1
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Siddiqui J, Codina J, Pagonabarraga I, Dobnikar J. The impact of viscosity asymmetry on phase separating binary mixtures with suspended colloids. SOFT MATTER 2024; 20:5564-5571. [PMID: 38963425 DOI: 10.1039/d3sm00955f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/05/2024]
Abstract
The introduction of neutrally wetting colloidal particles into coarsening binary fluids is known to arrest the dynamics of the phase separation, as the colloids tend to be captured by the growing interfaces to reduce the free energy of the system. This phenomenon has often been studied in systems with symmetric fluid viscosities. In this study, we investigate the behavior of colloidal particles introduced into asymmetric binary fluids with a viscosity contrast. Our results show that due to the broken symmetry the colloidal particles more easily escape from the interface towards the more viscous fluid, which reduces the lifetime of the jammed phase. Moreover, the presence of colloidal particles near the interfaces promotes the formation of micro-droplets with typical sizes comparable to the colloids.
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Affiliation(s)
- Javeria Siddiqui
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
| | - Joan Codina
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China.
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franqués 1, 08028 Barcelona, Spain.
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - Jure Dobnikar
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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2
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Assante R, Corbett D, Marenduzzo D, Morozov A. Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels. SOFT MATTER 2023; 19:189-198. [PMID: 36503973 DOI: 10.1039/d2sm01188c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one. We show that composition inhomogeneities are important in the latter phase, where we find three types of possible dynamical regimes. First, we observe regular patterns with defects and vortices: these exist close to the passive-active transition. Second, for larger activity, or deeper in the nematic phase, we find active turbulence, as in active gels of uniform composition, but with exceedingly large composition variation. In the third regime, which is uniquely associated with inhomogeneity and occurs for large nematic tendency and low activity, we observe spontaneous microphase separation into active and passive domains. The microphase separated regime is notable in view of the absence of an explicit demixing term in the underlying free energy which we use, and we provide a theoretical analysis based on the common tangent construction which explains its existence. We hope this regime can be probed experimentally in the future.
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Affiliation(s)
- Renato Assante
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Dom Corbett
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
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3
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He Q, Huang W, Yin Y, Li D, Hu Y. A Droplet-Manipulation Method Based on the Magnetic Particle-Stabilized Emulsion and Its Direct Numerical Simulation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:8211-8221. [PMID: 35763702 DOI: 10.1021/acs.langmuir.2c00459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Droplet manipulation has found broad applications in various engineering fields, such as microfluidic systems. This work reports a droplet-manipulation method based on particle-stabilized emulsions, where the magnetic particles adsorbed to the droplet surface serve as the actuator. The movement and the release of the droplet can be controlled by applying an external magnetic field. A lattice Boltzmann model for a three-phase system containing liquids and solid particles is adopted, which could provide a full coupling between fluids and particles. The effectiveness of the present droplet-manipulation method is validated through experiments and numerical simulations. Furthermore, the numerical simulation can provide insight into the interactions between the magnetic particles and the droplet during the droplet-driven process. To drive the droplet successfully, the magnetic particle needs to adhere to its surface and act as an "engine" to provide the driving force. As it is a surface-tension-dominant problem, the capillary effect can be considered as an "energy transfer station". The magnetic driving force on the particle is transmitted primarily to the droplet through interfacial capillary forces at the three-phase contact line, which assists the droplet in overcoming the viscous resistance and moving forward. A dimensionless number is proposed as a predictor of droplet transport and particle detachment.
