Secondary Dean flow characteristics of inelastic Bird-Carreau fluids in curved microchannels

Kyu Yoon; Hyun Wook Jung; Myung-Suk Chun

Korea-Australia Rheology Journal, Vol.32, No.1, 61-70, February, 2020

DOI10.1007/s13367-020-0007-4 Export Citation

Secondary Dean flow characteristics of inelastic Bird-Carreau fluids in curved microchannels

Kyu Yoon^{1, 2}, Hyun Wook Jung^{1, †}, and Myung-Suk Chun^{2, 3, †}

¹Department of Chemical and Biological Engineering, Korea University, Seoul 02841, Republic of Korea
²Complex Fluids Laboratory, National Agenda Research Division, Korea Institute of Science and Technology (KIST), Seoul 02792, Republic of Korea
³Bio-Med Department, KIST School, Korea University of Science and Technology, Seoul 02792, Republic of Korea

E-mail:,

To effectively control the mixing of target materials inside microfluidic devices, the Dean flow features of generalized-Newtonian Bird-Carreau (BC) fluids in curved rectangular channels are theoretically investigated, as a passive technique. Governing equations coupled with the Cauchy momentum equation and the BC model are solved using the finite volume scheme with a semi-implicit method for pressure-linked equations-revised (SIMPLER) algorithm. The effects of the rheological parameters of BC model, such as viscosity ratio, power-law index, and relaxation time constant, on the Dean flow are systematically examined in a wide range of Dean numbers (Dn), (very low to O(102)). The entire flow characteristics of BC fluids in curved microchannels with increasing Dn are quantified using flow skewness, DnRef/DnMFS, and magnitude of vorticity, resulting in two main findings of a more outward-skewed streamwise velocity profile and a more enhanced secondary Dean vortex for non-Newtonian fluids in comparison to the Newtonian case at the same Dn.

Keywords:secondary Dean flow;flow skewness;Bird-Carreau model;curved microchannel;microfluidics

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[Referenced By]

[1] Ait-Kadi A, Carreau PJ, Chauveteau G, J. Rheol., 31, 537 (1987)

[2] Amini H, Lee W, Di Carlo D, Lab Chip, 14, 2739 (2014)

[3] Bayat P, Rezai P, Sci. Rep., 7, 13655 (2017)

[4] Berger SA, Talbot L, Yao LS, Annu. Rev. Fluid Mech., 15, 461 (1983)

[5] Bharti RP, Chhabra RP, Eswaran V, Can. J. Chem. Eng., 84(4), 406 (2006)

[6] Bird RB, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids, John Wiley & Sons, New York 1987.

[7] Bossard F, El Kissi N, D'Aprea A, Alloin F, Sanchez JY, Dufresne A, Rheol. Acta, 49(5), 529 (2010)

[8] Chen H, Meiners JC, Appl. Phys. Lett., 84, 2193 (2004)

[9] Cheng KC, Lin RC, Ou JW, J. Fluids Eng., 98, 41 (1976)

[10] Cherry EM, Eaton JK, Phys. Fluids, 25, 073104 (2013)

[11] Chien SK, Yen TH, Yang YT, Chen CK, CMES-Comp. Model Eng., 29, 163 (2008)

[12] Cho CC, Chen CL, Chen CK, Electrophoresis, 33, 743 (2012)

[13] Chun MS, Ko MJ, J. Korean Phys. Soc., 61, 1108 (2012)

[14] Cruz DA, Coelho PM, Alves MA, J. Heat Transfer, 134, 091703 (2012)

[15] Culbertson CT, Jacobson SC, Ramsey JM, Anal. Chem., 70, 3781 (1998)

[16] De Vriend HJ, J. Fluid Mech., 107, 423 (1981)

[17] Dean WR, Philos. Mag., 4, 208 (1927)

[18] Di Carlo D, Lab Chip, 9, 3038 (2009)

[19] Ebagninin KW, Benchabane A, Bekkour K, J. Colloid Interface Sci., 336(1), 360 (2009)

[20] Eustice J, Proc. R. Soc. London Ser. A, 84, 107 (1910)

[21] Fan Y, Tanner RI, Phan-Thien N, J. Fluid Mech., 440, 327 (2001)

[22] Guan G, Wu L, Bhagat AAS, Li Z, Chen PCY, Chao S, Ong CJ, Han J, Sci. Rep., 3, 1475 (2013)

[23] Howell PB, Mott DR, Golden JP, Ligler FS, Lab Chip, 4, 663 (2004)

[24] Hsu CF, Patankar SV, AIChE J., 28, 610 (1982)

[25] Jarvas G, Guttman A, Trends. Biotechnol., 31, 696 (2013)

[26] Jung H, Chun MS, Chang MS, Analyst, 140, 1265 (2015)

[27] Koh CG, Kang X, Xie Y, Fei Z, Guan J, Yu B, Zhang X, Lee LJ, Mol. Pharm., 6, 1333 (2009)

[28] Lepchev D, Weihs D, J. Fluids Eng., 132, 071202 (2010)

[29] Martel JM, Toner M, Phys. Fluids, 24, 032001 (2012)

[30] McGrath J, Jimenez M, Bridle H, Lab Chip, 14, 4139 (2014)

[31] Nivedita N, Ligrani P, Papautsky I, Sci. Rep., 7, 44072 (2017)

[32] Ookawara S, Higashi R, Street D, Ogawa K, Chem. Eng. J., 101(1-3), 171 (2004)

[33] Patankar SV, 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York 1980.

[34] Rothert A, Deo SK, Millner L, Puckett LG, Madou MJ, Daunert S, Anal. Biochem., 342, 11 (2005)

[35] Rowe M, J. Fluid Mech., 43, 771 (1970)

[36] Shen S, Kou L, Zhang X, Wang D, Niu Y, Wang J, Adv. Theory. Simul., 1, 170003 (2018)

[37] Snyder B, Lovely C, Phys. Fluids A, 2, 1808 (1990)

[38] Song H, Cai Z, Noh HM, Bennett DJ, Lab Chip, 10, 734 (2010)

[39] Tan WH, Takeuchi S, Proc. Natl. Acad. Sci. USA, 104, 1146 (2007)

[40] Thangam S, Hur N, J. Fluid Mech., 217, 421 (1990)

[41] Volpe A, Paie P, Ancona A, Osellame R, Lugara PM, Pascazio G, J. Phys. D-Appl. Phys., 50, 255601 (2017)

[42] Wyatt NB, Liberatore MW, J. Appl. Polym. Sci., 114(6), 4076 (2009)

[43] Yamada M, Nakashima M, Seki M, Anal. Chem., 76, 5465 (2004)

[44] Yoon DH, Ha JB, Bahk YK, Arakawa T, Shoji S, Go JS, Lab Chip, 9, 87 (2009)

[45] Yoon K, Jung HW, Chun MS, Rheol. Acta, 56(11), 915 (2017)

[46] Yun JH, Chun MS, Jung HW, Phys. Fluids, 22, 052004 (2010)

[47] Zhao C, Yang C, Adv. Colloid Interface Sci., 201-202, 94 (2013)