Particle dynamics in viscoelastic liquids

Journal of Non-Newtonian Fluid Mechanics

Volumn 215, Issue , 2015, Pages 80-104

  D'Avino, G ^a   Maffettone, P L ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Active suspensions; Chaining; Migration; Rotation; Sedimentation; Soft particles

Indexed keywords

ACTIVE SUSPENSION SYSTEMS; DYNAMICS; HYDROELASTICITY; LIQUIDS; NON NEWTONIAN FLOW; ROTATION; SEDIMENTATION; SUSPENSIONS (COMPONENTS); VISCOELASTICITY;

ACTIVE SUSPENSION; BIOLOGICAL APPLICATIONS; CHAINING; HYDRODYNAMIC INTERACTION; MIGRATION; NON-BROWNIAN PARTICLES; SOFT PARTICLES; VISCOELASTIC SUSPENSIONS;

SUSPENSIONS (FLUIDS);

EID: 84919933229     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2014.09.014     Document Type: Review

References (215)

1. Hoffman R.L. Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability. Trans. Soc. Rheol. 1972, 16:155-173.
2. Barnes H.A. Shear-thickening (dilatancy) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J. Rheol. 1989, 33. 329-166.
3. Stickel J.J., Powell R.L. Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid. Mech. 2005, 37:129-149.
4. H.A. Barnes, A review of the rheology of filled viscoelastic systems, in: Rheology Reviews, British Society of Rheology, 2003.
5. Chhabra R.P. Bubbles, Drops and Particles in Non-Newtonian Fluids 2007, Taylor & Francis Group, New York.
6. Larson R.G. The Structure and Rheology of Complex Fluids 1999, Oxford University Press, New York.
7. Mewis J., Wagner N.J. Colloidal Suspension Rheology 2012, Cambridge University Press, New York.
8. Macosko C.W. Rheology: Principles, Measurements, and Applications 1994, John Wiley & Sons, New York.
9. Mewis J., Wagner N.J. Current trends in suspension rheology. J. Non-Newtonian Fluid Mech. 2009, 157:147-150.
10. Karimi A., Yazdi S., Ardekani A.M. Hydrodynamic mechanisms of cell and particle trapping in microfluidics. Biomicrofluidics 2013, 7:021501.
11. Fu S.-Y., Lauke B., Mai Y.-W. Science and Engineering of Short Fibre Reinforced Polymer Composites 2009, Woodhead Publishing, Cambridge.
12. Jain R., Lee L. Fiber Reinforced Polymer (FRP) Composites for Infrastructure Applications 2012, Springer, New York.
13. Whitesides G.M. The origins and the future of microfluidics. Nature 2006, 442:368-373.
14. Brunn P. The behavior of a sphere in non-homogeneous flows of a viscoelastic fluid. Rheol. Acta 1976, 15:589-611.
15. Leal L.G. The motion of small particles in non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 1979, 5:33-78.
16. Brunn P. The motion of rigid particles in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 1980, 7:271-288.
17. Adrian R.J., Westerweel J. Particle Image Velocimetry 2011, Cambridge University Press, New York.
18. Owens R.G., Phillips T.N. Computational Rheology 2002, Imperial College Press, London.
19. S. Guido, F. Greco, Dynamics of a liquid drop in a flowing immiscible liquid, in: Rheology Reviews 2004, British Society of Rheology, Aberystwyth, United Kingdom, 2004, pp. 99-142.
20. Rozhkov A.N. Dynamics and breakup of viscoelastic liquids (a review). Fluid Dyn. 2005, 40:835-853.
21. Van Puyvelde P., Vananroye A., Cardinaels R., Moldenaers P. Review on morphology development of immiscible blends in confined shear flow. Polymer 2008, 25:5363-5372.
22. Guido S. Shear-induced droplet deformation: effects of confined geometry and viscoelasticity. Curr. Opin. Chem. Biol. 2011, 16:61-70.