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Affiliation(s)
- Qiang He
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
| | - Weifeng Huang
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
| | - Yuan Yin
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
| | - Decai Li
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
| | - Yang Hu
- School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
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4
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Hans Tromp R, de Hoog EH. The effect of the viscosity ratio on band formation in sheared mixtures of phase-separated polymer solutions with ultralow interface tension. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1913253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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5
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He Q, Li Y, Huang W, Hu Y, Wang Y. Phase-field-based lattice Boltzmann model for liquid-gas-solid flow. Phys Rev E 2019; 100:033314. [PMID: 31639949 DOI: 10.1103/physreve.100.033314] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2019] [Indexed: 11/07/2022]
Abstract
Based on phase-field theory, we develop a lattice Boltzmann (LB) model for liquid-gas-solid flow from multiphase and particle dynamics algorithms. A modified bounce-back method is developed for the velocity-based LB approach. A curved boundary treatment with second-order accuracy based on velocity interpolation is developed. We propose a predictor-corrector scheme algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. In order to make the algorithm more stable, we combine the implicit particle velocity update scheme and the Galilean invariant momentum exchange method. The proposed method is validated through several single- and multicomponent fluid test cases. It was found the surface tension force associated with the interface acting on the solid structures can be captured. We simulate the sinking of a circular cylinder due to gravity, the numerical results agree well with the experimental data. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface.
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Affiliation(s)
- Qiang He
- Department of Mechanical Engineering, Tsinghua University, Beijing 10084, China
| | - Yongjian Li
- Department of Mechanical Engineering, Tsinghua University, Beijing 10084, China
| | - Weifeng Huang
- Department of Mechanical Engineering, Tsinghua University, Beijing 10084, China
| | - Yang Hu
- Department of Mechanical Engineering, Tsinghua University, Beijing 10084, China
| | - Yuming Wang
- Department of Mechanical Engineering, Tsinghua University, Beijing 10084, China
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6
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Barbot A, Araki T. Colloidal suspensions in one-phase mixed solvents under shear flow. SOFT MATTER 2017; 13:5911-5921. [PMID: 28770264 DOI: 10.1039/c7sm00861a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We numerically studied the behaviour of colloidal suspensions in one-phase binary liquid mixtures under shear flows. Far from the phase-separation point, the colloidal particles are well dispersed and the suspension exhibits a Newtonian viscosity. When the mixture is close to the coexistence curve, the colloidal particles aggregate by attractive interactions due to the concentration heterogeneity caused by surface wetting, and the viscosity of the suspension increases. Near the phase-separation point, the viscosity increases when the fraction of species favoured by the surface of a colloid particle is small. The mixture also exhibits shear thinning behaviour, since the aggregated structure is rearranged into small clusters due to the shear flow. Our simulations indicate that the concentration profile around each particle is not significantly disturbed by the shear flow at the onset of the structural rearrangements. The effective interaction is independent of the shear flow and remains isotropic.
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Affiliation(s)
- Armand Barbot
- Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan.
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7
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Gidituri H, Anand DV, Vedantam S, Panchagnula MV. Dissipative particle dynamics study of phase separation in binary fluid mixtures in periodic and confined domains. J Chem Phys 2017; 147:074703. [PMID: 28830165 DOI: 10.1063/1.4999096] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We investigate the phase separation behavior of binary mixtures in two-dimensional periodic and confined domains using dissipative particle dynamics. Two canonical problems of fluid mechanics are considered for the confined domains: square cavity with no-slip walls and lid-driven cavity with one driven wall. The dynamics is studied for both weakly and strongly separating mixtures and different area fractions. The phase separation process is analyzed using the structure factor and the total interface length. The dynamics of phase separation in the square cavity and lid-driven cavity are observed to be significantly slower when compared to the dynamics in the periodic domain. The presence of the no-slip walls and the inertial effects significantly influences the separation dynamics. Finally, we show that the growth exponent for the strongly separating case is invariant to changes in the inter-species repulsion parameter.
