Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods

Hamideh Rouhani Tazangi; Ataallah Soltani Goharrizi; Ebrahim Jahanshahi Javaran

Korea-Australia Rheology Journal, Vol.33, No.3, 293-306, August, 2021

DOI10.1007/s13367-021-0023-z Export Citation

Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods

Hamideh Rouhani Tazangi, Ataallah Soltani Goharrizi, and Ebrahim Jahanshahi Javaran^{1, †}

Department of Chemical Engineering, Shahid Bahonar University of Kerman, Kerman 7618868366, Iran
¹Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman 7618868366, Iran

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In the present work, a numerical algorithm based on a combination of the lattice Boltzmann method (LBM) and the improved smoothed profile method (iSPM) has been proposed to study the motion of one, two and many circular particles in a non-Newtonian fluid. At first, the velocity profile of the non-Newtonian fluid at various power law indexes (n) was analyzed and the findings were compared with the numerical results of the previous works. Then, the motion of one circular cylinder and the hydrodynamic interactions between two particles in a shear flow were investigated. It was observed that Reshear,p had no important impact on the rotation of a single cylinder. In the two particles interaction, increasing the shear rate caused the particles to tumble on each other more closely and during a longer time. Therefore, the effective viscosity of a particulate suspension was considered for different Reynolds numbers and solid volume fractions, showing a satisfactory agreement with the previously published data. The results, therefore, showed that inertia increased the particles contribution to the effective viscosity of the suspension.

Keywords:power-law fluid;shear flow;lattice-Boltzmann method;smoothed profile method;rheology

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[2] Alghalibi D, Lashgari I, Brandt L, Hormozi S, J. Fluid Mech., 852, 329 (2018)

[3] Batchelor GK, J. Fluid Mech., 41, 545 (1970)

[4] Bell BC, Surana KS, Int. J. Numer. Methods Fluids, 18, 127 (1994)

[5] Bharti RP, Chhabra RP, Ind. Eng. Chem. Res., 46(11), 3820 (2007)

[6] Brady JF, Bossis G, Annu. Rev. Fluid Mech., 20, 111 (1988)

[7] Chai ZH, Shi BC, Guo ZL, Rong FM, J. Non-Newton. Fluid Mech., 166(5-6), 332 (2011)

[8] Chhabra RP, Bubbles, Drops, and Particles in Non-Newtonian fluids, 2007.

[9] Chevalier T, Rodts S, Chateau X, Chevalier C, Coussot P, Phys. Rev. E, 89, 023002 (2014)

[10] Delouei AA, Nazari M, Kayhani MH, Kang SK, Succi S, Physica A, 447, 1 (2016)

[11] Einstein A, Ann. Phys., 19, 289 (1906)

[12] Feng ZG, Michaelides EE, J. Comput. Phys., 195, 602 (2004)

[13] Gabbanelli S, Drazer G, Koplik J, Phys. Rev. E, 72, 046312 (2005)

[14] Ghia U, Ghia KN, Shin CT, J. Comput. Phys., 48, 387 (1982)

[15] Jafari S, Yamamoto R, Rahnama M, Phys. Rev. E, 82, 026702 (2011)

[16] Javaran EJ, Rahnama M, Jafari S, Part. Sci. Technol., 31(6), 643 (2013)

[17] Krieger IM, Dougherty TJ, Trans. Soc. Rheol., 3, 137 (1959)

[18] Krieger IM, Trans. Soc. Rheol., 7, 101 (1963)

[19] Kromkamp J, van den Ende D, Kandhai D, van der Sman R, Boom R, Chem. Eng. Sci., 61(2), 858 (2006)

[20] Kromkamp J, van den Ende DTM, Kandhai D, van der Smani RGM, Boom RM, J. Fluid Mech., 529, 253 (2005)

[21] Kulkarni PM, Morris JF, Phys. Fluids, 20, 040602 (2008)

[22] Ladd AJC, J. Fluid Mech., 271, 285 (1994)

[23] Ladd AJC, J. Fluid Mech., 271, 311 (1994)

[24] Luo X, Maxey MR, Karniadakis GE, J. Comput. Phys., 228, 1750 (2009)

[25] Mendu SS, Das PK, J. Non-Newton. Fluid Mech., 175-176, 10 (2012)

[26] Mino Y, Shinto H, Sakai S, Matsuyama H, Phys. Rev. E, 95, 043309 (2017)

[27] Nakayama Y, Yamamoto R, Phys. Rev. E, 71, 036707 (2005)

[28] Neofytou P, Adv. Eng. Softw., 36, 664 (2005)

[29] Pal R, Can. J. Chem. Eng., 93(1), 166 (2015)

[30] Qi Z, Kuang SB, Rong LW, Yu AB, Powder Technol., 326, 208 (2018)

[31] Shakib-Manesh A, Raiskinmaki P, Koponen A, Kataja M, Timonen J, J. Stat. Phys., 1007, 67 (2002)

[32] Succi S, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York, 2001.

[33] Tao S, Guo ZL, Wang LP, Powder Technol., 315, 126 (2017)

[34] Taylor GI, Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci., 138, 41 1932.

[35] Wang CH, Ho JR, Comput. Math. Appl., 62, 75 (2011)

[36] Yun BM, Dasi LP, Aidun CK, Yoganathan AP, J. Fluid Mech., 743, 170 (2014)