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A three-dimensional coupled model for particle inertial migration in the presence of micro flows is proposed and implemented. In the present model, the kinetic theory based lattice Boltzmann method is used to describe the fluid flows, and the Newton dynamics equation based model is used to describe the translation and rotation of the particle. The fluid and particle model are coupled by the LBM bounceback scheme based moving boundary method. The processes of particle settlement under gravity and particle rotation in the condition of Couette flow take place. The reliability of the present model and algorithm is validated through comparisons between the present simulation and the benchmark tests in the literature. The simulations of particle migration with various radii in an annular curved channel are performed, and the classic velocity distribution of the secondary flow in the channel cross-section is reproduced successfully. The mechanism of the particle radius influencing the particle equilibrium position in the curved channel is discussed. The results show that the particle equilibrium position in the curved channel will approach to the channel inner wall with the increase of radius. The present model is of important value for detailed study of the particle dynamics in micro flows as well as for the design and development of new micro fluidic particle selective chips and devices.
[1] Di Carlo D 2009 Lab. Chip 9 3038
[2] Hur S C, Choi S E, Kwon S, Di Carlo D 2011 Appl. Phys. Lett. 99 044101
[3] Choi Y S, Seo K W, Lee S J 2011 Lab. Chip 11 460
[4] Kuntaegowdanahalli S S, Bhagat A A S, Kuma G, Papautsky I 2009 Lab. Chip 9 2973
[5] Di Carlo D, Irimia D,Tompkins R G, Toner M 2007 Proc. Natl. Acad. Sci. USA 104 18892
[6] Ookawara S, Higashi R, Street D, Ogawa K 2004 Chem. Eng. J. 101 171
[7] Ookawara S, Street D, Ogawa K 2006 Chem. Eng. Sci. 61 3714
[8] Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I 2008 Lab. Chip 8 1906
[9] Mao X, Waldeisen J R, Huang T J 2007 Lab. Chip 7 1260
[10] Di Carlo D, Edd J F, Humphry K J, Stone H A, Toner H 2009 Phys. Rev. Lett. 102 094503
[11] Zeng J B, Li L J, Liao Q, Jiang F M 2011 Acta Phys. Sin. 60 066401 (in Chinese) [曾建邦, 李隆键, 廖全, 蒋方明 2011 物理学报 60 066401]
[12] Ladd A J C 1994 J. Fluid Mech. 271 285
[13] Ladd A J C 1994 J. Fluid Mech. 271 311
[14] Chun B, Ladd A J C, 2006 Phys. Fluids 18 031704
[15] Aidun C K, Lu Y, Ding E J 1998 J. Fluid Mech. 373 287
[16] Humphry K J, Kulkarni P M, Weitz D A, Morris J F, Stone H A 2010 Phys. Fluids 22 081703
[17] Kilimnik A, Mao W, Alexeev A 2011 Phys. Fluids 23 123302
[18] Iglberger K 2005 Master Thesis (Germany: University of Erlangen-Nuremberg)
[19] Guo Z L, Zhao T S, Shi Y 2006 Phys. Fluids 18 067107
[20] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[21] Mordant N, Pinton J F 2000 Eur. Phys. J. B 18 343
[22] Sharma N, Patankar N A 2005 J. Comput. Phys. 205 439
[23] Do-Quang M, Amberg G 2008 J. Comput. Phys. 227 1772
[24] Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I 2008 Lab. Chip 8 1906
[25] Yoon D H, Ha J B, Bahk Y K, Arakawa T, Shoji S, Go J S 2009 Lab. Chip 9 87
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[1] Di Carlo D 2009 Lab. Chip 9 3038
[2] Hur S C, Choi S E, Kwon S, Di Carlo D 2011 Appl. Phys. Lett. 99 044101
[3] Choi Y S, Seo K W, Lee S J 2011 Lab. Chip 11 460
[4] Kuntaegowdanahalli S S, Bhagat A A S, Kuma G, Papautsky I 2009 Lab. Chip 9 2973
[5] Di Carlo D, Irimia D,Tompkins R G, Toner M 2007 Proc. Natl. Acad. Sci. USA 104 18892
[6] Ookawara S, Higashi R, Street D, Ogawa K 2004 Chem. Eng. J. 101 171
[7] Ookawara S, Street D, Ogawa K 2006 Chem. Eng. Sci. 61 3714
[8] Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I 2008 Lab. Chip 8 1906
[9] Mao X, Waldeisen J R, Huang T J 2007 Lab. Chip 7 1260
[10] Di Carlo D, Edd J F, Humphry K J, Stone H A, Toner H 2009 Phys. Rev. Lett. 102 094503
[11] Zeng J B, Li L J, Liao Q, Jiang F M 2011 Acta Phys. Sin. 60 066401 (in Chinese) [曾建邦, 李隆键, 廖全, 蒋方明 2011 物理学报 60 066401]
[12] Ladd A J C 1994 J. Fluid Mech. 271 285
[13] Ladd A J C 1994 J. Fluid Mech. 271 311
[14] Chun B, Ladd A J C, 2006 Phys. Fluids 18 031704
[15] Aidun C K, Lu Y, Ding E J 1998 J. Fluid Mech. 373 287
[16] Humphry K J, Kulkarni P M, Weitz D A, Morris J F, Stone H A 2010 Phys. Fluids 22 081703
[17] Kilimnik A, Mao W, Alexeev A 2011 Phys. Fluids 23 123302
[18] Iglberger K 2005 Master Thesis (Germany: University of Erlangen-Nuremberg)
[19] Guo Z L, Zhao T S, Shi Y 2006 Phys. Fluids 18 067107
[20] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[21] Mordant N, Pinton J F 2000 Eur. Phys. J. B 18 343
[22] Sharma N, Patankar N A 2005 J. Comput. Phys. 205 439
[23] Do-Quang M, Amberg G 2008 J. Comput. Phys. 227 1772
[24] Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I 2008 Lab. Chip 8 1906
[25] Yoon D H, Ha J B, Bahk Y K, Arakawa T, Shoji S, Go J S 2009 Lab. Chip 9 87
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