Abstract
The lateral migration of a spherical particle in a sheared Giesekus fluid is numerically studied by the direct-forcing fictitious domain method. The model is first validated by comparing the simulation results with the available data in the literature. Effects of the viscosity ratio, shear thinning, Weissenberg number, and wall confinement on the particle migration are examined. Results show that the particle migrates toward the wall, irrespective of whether the fluid is shear thinning. The wall confinement, shear thinning, and high Weissenberg number could respectively facilitate the particle lateral migration. While the effect of viscosity ratio on the particle migration is not monotonic, a separatrix value is found which divides the viscosity ratio into two ranges. Moreover, effects of rheological properties on the particle angular velocity and its variation throughout the migration pathway are also explored, and the position where the angular velocity starts to decrease is affected by fluid rheological properties.
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References
Asmolov ES (1990) Dynamics of a spherical particle in a laminar boundary layer. Fluid Dyn 25(6):886–890
D'Avino G, Tuccillo T, Maffettone PL et al (2010a) Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow. Comput Fluids 39(4):709–721
D'Avino G, Maffettone PL, Greco F et al (2010b) Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J Non-Newtonian Fluid Mech 165(9–10):466–474
D'Avino G, Snijkers F, Pasquino R et al (2012) Migration of a sphere suspended in viscoelastic liquids in Couette flow: experiments and simulations. Rheol Acta 51(3):215–234
Garduno IE, Tamaddon-Jahromi HR, Webster MF (2015) Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number. Rheol Acta 54(3):235–251
Gauthier F, Goldsmith HL, Mason SG (1971) Particle motions in non-Newtonian media. I: Couette flow. Rheol Acta 10(3):344–364
Glowinski R, Pan TW, Hesla TI, Joseph DD, Périaux J (1999) A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: application to particulate flow. Int J Numer Methods Fluids 30(8):1043–1066
Halow JS, Wills GB (1970) Experimental observations of sphere migration in Couette systems. Ind Eng Chem Fundam 9(4):603–607
Halow JS, Wills GB (1970a) Experimental observations of sphere migration in Couettesystems. Ind Eng Chem Fundam 9(4):603–607
Halow JS, Wills GB (1970b) Radical migration of spherical particles in Couette systems. AICHE J 16(2):281–286
Ho BP, Leal LG (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65(2):365–400
Ho BP, Leal LG (1976) Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J Fluid Mech 76(04):783–799
Huang PY, Feng J, Hu HH et al (1997) Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. J Fluid Mech 343:73–94
Karnis A, Mason SG (1966) Particle motions in sheared suspensions. XIX. Viscoelastic media. Trans Soc Rheol 10(2):571–592
Kim YW, Yoo JY (2009) Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications. Biosens Bioelectron 24(12):3677–3682
Leer BV (1979) Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J Comput Phys 32(1):101–136
Lormand BM, Phillips RJ (2004) Sphere migration in oscillatory Couette flow of a viscoelastic fluid. J Rheol 48(3):551–570
Manski JM, van der Goot AJ, Boom RM (2007) Advances in structure formation of anisotropic protein-rich foods through novel processing concepts. Trends Food Sci Technol 18(11):546–557
Mclaughlin JB (1991) Inertial migration of a small sphere in linear shear flows. J Fluid Mech 224:261–274
Pamme N (2007) Continuous flow separations in microfluidic devices. Lab Chip 7(12):1644–1659
Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22(02):385–400
Segré G, Silberberg A (1961) Radial particle displacements in Poiseuille flow of suspensions. Nature 189(4760):209–210
Segré G, Silberberg A (1962) Behaviour of macroscopic rigid spheres in Poiseuille flow part 2. Experimental results and interpretation. J Fluid Mech 14(01):136–157
Shao X, Yu Z, Sun B (2008) Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys Fluids 20(10):103307
Snijkers F, D'Avino G, Maffettone PL, Greco F, Hulsen MA, Vermant J (2011) Effect of viscoelasticity on the rotation of a sphere in shear flow. J Non-Newton Fluid 166:363–372
Song HY, Lee SH, Salehiyan R, Hyun K (2016) Relationship between particle focusing and dimensionless numbers in elasto-inertial focusing. Rheol Acta 55(11–12):889–900
Sroka J, Kordecka A, Włosiak P, Madeja Z, Korohoda W (2009) Separation methods for isolation of human polymorphonuclear leukocytes affect their motile activity. Eur J Cell Biol 88(9):531–539
Sullivan MT, Karina M, Stone HA (2008) Transverse instability of bubbles in viscoelastic channel flows. Phys Rev Lett 101(24):244503
Wang P, Yu Z, Lin J (2018) Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids. J Non-Newtonian Fluid Mech 262:142–148
Whitesides GM (2006) The origins and the future of microfluidics. Nature 442(7101):368–373
Yu Z, Shao X (2007) A direct-forcing fictitious domain method for particulate flows. J Comput Phys 227(1):292–314
Yu Z, Wachs A (2007) A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J Non-Newtonian Fluid Mech 145(2–3):78–91
Yu Z, Phan-Thien N, Fan Y, Tanner RI (2002) Viscoelastic mobility problem of a system of particles. J Non-Newtonian Fluid Mech 104(2):87–124
Yu Z, Wachs A, Peysson Y (2006) Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J Non-Newtonian Fluid Mech 136(2–3):126–139
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The authors would like to thank the Major Program of National Natural Science Foundation of China for their financial support (Grant nos. 11632016, 91852102, and 51876191).
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Liu, B., Lin, J., Ku, X. et al. Migration of spherical particles in a confined shear flow of Giesekus fluid. Rheol Acta 58, 639–646 (2019). https://doi.org/10.1007/s00397-019-01164-w
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DOI: https://doi.org/10.1007/s00397-019-01164-w