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Magnetic fluid is a stable suspension of solid phase magnetic particles of diameter about 10 nm in a nonmagnetic carrier fluid like water or alcohol. Nowadays, the magnetic fluid is widely used in industry areas such as sealing, damping, lubricating, sound regulation, heat dissipation, and MHD beneficiation. Researchers have paid great attention to the behaviors of non-magnetic particles (NPs) in the magnetic field because magnetic fluid containing NPs can form different microstructures, which are easily controlled by applying a magnetic field. In order to appropriately use the properties of magnetic fluid in industry, it is necessary to study the interaction among NPs in detail. In this paper, a multi-physical numerical model is employed to investigate the sedimentation of two NPs in magnetic fluid subjected to an applied magnetic field. The magnetic fluid flow is simulated by lattice Boltzmann method, and magneto hydrodynamics is calculated with a self-correcting procedure of a Poisson equation solver, which enables the Ohm's law to satisfy its conservation law. A dipole force model is used to obtain the dipole interaction force between particles. In addition, as the permeability of the magnetic fluid is quite different from those of the NPs and magnetic fluid, correctly establishing the conjugate boundary condition of the magnetic intensity at the interface between the particles and surrounding fluid is a key because it affects the magnetic induction in the fluid-structure interaction area. A smooth transition scheme of the conjugate boundary condition for magnetic intensity at the interface between the particles and surrounding fluid is used in this work. The aim of this work is to investigate sedimentation of two NPs in magnetized magnetic fluid. By changing the ratio of magnetic permeability and the magnetic parameter, it is found that altering the ratio of magnetic permeability is more effective to change the trajectories of NPs, while changing the magnetic parameter can just give rise to a slight transform of particle trajectories. This can provide good theoretical support for the application of magnetic fluid in industry area, because the results in the present simulation can quantitatively analyze the controlling of the movement of NPs.
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Keywords:
- magnetic fluid /
- non-magnetic particles /
- self-corrected process /
- conjugate boundary condition
[1] Halsey T C, Toor W 1990 J. Stat. Phys. 61 1257
[2] Islam M F, Lin K H, Lacoste D, Lubensky T C, Yodh A G 2003 Phys. Rev. E 67 021402
[3] Zhu Y, Umehara N, Ido Y, Sato A 2006 J. Magn. Magn. Mater. 302 96
[4] Ido Y, Inagaki T, Umehara N 2008 Magnetohydrodynamics 44 83
[5] Ido Y, Inagaki T, Yamaguchi T 2010 J. Phys.:Condens. Matter 22 324103
[6] Chen Q, Bae S C, Granick S 2011 Nature 469 381
[7] Iwamoto Y, Yoshioka A, Naito T, Cuya J, Ido Y, Okawa R, Yamaguchi H 2016 Exp. Therm. Fluid Sci. 79 111
[8] Kaiser R, Mir L, Curtis R A 1976 US Patent 3951785
[9] Skjeltorp A T 1983 Phys. Rev. Lett. 51 2306
[10] Fujita T, Mamiya M 1987 J. Magn. Magn. Mater. 65 207
[11] Furst E M, Gast A P 2000 Phys. Rev. E 61 6732
[12] Gao Y, Jian Y C, Zhang L F, Huang J P 2007 J. Phys. Chem. C 111 10785
[13] Peng X, Min Y, Ma T, Luo W, Yan M 2009 T J. Magn. Magn. Mater. 321 1221