23. McKinley G.H. Steady and transient motion of spherical particles in viscoelastic liquids. Transport Processes in Bubbles, Drops and Particles 2001, Taylor & Francis, New York. R.P. Chhabra, D. De Kee (Eds.).
24. Larson R.G. Constitutive Equations for Polymer Melts and Solutions 1988, Butterworth-Heinemann.
25. R. Keunings, Finite element methods for integral viscoelastic fluids, in: Rheology Reviews 2003, British Society of Rheology, Aberystwyth, United Kingdom, 2003, pp. 167-195.
26. Einstein A. Eine Neue Bestimmung der Moleküldimensionen. Ann. Phys. 1906, 19:289-306.
27. Einstein A. Berichtigung zu Meiner Arbeit: Eine Neue Bestimmung der Moleküldimensionen. Ann. Phys. 1911, 34:591-592.
28. Trevelyan B.J., Mason S.G. Particle motions in sheared suspensions. I. Rotations. J. Colloid Sci. 1951, 6:354-367.
29. Snijkers F., D'Avino G., Maffettone P.L., Greco F., Hulsen M.A., Vermant J. Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part II Exp. Results. J. Rheol. 2009, 53(2):459-480.
30. Vand V. Viscosity of solutions and suspensions. II. Experimental determination of the viscosity-concentration function of spherical suspensions. J. Phys. Colloid Chem. 1948, 52:300-314.
31. Cox R.G., Zia I.Y.Z., Mason S.G. Particle motions in sheared suspensions. XXV. Streamlines around cylinders and spheres. J. Colloid Sci. 1968, 27:7-18.
32. Gauthier F., Goldsmith H.L., Mason S.G. Particle motions in non-Newtonian media. I. Couette flow. Rheol. Acta 1971, 10:344-364.
33. Gauthier F., Goldsmith H.L., Mason S.G. Particle motions in non-Newtonian media. II. Poiseuille flow. Trans. Soc. Rheol. 1971, 15:297-330.
34. Bartram E., Goldsmith H.L., Mason S.G. Particle motions in non-newtonian media llI. Further observations in elasticoviscous fluids. Rheol. Acta 1975, 14:776-782.
35. Brunn P.O. Slow motion of a sphere in a second-order fluid. Rheol. Acta 1976, 15:163-171.
36. Greco F., D'Avino G., Maffettone P.L. Stress tensor of a dilute suspension of spheres in a viscoelastic liquid. Phys. Rev. Lett. 2005, 95:246001.
37. Greco F., D'Avino G., Maffettone P.L. Erratum. Phys. Rev. Lett. 2007, 98:109904.
38. Koch D.L., Subramanian G. The stress in a dilute suspension of spheres suspended in a second-order fluid subject to a linear velocity field. J. Non-Newtonian Fluid Mech. 2006, 138:87-97.
39. Greco F., D'Avino G., Maffettone P.L. Rheology of a dilute suspension of rigid spheres in a second order fluid. J. Non-Newtonian Fluid Mech. 2007, 147:1-10.
40. Astruc M., Vervoort S., Nouatin H.O., Coupez T., De Puydt Y., Navard P., Peuvrel-Disdier E. Experimental and numerical study of the rotation and the erosion of fillers suspended in viscoelastic fluids under simple shear flow. Rheol. Acta 2003, 42:421-431.
41. Hwang W.R., Hulsen M.A., Meijer H.E.H. Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J. Non-Newtonian Fluid Mech. 2004, 121:15-33.
42. D'Avino G., Hulsen M.A., Snijkers F., Vermant J., Greco F., Maffettone P.L. Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part I: Simulation results. J. Rheol. 2008, 52:1331-1346.
43. Housiadas K.D., Tanner R.I. The angular velocity of a freely rotating sphere in a weakly viscoelastic matrix fluid. Phys. Fluids 2011, 23:051702.
44. Housiadas K.D., Tanner R.I. Perturbation solution for the viscoelastic 3D flow around a rigid sphere subject to simple shear. Phys. Fluids 2011, 23:083101.
45. Ji S., Jiang R., Winkler R.G., Gompper G. Mesoscale hydrodynamic modeling of a colloid in shear-thinning viscoelastic fluids under shear flow. J. Chem. Phys. 2011, 135:134116.
