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

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  20 June 2017

Xiaoyu Wang ,
Jie Ouyang ,
Heng Yang  and
Jianwei Liu
Xiaoyu Wang
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Jie Ouyang*
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Heng Yang
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Jianwei Liu
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
*
*Corresponding author. Email address:[email protected] (J. Ouyang)
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Abstract

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.

Keywords

Phase separationreversible chemical reactionlattice Boltzmann methodsheared binary fluids

MSC classification

Secondary: 76D06: Statistical solutions of Navier-Stokes and related equations 76D07: Stokes and related (Oseen, etc.) flows
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 3 , August 2017 , pp. 656 - 670
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Isojima, T., Kato, H., and Hamano, K., Effective viscosities of a phase-separating binary mixture imposed to shear, Physics Letters A, 240(4) (1998), pp. 271–275.CrossRefGoogle Scholar
[2] Chen, X. B., Niu, L. S. and Shi, H. J., Modeling the phase separation in binary lipid membrane under externally imposed oscillatory shear flow, Colloid. Surface. B., 65(2) (2008), pp. 203–212.CrossRefGoogle ScholarPubMed
[3] Qin, R. S., Thermodynamic properties of phase separation in shear flow, Computers & Fluids, 117(2015), pp. 11–16.CrossRefGoogle Scholar
[4] XU, A. G., Gonnella, G., and Lamura, A., Phase-separating binary fluids under oscillatory shear, Phys. Rev. E, 67(5) (2003), 056105.CrossRefGoogle ScholarPubMed
[5] Cui, J., Ma, Z. W., Li, W., and Jiang, W., 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. 81–87.CrossRefGoogle Scholar
[6] Wagner, A. J. and Yeomans, J. M., Phase separation under shear in two-dimensional binary fluids, Phys. Rev. E, 59(4) (1999), pp. 4366–4373.CrossRefGoogle Scholar
[7] Chen, X. B., Niu, L. S., and Shi, H. J., Numerical simulation of the phase separation in binary lipid membrane under the effect of stationary shear flow, Biophys. chem., 135(1) (2008), pp. 84–94.CrossRefGoogle ScholarPubMed
[8] Lamura, A. and Gonnella, G., Lattice boltzmann simulations of segregating binary fluid mixtures in shear flow, Physica A, 294(3) (2001), pp. 295–312.CrossRefGoogle Scholar
[9] LI, Y. C., Shi, R. P., Wang, C. P., Liu, X. J., and Wang, Y. Z., Phase field study on the effect of shear flow on polymer phase separation, Procedia Engineering, 27(2012), pp. 1502–1507.CrossRefGoogle Scholar
[10] Xie, F., Zhou, C. X., Yu, W., and Liu, J. Y., Heterogeneous polymeric reaction under shear flow, J. appl. polym. sci., 109(4) (2008), pp. 2737–2745.CrossRefGoogle Scholar
[11] Xie, F., Zhou, C. X., and Yu, W., Effects of small-amplitude oscillatory shear on polymeric reaction, Polym. Composite., 29(1) (2008), pp. 72–76.CrossRefGoogle Scholar
[12] Huo, Y. L., Jiang, X. L., Zhang, H. D., and Yang, Y. L., Hydrodynamic effects on phase separation of binary mixtures with reversible chemical reaction, J. Chem. Phys., 118(21) (2003), pp. 9830–9837.CrossRefGoogle Scholar
[13] Furtado, K. and Yeomans, J. M., Lattice boltzmann simulations of phase separation in chemically reactive binary fluids, Phys. Rev. E, 73(6) (2006), 066124.CrossRefGoogle ScholarPubMed
[14] Yan, Y. Y., Zu, Y. Q., and Dong, B., LBM, a useful tool for mesoscale modelling of single-phase and multiphase flow, Appl. Therm. Eng., 31(5) (2001), pp. 649–655.CrossRefGoogle Scholar
[15] Leclaire, S., Pellerin, N., Reggio, M., and Yves Trépanier, J., Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method, Physica A, 406(2014), pp. 307–319.CrossRefGoogle Scholar
[16] Huang, H. B., Huang, J. J., and Lu, X. Y., A mass-conserving axisymmetric multiphase lattice boltzmann method and its application in simulation of bubble rising, J. Comput. Phys., 269 (2014), pp. 386–402.CrossRefGoogle Scholar
[17] Zhang, J. F., Wang, L. M., and Ouyang, J., Lattice boltzmann model for the volume-averaged navier-stokes equations, EPL (Europhysics Letters), 107(2) (2014), 20001.CrossRefGoogle Scholar
[18] Fakhari, A. and Lee, T. H., Numerics of the lattice Boltzmann method on nonuniform grids: standard lbm and finite-difference lbm, Computers & Fluids, 107 (2015), pp. 205–213.CrossRefGoogle Scholar
[19] Succi, S., Foti, E., and Higuera, F., Three-dimensional flows in complex geometries with the lattice Boltzmann method, EPL (Europhysics Letters), 10(5) (1989), pp. 433.CrossRefGoogle Scholar
[20] Higuera, F. J. et al, Boltzmann approach to lattice gas simulations, EPL (Europhysics Letters), 9(7) (1989), pp. 663.CrossRefGoogle Scholar
[21] Xu, A. G., Gonnella, G., and Lamura, A., Phase separation of incompressible binary fluids with lattice Boltzmann methods, Physica A, 331(1) (2004), pp. 10–22.CrossRefGoogle Scholar
[22] Swift, M. R., Osborn, W. R., and Yeomans, J. M., Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75(5) (1995), pp. 830.CrossRefGoogle ScholarPubMed
[23] Swift, M. R., Orlandini, E., Osborn, W. R., and Yeomans, J. M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev.E, 54(5) (1996), pp. 5041.CrossRefGoogle ScholarPubMed
[24] Chen, S. Y., Chen, H. D., Martnez, D. and Matthaeus, W., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett., 67(27) (1991), pp. 3776.CrossRefGoogle ScholarPubMed
[25] Qian, Y. H., D’Humières, D.Q., and Lallemand, P., Lattice BGK models for Navier-Stokes equation, EPL (Europhysics Letters), 17(6) (1992), pp. 479.CrossRefGoogle Scholar
[26] Qian, Y. H. and Orszag, S. A., Lattice bgk models for the navier-stokes equation: Nonlinear deviation in compressible regimes, EPL (Europhysics Letters), 21(3) (1993), pp. 255.CrossRefGoogle Scholar
[27] Shi, B. C. and Guo, Z. L., Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E, 79(1) (2009), 016701.CrossRefGoogle ScholarPubMed
[28] J. S, , Ouyang, J., Wang, X. D., and Yang, B. X., Lattice Boltzmann method coupled with the oldroyd-b constitutive model for a viscoelastic fluid, Phys. Rev. E, 88(5) (2013), 053304.Google Scholar
[29] Wagner, A. J. and Pagonabarraga, I., Lees–edwards boundary conditions for lattice boltzmann, J. stat. phys., 107(1-2) (2002), pp. 521–537.CrossRefGoogle Scholar
[30] Zou, Q. S. and He, X. Y., On pressure and velocity boundary conditions for the lattice boltzmann bgk model, Phys. Fluids, 9(6) (1957), pp. 1591–1598.CrossRefGoogle Scholar
[31] Tanaka, H. and Araki, T., Spontaneous double phase separation induced by rapid hydrodynamic coarsening in two-dimensional fluid mixtures, Phys. Rev. Lett., 81(2) (1989), pp. 389.CrossRefGoogle Scholar