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Affiliation(s)
- Harinadha Gidituri
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
| | - D Vijay Anand
- Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India
| | - Srikanth Vedantam
- Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India
| | - Mahesh V Panchagnula
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
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8
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Perlekar P, Pal N, Pandit R. Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade. Sci Rep 2017; 7:44589. [PMID: 28322219 PMCID: PMC5359549 DOI: 10.1038/srep44589] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Accepted: 02/10/2017] [Indexed: 11/28/2022] Open
Abstract
We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of any coupling, we choose parameters that lead (a) to spinodal decomposition and domain growth, which is characterized by the spatiotemporal evolution of the Cahn-Hilliard order parameter ϕ, and (b) the formation of an inverse-energy-cascade regime in the energy spectrum E(k), in which energy cascades towards wave numbers k that are smaller than the energy-injection scale kin j in the turbulent fluid. We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale Lc, which we evaluate from S(k), the spectrum of the fluctuations of ϕ. We demonstrate that (a) Lc ~ LH, the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) Lc is independent, within error bars, of the diffusivity D. We elucidate how this coupling modifies E(k) by blocking the inverse energy cascade at a wavenumber kc, which we show is ≃2π/Lc. We compare our work with earlier studies of this problem.
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Affiliation(s)
- Prasad Perlekar
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Nairita Pal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012 India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012 India.,Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, India
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9
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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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10
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Xu XH, Guo XW, Cao Y, Ren XG, Chen J, Yang XJ. Multi-scale simulation of non-equilibrium phase transitions under shear flow in dilute polymer solutions. RSC Adv 2015. [DOI: 10.1039/c5ra06099k] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
In this paper we propose a multi-scale two-fluid model that couples a coarse-grained microscopic method to the two-fluid framework for studying multi-phase fluids under shear flow.
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Affiliation(s)
- Xin-Hai Xu
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
| | - Xiao-Wei Guo
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
| | - Yu Cao
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
| | - Xiao-Guang Ren
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
| | - Juan Chen
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
| | - Xue-Jun Yang
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- China
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11
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Reinhardt J, Scacchi A, Brader JM. Microrheology close to an equilibrium phase transition. J Chem Phys 2014; 140:144901. [DOI: 10.1063/1.4870497] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Tran C, Kalra V. Molecular dynamics study on effect of elongational flow on morphology of immiscible mixtures. J Chem Phys 2014; 140:134902. [DOI: 10.1063/1.4869404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Stenhammar J, Marenduzzo D, Allen RJ, Cates ME. Phase behaviour of active Brownian particles: the role of dimensionality. SOFT MATTER 2014; 10:1489-99. [PMID: 24651885 DOI: 10.1039/c3sm52813h] [Citation(s) in RCA: 193] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Recently, there has been much interest in activity-induced phase separations in concentrated suspensions of "active Brownian particles" (ABPs), self-propelled spherical particles whose direction of motion relaxes through thermal rotational diffusion. To date, almost all these studies have been restricted to 2 dimensions. In this work we study activity-induced phase separation in 3D and compare the results with previous and new 2D simulations. To this end, we performed state-of-the-art Brownian dynamics simulations of up to 40 million ABPs - such very large system sizes are unavoidable to evade finite size effects in 3D. Our results confirm the picture established for 2D systems in which an activity-induced phase separation occurs, with strong analogies to equilibrium gas-liquid spinodal decomposition, in spite of the purely non-equilibrium nature of the driving force behind the phase separation. However, we also find important differences between the 2D and 3D cases. Firstly, the shape and position of the phase boundaries is markedly different for the two cases. Secondly, for the 3D coarsening kinetics we find that the domain size grows in time according to the classical diffusive t(1/3) law, in contrast to the nonstandard subdiffusive exponent observed in 2D.
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Affiliation(s)
- Joakim Stenhammar
- SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB Kings Buildings, Edinburgh EH9 3JZ, UK.
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14
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Guo XW, Zou S, Yang X, Yuan XF, Wang M. Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow. RSC Adv 2014. [DOI: 10.1039/c4ra08448a] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
The numerical results of RP–FH model reveal another possible cause of the rheochaos: a vortex structure emerges within the central band.
