggests a power-law dependence on the reaction rate ε:ℓ(eq)∼ε(-θ) with θ≃1.0.
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Affiliation(s)
- Raishma Krishnan
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Zwicker D, Hyman AA, Jülicher F. Suppression of Ostwald ripening in active emulsions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012317. [PMID: 26274171 DOI: 10.1103/physreve.92.012317] [Citation(s) in RCA: 100] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2015] [Indexed: 05/06/2023]
Abstract
Emulsions consisting of droplets immersed in a fluid are typically unstable since they coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Stability of emulsions is relevant not only in complex fluids but also in biological cells, which contain liquidlike compartments, e.g., germ granules, Cajal bodies, and centrosomes. Such cellular systems are driven away from equilibrium, e.g., by chemical reactions, and thus can be called active emulsions. In this paper, we study such active emulsions by developing a coarse-grained description of the droplet dynamics, which we analyze for two different chemical reaction schemes. We first consider the simple case of first-order reactions, which leads to stable, monodisperse emulsions in which Ostwald ripening is suppressed within a range of chemical reaction rates. We then consider autocatalytic droplets, which catalyze the production of their own droplet material. Spontaneous nucleation of autocatalytic droplets is strongly suppressed and their emulsions are typically unstable. We show that autocatalytic droplets can be nucleated reliably and their emulsions stabilized by the help of chemically active cores, which catalyze the production of droplet material. In summary, different reaction schemes and catalytic cores can be used to stabilize emulsions and to control their properties.
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Affiliation(s)
- David Zwicker
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Anthony A Hyman
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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Gan Y, Xu A, Zhang G, Li Y, Li H. Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046715. [PMID: 22181315 DOI: 10.1103/physreve.84.046715] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2010] [Revised: 09/11/2011] [Indexed: 05/31/2023]
Abstract
We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the local flow velocity depends not only on viscosity but also on temperature.
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Affiliation(s)
- Yanbiao Gan
- State Key Laboratory for GeoMechanics and Deep Underground Engineering, SMCE, China University of Mining and Technology (Beijing), Beijing 100083, PR China
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Self-assembly of diblock copolymers under shear flow: A simulation study by combining the self-consistent field and lattice Boltzmann method. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.06.012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Gan Y, Xu A, Zhang G, Li Y. Lattice Boltzmann study on Kelvin-Helmholtz instability: roles of velocity and density gradients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056704. [PMID: 21728690 DOI: 10.1103/physreve.83.056704] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2010] [Revised: 01/26/2011] [Indexed: 05/31/2023]
Abstract
A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible fluids is proposed. The fifth-order weighted essentially nonoscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions [G. A. Sod, J. Comput. Phys. 27, 1 (1978).]. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that the linear growth rate γ for the KHI decreases by increasing the width of velocity transition layer D(v) but increases by increasing the width of density transition layer D(ρ). After the initial transient period and before the vortex has been well formed, the linear growth rates γ(v) and γ(ρ), vary with D(v) and D(ρ) approximately in the following way, lnγ(v)=a-bD(v) and γ(ρ)=c+elnD(ρ)(D(ρ)<D(ρ)(E)), where a, b, c, and e are fitting parameters and D(ρ)(E) is the effective interaction width of the density transition layer. When D(ρ)>D(ρ)(E) the linear growth rate γ(ρ) does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang et al., Phys. Plasma 17, 042103 (2010)].
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Affiliation(s)
- Yanbiao Gan
- State Key Laboratory for GeoMechanics and Deep Underground Engineering, SMCE, China University of Mining and Technology (Beijing), Beijing 100083, PR China
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Chen S, Tölke J, Krafczyk M. Simulation of buoyancy-driven flows in a vertical cylinder using a simple lattice Boltzmann model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:016704. [PMID: 19257163 DOI: 10.1103/physreve.79.016704] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2008] [Indexed: 05/27/2023]
Abstract
Axisymmetric thermal flow is of fundamental interest and practical importance. However, the work to design suitable and efficient lattice Boltzmann models on axisymmetric thermal flows is quite rare. In order to bridge the gap, a simple lattice Boltzmann model for axisymmetric thermal flow is proposed in this paper. In the present study, we show how to transform the governing equation for temperate field in the cylindrical coordinate system to the pseudo-Cartesian representation in the same way as that for the flow field. Therefore the flow field and the temperature field both are solved by the two-dimensional five-speed (D2Q5) lattice Boltzmann model. The treatment of the "geometrical forcing" due to the coordinate transformation and the physical forcing due to the temperature field is simpler than that in all existing models. Thanks to its intrinsic features, the present model is more efficient, more stable, and much simpler than the existing models. In this paper, several kinds of nontrivial thermal buoyancy-driven flows in vertical cylinders, which are of interest from the standpoint of both basic fluid dynamics and practical applications, are simulated by the present model.
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Affiliation(s)
- Sheng Chen
- Institute for Computational Modeling in Civil Engineering, Technical University, Braunschweig 38106, Germany.
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Chen S, Tölke J, Geller S, Krafczyk M. Lattice Boltzmann model for incompressible axisymmetric flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:046703. [PMID: 18999557 DOI: 10.1103/physreve.78.046703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2008] [Indexed: 05/27/2023]
Abstract
A lattice Boltzmann model for incompressible axisymmetric flow is proposed in this paper. Unlike previous axisymmetric lattice Boltzmann models, which were based on "primitive-variables" Navier-Stokes equations, the target macroscopic equations of the present model are vorticity-stream-function formulations. Due to the intrinsic features of vorticity-stream-function formulations, the present model is more efficient, more stable, and much simpler than the existing models. The advantages of the present model are validated by numerical experiments.
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Affiliation(s)
- Sheng Chen
- Institute for Computational Modeling in Civil Engineering, Technical University, Braunschweig 38106, Germany.
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Krzyzewski F, Załuska-Kotur MA. Segregation in a noninteracting binary mixture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031502. [PMID: 18517383 DOI: 10.1103/physreve.77.031502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2007] [Revised: 10/23/2007] [Indexed: 05/26/2023]
Abstract
Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of small particles, induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential created by the site blocking due to the small ones.
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Affiliation(s)
- Filip Krzyzewski
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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Liu H, Qian HJ, Zhao Y, Lu ZY. Dissipative particle dynamics simulation study on the binary mixture phase separation coupled with polymerization. J Chem Phys 2007; 127:144903. [DOI: 10.1063/1.2790005] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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