Numerical simulation of a shear-thinning fluid through packed spheres

Hai Long Liu; Jong Sin Moon; Wook Ryol Hwang

Korea-Australia Rheology Journal, Vol.24, No.4, 297-306, December, 2012

DOI10.1007/s13367-012-0036-8 Export Citation

Numerical simulation of a shear-thinning fluid through packed spheres

Hai Long Liu, Jong Sin Moon¹, and Wook Ryol Hwang^†

School of Mechanical Engineering, Research Center for Aircraft Parts Technology (ReCAPT), Gyeongsang National University, Gajwa-dong 900, Jinju, Republic of Korea, 660-701
¹Tech Center, LG Chem Ltd, Jang-dong 84, Daejeon, Republic of Korea, 305-343

E-mail:

Flow behaviors of a non-Newtonian fluid in spherical microstructures have been studied by a direct numerical simulation. A shear-thinning (power-law) fluid through both regular and randomly packed spheres has been numerically investigated in a representative unit cell with the tri-periodic boundary condition, employing a rigorous three-dimensional finite-element scheme combined with fictitious-domain mortar-element methods. The present scheme has been validated for the classical spherical packing problems with literatures. The flow mobility of regular packing structures, including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), as well as randomly packed spheres, has been investigated quantitatively by considering the amount of shear-thinning, the pressure gradient and the porosity as parameters. Furthermore, the mechanism leading to the main flow path in a highly shear-thinning fluid through randomly packed spheres has been discussed.

Keywords:flows in porous media;shear-thinning fluid;mobility and permeability

[References]

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Cai Z, J. Adv. Mater., 25, 58 (1993)
Dazhi G, Tanner RI, J. Non-Newtonian Fluid Mech., 17, 1 (1985)
Gebart BR, J. Compos. Mater., 26, 1100 (1992)
Hamalainen J, Hasimoto H, J. Fluid Mech., 5, 317 (328)
Hwang WR, Kim WY, Lee ES, Park CH, Korea-Aust. Rheol. J., 23, 173 (2011)
Jung Y, Torquato S, Phys. Rev. E., 72, 525 (2005)
Larson RE, Higdon JJL, Phys. Fluids A., 1, 38 (1989)
Liu C, Evett JB, Soils and foundations, 3rd edition, Prentice-Hall, New Jersey. (1992)
Liu HL, Hwang WR, Composites Part A., 43, 2030 (2012)
Liu HL, Hwang WR, Korea-Aust. Rheol. J., 21(1), 71 (2009)
Lundstrom TS, Sundlof H, Holmberg JA, J. Compos. Mater., 40, 283 (2006)
Morais AF, Seybold H, Herrmann HJ, Andrade JS, Phys. Rev. Lett., 103, 194502 (2009)
Orgeas L, Idris Z, Geindreau C, Bloch JF, Auriault JL, Chem. Eng. Sci., 61(14), 4490 (2006)
Park JM, Park SJ, Korea-Aust.Rheol. J., 23, 219 (2011)
Pan C, Prins JF, Miller CT, Comput. Phys. Commun., 158, 89 (2004)
Pan C, Luo L, Miller CT, Comput. Fluids., 35, 898 (2006)
Nield DA, Bejan A, Convection in porous media, Springer, New York. (1996)
Saff EB, Kuijlaars ABJ, Math. Intelligencer., 19, 5 (1997)
Sangani AS, Acrivos A, Int. J. Multiphase Flow., 8, 343 (1982)
Sochi T, J. Polym. Sci. B: Polym. Phys., 48(23), 2437 (2010)
Song DY, Gupta RK, Chhabra RP, Ind. Eng. Chem. Res., 50(23), 13105 (2011)
Wang JF, Hwang WR, J. Compos. Mater., 45, 883 (2011)
Wang Q, Maze B, Tafreshi HV, Pourdeyhimi B, Modelling Simul. Mater. Sci. Eng., 15, 855 (2007)
Woods JK, Spelt PDM, Selerland T, Lawrence CJ, J. Non-Newton. Fluid Mech., 111(2-3), 211 (2003)
Zaman E, Jalali P, Physica A., 389, 205 (2010)
Zick AA, Homsy GM, J. Fluid. Mech., 115, 13 (1982)

[Referenced By]

[1] Bruschke MV, Advani SG, J. Rheol., 37, 479 (1992)

[2] Cai Z, J. Adv. Mater., 25, 58 (1993)

[3] Dazhi G, Tanner RI, J. Non-Newtonian Fluid Mech., 17, 1 (1985)

[4] Gebart BR, J. Compos. Mater., 26, 1100 (1992)

[5] Hamalainen J, Hasimoto H, J. Fluid Mech., 5, 317 (328)

[6] Hwang WR, Kim WY, Lee ES, Park CH, Korea-Aust. Rheol. J., 23, 173 (2011)

[7] Jung Y, Torquato S, Phys. Rev. E., 72, 525 (2005)

[8] Larson RE, Higdon JJL, Phys. Fluids A., 1, 38 (1989)

[9] Liu C, Evett JB, Soils and foundations, 3rd edition, Prentice-Hall, New Jersey. (1992)

[10] Liu HL, Hwang WR, Composites Part A., 43, 2030 (2012)

[11] Liu HL, Hwang WR, Korea-Aust. Rheol. J., 21(1), 71 (2009)

[12] Lundstrom TS, Sundlof H, Holmberg JA, J. Compos. Mater., 40, 283 (2006)

[13] Morais AF, Seybold H, Herrmann HJ, Andrade JS, Phys. Rev. Lett., 103, 194502 (2009)

[14] Orgeas L, Idris Z, Geindreau C, Bloch JF, Auriault JL, Chem. Eng. Sci., 61(14), 4490 (2006)

[15] Park JM, Park SJ, Korea-Aust.Rheol. J., 23, 219 (2011)

[16] Pan C, Prins JF, Miller CT, Comput. Phys. Commun., 158, 89 (2004)

[17] Pan C, Luo L, Miller CT, Comput. Fluids., 35, 898 (2006)

[18] Nield DA, Bejan A, Convection in porous media, Springer, New York. (1996)

[19] Saff EB, Kuijlaars ABJ, Math. Intelligencer., 19, 5 (1997)

[20] Sangani AS, Acrivos A, Int. J. Multiphase Flow., 8, 343 (1982)

[21] Sochi T, J. Polym. Sci. B: Polym. Phys., 48(23), 2437 (2010)

[22] Song DY, Gupta RK, Chhabra RP, Ind. Eng. Chem. Res., 50(23), 13105 (2011)

[23] Wang JF, Hwang WR, J. Compos. Mater., 45, 883 (2011)

[24] Wang Q, Maze B, Tafreshi HV, Pourdeyhimi B, Modelling Simul. Mater. Sci. Eng., 15, 855 (2007)

[25] Woods JK, Spelt PDM, Selerland T, Lawrence CJ, J. Non-Newton. Fluid Mech., 111(2-3), 211 (2003)

[26] Zaman E, Jalali P, Physica A., 389, 205 (2010)

[27] Zick AA, Homsy GM, J. Fluid. Mech., 115, 13 (1982)