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Affiliation(s)
- Xiao-Wei Guo
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- Changsha, China
- School of Chemical Engineering and Analytical Science
- Manchester Institute of Biotechnology
| | - Shun Zou
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- Changsha, China
| | - Xuejun Yang
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- Changsha, China
| | - Xue-Feng Yuan
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- Changsha, China
- School of Chemical Engineering and Analytical Science
- Manchester Institute of Biotechnology
| | - Miao Wang
- State Key Laboratory of High Performance Computing
- National University of Defense Technology
- Changsha, China
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15
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Saracco GP, Gonnella G, Marenduzzo D, Orlandini E. Shearing self-propelled suspensions: arrest of coarsening and suppression of giant density fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031930. [PMID: 22060426 DOI: 10.1103/physreve.84.031930] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2011] [Indexed: 05/31/2023]
Abstract
We study the effect of a linear shear flow on a collection of interacting active, self-propelled particles modeled via the Vicsek model. The imposed flow has a dramatic effect on the behavior of the model. We find that in the presence of shear there is no order-disorder transition, and that coarsening of the domains is arrested. Shear also suppresses the so-called giant density fluctuations that are observed in the quiescent limit.
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Affiliation(s)
- G P Saracco
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), CCT La Plata, CONICET, UNLP, Casilla de Correo 16, Sucursal 4 (1900) La Plata, Argentina
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16
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Kim E, Stratford K, Cates ME. Bijels containing magnetic particles: a simulation study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:7928-7936. [PMID: 20229993 DOI: 10.1021/la904809g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Bicontinuous, interfacially jammed emulsion gels (bijels) represent a class of soft solid materials in which interpenetrating domains of two immiscible fluids are stabilized by an interfacial colloidal monolayer. Such structures can be formed by arrested spinodal decomposition from an initially single-phase colloidal suspension. Here, we explore by lattice Boltzmann simulation the possible effects of using magnetic colloids in bijels. This may allow additional control over the structure, during or after formation, by application of a magnetic field or field gradient. These effects are modest for typical parameters based on the magnetic nanoparticles used in conventional ferrofluids, although significantly larger particles might be appropriate here. Field gradient effects, which are cumulative across a sample, could then allow a route for controlled breakdown of bijels as they do for particle-stabilized droplet emulsions.
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Affiliation(s)
- Eunhye Kim
- SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB, The Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
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17
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Jelić A, Ilg P, Ottinger HC. Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011131. [PMID: 20365347 DOI: 10.1103/physreve.81.011131] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2009] [Revised: 12/16/2009] [Indexed: 05/29/2023]
Abstract
We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.
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Affiliation(s)
- Asja Jelić
- Polymer Physics, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland.
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18
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Kim E, Stratford K, Camp PJ, Cates ME. Hydrodynamic Interactions in Colloidal Ferrofluids: A Lattice Boltzmann Study. J Phys Chem B 2008; 113:3681-93. [DOI: 10.1021/jp806678m] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Eunhye Kim
- SUPA, School of Physics, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., Edinburgh Parallel Computing Centre, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., and School of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, U.K
| | - Kevin Stratford
- SUPA, School of Physics, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., Edinburgh Parallel Computing Centre, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., and School of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, U.K
| | - Philip J. Camp
- SUPA, School of Physics, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., Edinburgh Parallel Computing Centre, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., and School of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, U.K
| | - Michael E. Cates
- SUPA, School of Physics, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., Edinburgh Parallel Computing Centre, The University of Edinburgh, JCMB, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, U.K., and School of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, U.K
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19
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Thakre AK, Padding JT, den Otter WK, Briels WJ. Molecular dynamics simulation of phase separating binary liquids in cylindrical Couette flow. J Chem Phys 2008; 128:154707. [DOI: 10.1063/1.2872941] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Fielding SM. Role of inertia in nonequilibrium steady states of sheared binary fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021504. [PMID: 18352031 DOI: 10.1103/physreve.77.021504] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2007] [Indexed: 05/26/2023]
Abstract
We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing and spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite-domain-size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite-size effects: Coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.
