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Lattice Boltzmann Method for Simulating Phase Separation of Sheared Binary Fluids with Reversible Chemical Reaction

  • Xiaoyu Wang (a1), Jie Ouyang (a1), Heng Yang (a1) and Jianwei Liu (a1)

A lattice Boltzmann method is utilized for governing equations which control phase separation of binary fluids with reversible chemical reaction in presence of a shear flow in this paper. We first present the morphology modeling of sheared binary fluids with reversible chemical reaction. We then validate the model by taking the unsheared binary fluids as an example. It is found that the results fit well with the references. The paper shows structures of the sheared system and gives the detailed analysis for the morphology of sheared binary fluids with reversible chemical reaction. The phase separation of the domain structures with different chemical reaction rates is discussed. Through simulations of the sheared binary fluids, two interesting phenomena are observed, which do not exist in a binary mixture without reversible chemical reaction. One is that the same results appear in both low and high viscosity, and the other is that the domain growth exponent with both low and high viscosities presents wave due to the competition of the viscosity and phase separation. In addition, we find that the finite size effects resulting in the growth exponent decreasing appear faster than that of the unsheared blend at a large time when the size of domains is comparable with the lattice size.

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*Corresponding author. Email address: (J. Ouyang)
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[1] T. Isojima , H. Kato , and K. Hamano , Effective viscosities of a phase-separating binary mixture imposed to shear, Physics Letters A, 240(4) (1998), pp. 271275.

[2] X. B. Chen , L. S. Niu and H. J. Shi , Modeling the phase separation in binary lipid membrane under externally imposed oscillatory shear flow, Colloid. Surface. B., 65(2) (2008), pp. 203212.

[3] R. S. Qin , Thermodynamic properties of phase separation in shear flow, Computers & Fluids, 117(2015), pp. 1116.

[5] J. Cui , Z. W. Ma , W. Li , and W. Jiang , Self-assembly of diblock copolymers under shear flow: A simulation study by combining the self-consistent field and lattice boltzmann method, Chem. Phys., 386(1) (2011), pp. 8187.

[6] A. J. Wagner and J. M. Yeomans , Phase separation under shear in two-dimensional binary fluids, Phys. Rev. E, 59(4) (1999), pp. 43664373.

[7] X. B. Chen , L. S. Niu , and H. J. Shi , Numerical simulation of the phase separation in binary lipid membrane under the effect of stationary shear flow, Biophys. chem., 135(1) (2008), pp. 8494.

[8] A. Lamura and G. Gonnella , Lattice boltzmann simulations of segregating binary fluid mixtures in shear flow, Physica A, 294(3) (2001), pp. 295312.

[9] Y. C. LI , R. P. Shi , C. P. Wang , X. J. Liu , and Y. Z. Wang , Phase field study on the effect of shear flow on polymer phase separation, Procedia Engineering, 27(2012), pp. 15021507.

[10] F. Xie , C. X. Zhou , W. Yu , and J. Y. Liu , Heterogeneous polymeric reaction under shear flow, J. appl. polym. sci., 109(4) (2008), pp. 27372745.

[11] F. Xie , C. X. Zhou , and W. Yu , Effects of small-amplitude oscillatory shear on polymeric reaction, Polym. Composite., 29(1) (2008), pp. 7276.

[12] Y. L. Huo , X. L. Jiang , H. D. Zhang , and Y. L. Yang , Hydrodynamic effects on phase separation of binary mixtures with reversible chemical reaction, J. Chem. Phys., 118(21) (2003), pp. 98309837.

[14] Y. Y. Yan , Y. Q. Zu , and B. Dong , LBM, a useful tool for mesoscale modelling of single-phase and multiphase flow, Appl. Therm. Eng., 31(5) (2001), pp. 649655.

[15] S. Leclaire , N. Pellerin , M. Reggio , and J. Yves Trépanier , Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method, Physica A, 406(2014), pp. 307319.

[16] H. B. Huang , J. J. Huang , and X. Y. Lu , A mass-conserving axisymmetric multiphase lattice boltzmann method and its application in simulation of bubble rising, J. Comput. Phys., 269 (2014), pp. 386402.

[17] J. F. Zhang , L. M. Wang , and J. Ouyang , Lattice boltzmann model for the volume-averaged navier-stokes equations, EPL (Europhysics Letters), 107(2) (2014), 20001.

[18] A. Fakhari and T. H. Lee , Numerics of the lattice Boltzmann method on nonuniform grids: standard lbm and finite-difference lbm, Computers & Fluids, 107 (2015), pp. 205213.

[19] S. Succi , E. Foti , and F. Higuera , Three-dimensional flows in complex geometries with the lattice Boltzmann method, EPL (Europhysics Letters), 10(5) (1989), pp. 433.

[20] F. J. Higuera et al, Boltzmann approach to lattice gas simulations, EPL (Europhysics Letters), 9(7) (1989), pp. 663.

[22] M. R. Swift , W. R. Osborn , and J. M. Yeomans , Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75(5) (1995), pp. 830.

[23] M. R. Swift , E. Orlandini , W. R. Osborn , and J. M. Yeomans , Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev.E, 54(5) (1996), pp. 5041.

[25] Y. H. Qian , D.Q. D’Humières , and P. Lallemand , Lattice BGK models for Navier-Stokes equation, EPL (Europhysics Letters), 17(6) (1992), pp. 479.

[26] Y. H. Qian and S. A. Orszag , Lattice bgk models for the navier-stokes equation: Nonlinear deviation in compressible regimes, EPL (Europhysics Letters), 21(3) (1993), pp. 255.

[27] B. C. Shi and Z. L. Guo , Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E, 79(1) (2009), 016701.

[30] Q. S. Zou and X. Y. He , On pressure and velocity boundary conditions for the lattice boltzmann bgk model, Phys. Fluids, 9(6) (1957), pp. 15911598.

[31] H. Tanaka and T. Araki , Spontaneous double phase separation induced by rapid hydrodynamic coarsening in two-dimensional fluid mixtures, Phys. Rev. Lett., 81(2) (1989), pp. 389.

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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
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