[14] Li H, Peng X 2012 J. Comput. Phys. 7 1405
[15] Peskin C S 1977 J. Comput. Phys. 25 220
[16] Peskin C S 2002 Acta Numerica 11 479
[17] Niu X D, Shu C, Chew Y T, Pemg Y 2006 Phys. Lett. A 354 173
[18] He Y L, Wang Y, Li Q 2008 Lattice Boltzmann Method:Theory and Applications (Beijing:Science Press) p31-55(in Chinese)[何雅玲, 王勇, 李庆2008格子Boltzmann方法的理论及应用(第一版) (北京:科学出版社)第31–55页]
[19] Niu X D, Yamaguchi H, Yoshikawa K 2009 Phys. Rev. E 79 046713
[20] Hu P, Zhang X W, Niu X D, Meng H 2014 Acta Mech. Sin. 46 673 (in Chinese)[胡平, 张兴伟, 牛小东, 孟辉2014力学学报46 673]
[21] Chen M F, Niu X D, Ma Y R, Yamaguchi H, Iwamoto Y 2015 Procedia Engineering 126 691
[22] Araseki H, Kotake S 1994 J. Comput. Phys. 110 301
[23] Yamasaki H, Yamaguchi H 2017 J. Magn. Magn. Mater. 431 164
[24] Li L, Chen C, Mei R, Klausner, J F 2014 Phys. Rev. E 89 043308
[25] Guo K, Li L, Xiao G, Au Yeung N, Mei R 2015 Int. J. Heat Mass Transfer 88 306
[26] Hu Y, Li D, Shu S, Niu X D 2015 Comput. Math. Appl. 70 2227
[27] Feng J, Hu H H, Joseph D D 1994 J. Fluid Mech. 261 95
[28] Feng Z G, Michaelides E E 2004 J. Comput. Phys. 195 602
[29] Zhang H, Tan Y, Shu S, Niu X D, Trias F X, Yang D, Sheng Y 2014 Comput. Fluids 94 37
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[1] Halsey T C, Toor W 1990 J. Stat. Phys. 61 1257
[2] Islam M F, Lin K H, Lacoste D, Lubensky T C, Yodh A G 2003 Phys. Rev. E 67 021402
[3] Zhu Y, Umehara N, Ido Y, Sato A 2006 J. Magn. Magn. Mater. 302 96
[4] Ido Y, Inagaki T, Umehara N 2008 Magnetohydrodynamics 44 83
[5] Ido Y, Inagaki T, Yamaguchi T 2010 J. Phys.:Condens. Matter 22 324103
[6] Chen Q, Bae S C, Granick S 2011 Nature 469 381
[7] Iwamoto Y, Yoshioka A, Naito T, Cuya J, Ido Y, Okawa R, Yamaguchi H 2016 Exp. Therm. Fluid Sci. 79 111
[8] Kaiser R, Mir L, Curtis R A 1976 US Patent 3951785
[9] Skjeltorp A T 1983 Phys. Rev. Lett. 51 2306
[10] Fujita T, Mamiya M 1987 J. Magn. Magn. Mater. 65 207
[11] Furst E M, Gast A P 2000 Phys. Rev. E 61 6732
[12] Gao Y, Jian Y C, Zhang L F, Huang J P 2007 J. Phys. Chem. C 111 10785
[13] Peng X, Min Y, Ma T, Luo W, Yan M 2009 T J. Magn. Magn. Mater. 321 1221
[14] Li H, Peng X 2012 J. Comput. Phys. 7 1405
[15] Peskin C S 1977 J. Comput. Phys. 25 220
[16] Peskin C S 2002 Acta Numerica 11 479
[17] Niu X D, Shu C, Chew Y T, Pemg Y 2006 Phys. Lett. A 354 173
[18] He Y L, Wang Y, Li Q 2008 Lattice Boltzmann Method:Theory and Applications (Beijing:Science Press) p31-55(in Chinese)[何雅玲, 王勇, 李庆2008格子Boltzmann方法的理论及应用(第一版) (北京:科学出版社)第31–55页]
[19] Niu X D, Yamaguchi H, Yoshikawa K 2009 Phys. Rev. E 79 046713
[20] Hu P, Zhang X W, Niu X D, Meng H 2014 Acta Mech. Sin. 46 673 (in Chinese)[胡平, 张兴伟, 牛小东, 孟辉2014力学学报46 673]
[21] Chen M F, Niu X D, Ma Y R, Yamaguchi H, Iwamoto Y 2015 Procedia Engineering 126 691
[22] Araseki H, Kotake S 1994 J. Comput. Phys. 110 301
[23] Yamasaki H, Yamaguchi H 2017 J. Magn. Magn. Mater. 431 164
[24] Li L, Chen C, Mei R, Klausner, J F 2014 Phys. Rev. E 89 043308
[25] Guo K, Li L, Xiao G, Au Yeung N, Mei R 2015 Int. J. Heat Mass Transfer 88 306
[26] Hu Y, Li D, Shu S, Niu X D 2015 Comput. Math. Appl. 70 2227
[27] Feng J, Hu H H, Joseph D D 1994 J. Fluid Mech. 261 95
[28] Feng Z G, Michaelides E E 2004 J. Comput. Phys. 195 602
[29] Zhang H, Tan Y, Shu S, Niu X D, Trias F X, Yang D, Sheng Y 2014 Comput. Fluids 94 37
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