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Affiliation(s)
- Suzanne M Fielding
- School of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester, Manchester, UK.
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Stratford K, Desplat JC, Stansell P, Cates ME. Binary fluids under steady shear in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:030501. [PMID: 17930189 DOI: 10.1103/physreve.76.030501] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2007] [Indexed: 05/25/2023]
Abstract
We simulate by the lattice Boltzmann method the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations, we obtain at moderately high Reynolds numbers apparent scaling exponents comparable to those found by us previously in two dimensions (2D). However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resources than used here.
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Affiliation(s)
- K Stratford
- SUPA, School of Physics, The University of Edinburgh, JCMB The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom
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Harting J, Giupponi G, Coveney PV. Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:041504. [PMID: 17500899 DOI: 10.1103/physreve.75.041504] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2007] [Indexed: 05/15/2023]
Abstract
We investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear by means of three-dimensional lattice Boltzmann simulations. We show that the growth of individual fluid domains can be arrested by adding surfactant to the system, thus forming a bicontinuous microemulsion. We demonstrate that the maximum domain size and the time of arrest depend linearly on the concentration of amphiphile molecules. In addition, we find that for a well-defined threshold value of amphiphile concentration, the maximum domain size and time of complete arrest do not change. For systems under constant and oscillatory shear we analyze domain growth rates in directions parallel and perpendicular to the applied shear. We find a structural transition from a sponge to a lamellar phase by applying a constant shear and the occurrence of tubular structures under oscillatory shear. The size of the resulting lamellae and tubes depends strongly on the amphiphile concentration, shear rate, and shear frequency.
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Affiliation(s)
- J Harting
- Institute for Computational Physics, University of Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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Gonnella G, Lamura A. Long-time behavior and different shear regimes in quenched binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011501. [PMID: 17358154 DOI: 10.1103/physreve.75.011501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2006] [Indexed: 05/14/2023]
Abstract
The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains L_{y} and of the maximum of excess viscosity (Deltaeta)_{M} is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of gamma_{c} approximately 1t_{D} where t_{D} is the diffusive time. L_{y} and (Deltaeta)_{M} behave as L_{y} approximately gamma;{-alpha} and (Deltaeta)_{M} approximately gamma;{nu} with alpha=alpha_{s}=0.18+/-0.02 , nu=nu_{s}=-2.00+/-0.01 and alpha=alpha_{w}=0.25+/-0.01 , nu=nu_{w}=-0.68+/-0.04 in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.
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Affiliation(s)
- G Gonnella
- Dipartimento di Fisica, Università di Bari, and INFN, Sezione di Bari, Via Amendola 173, 70126 Bari, Italy.
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Xu A, Gonnella G, Lamura A. Morphologies and flow patterns in quenching of lamellar systems with shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011505. [PMID: 16907098 DOI: 10.1103/physreve.74.011505] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Revised: 03/02/2006] [Indexed: 05/11/2023]
Abstract
We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.
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Affiliation(s)
- Aiguo Xu
- Dipartimento di Fisica, Università di Bari, via Amendola 173, 70126 Bari, Italy
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Lishchuk SV, Halliday I, Care CM. Shear viscosity of bulk suspensions at low Reynolds number with the three-dimensional lattice Boltzmann method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:017701. [PMID: 16907217 DOI: 10.1103/physreve.74.017701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2006] [Indexed: 05/11/2023]
Abstract
We report three-dimensional parallel Lagrangian particle simulations using the lattice Boltzmann method, conducted at a low Reynolds number. Using modified Lees-Edwards boundary conditions and directly calculated viscous dissipation, we show that it is possible to recover excellent agreement with the Einstein viscosity formula in the low concentration limit and to predict viscosity corrections for larger concentrations.
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Affiliation(s)
- S V Lishchuk
- Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, United Kingdom
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