Abstract
Particle migration induced by hydrodynamic interparticle interaction in a Poiseuille flow of Giesekus viscoelastic fluid is studied numerically using the direct forcing/fictitious domain method with Weissenberg number 0.1 ≤ Wi ≤ 1.5, mobility parameter 0.1 ≤ α ≤ 0.7, viscosity ratio 0.1 ≤ β ≤ 0.7, block ratio 0.2 ≤ ε ≤ 0.4, initial interparticle spacing 0.1 ≤ s ≤ 2.0, and initial vertical position 0.1 ≤ y0 ≤ 0.2. The method is validated by comparing the present results with previous numerical results. The effects of Wi, α, β, ε, s and y0 on the particle migration are analyzed. The results showed that a particle tends to move toward the wall with the increases of the elastic effect of the fluid, shear thinning effect, solvent viscosity and block ratio. For three particles in initial parallel arrangement, the trajectory of two particles on the edge is obviously different from that of a single particle. A single particle would move toward the centerline at a definite y0. However, for the case of three particles at a same y0, the upstream particle first migrates a distance toward the wall and then return toward the centerline, while downstream particle migrates quickly to the centerline. This is called abnormal migration. The phenomenon of abnormal migration disappears when the initial interparticle spacing is large enough, and is more obvious when the initial vertical position of particles is close to the wall. The phenomenon of abnormal migration tends to be obvious with the increases of the shear thinning effect, solvent viscosity and the block ratio, but with the decrease of elastic effect of the fluid.
Similar content being viewed by others
References
Masaeli M, Sollier E, Amini H, Mao W, Camacho K, Doshi N (2012) Continuous inertial focusing and separation of particles by shape. Phys Rev X 2:031017
Fan LL, Wu X, Zhang H et al (2019) Continuous sheath-free focusing of microparticles in viscoelastic and Newtonian fluids. Microfluid Nanofluid 23(10):117
Lu X, Liu C, Hu G, Xuan X (2017) Particle manipulations in non-Newtonian microfluidics: a review. J Colloid Interface Sci 500:182–201
Pamme N (2007) Continuous flow separations in microfluidic devices. Lab Chip 7:1644–1659
Pratt ED, Huang C, Hawkins BG, Gleghorn JP, Kirby BJ (2011) Rare cell capture in microfluidic devices. Chem Eng Sci 66:1508–1522
Segré G, Silberberg A (1961) Radical particle displacements in Poiseuille flow of suspensions. Nature 189:209–210
Ho BP, Leal J (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65:365–400
Ishii K, Hasimoto H (1980) Lateral migration of a spherical particle in flows in a circular tube. J Phys Soc Jpn 48:2144–2153
de Siqueira IR, da Carvalho MS (2018) Shear-induced particle migration in the flow of particle suspensions through a sudden plane expansion. J Brazilian Soc Mech Sci Eng. https://doi.org/10.1007/s40430-018-1155-z
Karnis A, Mason SG (1966) Particle motions in sheared suspensions. xix. viscoelastic media. Trans Soc Rheol 10:571–592
Ho BP, Leal LG (1976) Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J Fluid Mech 76:783–799
Dhahir SA, Walters K (1989) On non-Newtonian flow past a cylinder in a confined flow. J Rheol 33:781–804
Yu ZS, Lin JZ (1998) Numerical research on the coherent structure in the viscoelastic second-order mixing layers. Appl Math Mech-Engl Edn 19:717–723
Wang YL, Lin JZ, Zhang PJ (2018) Vortex behavior of particle suspension flow in a wedge for the second-order fluid. J Brazilian Soc Mech Sci Eng. https://doi.org/10.1007/s40430-017-0944-0
Villone MM, D’Avino G, Hulsen MA, Greco F, Maffettone PL (2011) Direct simulations of particle suspensionsin a viscoelastic fluid in sliding bi-periodic frames. J Non-Newtonian Fluid Mech 166:1396–1405
Li D, Xuan X (2018) Fluid rheological effects on particle migration in a straight rectangular microchannel. Microfluid Nanofluid 22:49
Hwang WR, Hulsen MA, Meijer HEH (2004) Direct simulations of particle suspensionsin a viscoelastic fluid in sliding bi-periodic frames. J Non-Newtonian Fluid Mech 121:15–33
Liu BR, Lin JZ, Ku XK, Yu ZS (2020) Particle migration in bounded shear flow of Giesekus fluids. J Non-Newtonian Fluid Mech 276:104233
Snijkers F, Pasquino R, Vermant J (2013) Hydrodynamic interactions between twoequally sized spheres in viscoelastic fluids in shear flow. Langmuir 29:5701–5713
D’Avino G, Hulsen MA, Maffettone PL (2013) Dynamics of pairs and triplets ofparticles in a viscoelastic fluid flowing in a cylindrical channel. Comput Fluids 86:45–55
Del Giudice F, D’Avino G, Greco F, Maffettone PL, Shen AQ (2018) Fluid viscoelasticity drives self-assembly of particle trains in a straight microfluidic channel. Phys Rev Appl 10:064058
D’Avino G, Maffettone PL (2019) Numerical simulations on the dynamics of a particle pair in a viscoelastic fluid in a microchannel: effect of rheology, particle shape, and confinement. Microfluid Nanofluid 23:82
D’Avino G, Maffettone PL (2020) Numerical simulations on the dynamics of trains of particles in a viscoelastic fluid flowing in a microchannel. Meccanica 55(2):317–330
Raoufi MA, Mashhadian A, Niazmand H et al (2019) Experimental and numerical study of elasto-inertial focusing in straight channels. Biomicrofluidics 13(3):034103
Yu Z, Wachs A (2007) A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J Non-Newtonian Fluid Mech 145:78–91
Yu Z, Shao X (2007) A direct-forcing fictitious domain method for particulate flows. J Comput Phys 227:292–314
Leer BV (1979) Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J Comput Phys 32:101–136
Shao X, Yu Z, Sun B (2008) Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys Fluids 20:103307
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
Hu HH, Patankar NA, Zhu MY (2001) Direct numerical simulations of fluid–solidsystems using the arbitrary Lagrangian-Eulerian technique. J Comput Phys 169:427–462
Acknowledgements
This work was supported by the National Natural Science Foundation of China with Grant Nos. 91852102 and 11632016.
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Daniel Onofre de Almeida Cruz, D.Sc.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, B., Lin, J. & Ku, X. Particle migration induced by hydrodynamic interparticle interaction in the Poiseuille flow of a Giesekus fluid. J Braz. Soc. Mech. Sci. Eng. 43, 106 (2021). https://doi.org/10.1007/s40430-021-02852-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-021-02852-6