46. Goyal N., Derksen J.J. Direct simulations of spherical particles sedimenting in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 2012, 183-184:1-13.
47. Subramanian G., Koch D.L. Heat transfer from a neutrally buoyant sphere in a second-order fluid. J. Non-Newtonian Fluid Mech. 2007, 144:49-57.
48. Snijkers F., D'Avino G., Maffettone P.L., Greco F., Hulsen M.A., Vermant J. Effect of viscoelasticity on the rotation of a sphere in shear flow. J. Non-Newtonian Fluid Mech. 2011, 166:363-372.
49. Jeffery G.B. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. London, Ser. A 1922, 102:161-179.
50. Goldsmith H.L., Mason S.G. The microrheology of dispersions. Rheology: Theory and Applications 1967, vol. 4:85-250. Academic Press Inc., New York.
51. Okagawa A., Cox R.G., Mason S.G. The kinetics of flowing dispersions. VI. Transient orientation and rheological phenomena of rods and discs in shear flows. J. Colloid Interface Sci. 1973, 43:303-329.
52. Frattini P.L., Fuller G.G. Rheo-optical studies of the effect of weak Brownian rotations in sheared suspensions. J. Fluid Mech. 1986, 168:119-150.
53. Johnson S.G., Fuller G.G. The optical anisotropy of sheared hematite suspensions. J. Colloid Interface Sci. 1988, 124:441-451.
54. Vermant J., Yang H., Fuller G.G. Rheo-optical determination of aspect ratio and polydispersity of non-spherical particles. AIChE J. 2001, 47:790-798.
55. Harper E.Y., Chang I.-D. Maximum dissipation resulting from lift in a slow viscous shear flow. J. Fluid Mech. 1968, 33:209-225.
56. Breherton F.P. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 1962, 14:284-304.
57. Johnson S.J., Salem A.J., Fuller G.G. Dynamics of colloidal particles in sheared, non-newtonian fluids. J. Non-Newtonian Fluid Mech. 1990, 34:89-121.
58. Iso Y., Koch D.L., Cohen C. Orientation in simple shear flow of semi-dilute fiber suspensions 1. Weakly elastic fluids. J. Non-Newtonian Fluid Mech. 1996, 62:115-134.
59. Iso Y., Koch D.L., Cohen C. Orientation in simple shear flow of semi-dilute fiber suspensions 2. Highly elastic fluids. J. Non-Newtonian Fluid Mech. 1996, 62:135-153.
60. Gunes D.Z., Scirocco R., Mewis J., Vermant J. Flow-induced orientation of non-spherical particles: effect of aspect ratio and medium rheology. J. Non-Newtonian Fluid Mech. 2008, 155:39-50.
61. Leal L.G. The slow motion of slender rod-like particles in a second-order fluid. J. Fluid Mech. 1975, 69:305-337.
62. Brunn P. The slow motion of a rigid particle in a second-order fluid. J. Fluid Mech. 1977, 82:529-547.
63. Harlen O.G., Koch D.L. Simple shear-flow of a suspension of fibers in a dilute polymer-solution at high Deborah number. J. Fluid Mech. 1993, 252:187-207.
64. Phan-Thien N., Fan X.-J. Viscoelastic mobility problem using a boundary element method. J. Non-Newtonian Fluid Mech. 2002, 105:131-152.
65. Nguyen-Hoang H., Phan-Thien N., Khoo B.C., Fan X.-J., Dou H.-S. Completed double layer boundary element method for periodic fibre suspension in viscoelastic fluid. Chem. Eng. Sci. 2008, 63:3898-3908.
66. D'Avino G., Hulsen M.A., Greco F., Maffettone P.L. Bistability and metabistability scenario in the dynamics of an ellipsoidal particle in a sheared viscoelastic fluid. Phys. Rev. E 2014, 89:043006.
67. Segré S., Silberberg A. Radial particle displacements in Poiseuille flow of suspensions. Nature 1961, 189:209-210.
68. Halow J.S., Wills G.B. Experimental observations of sphere migration in Couette systems. Ind. Eng. Chem. Fundam. 1970, 9:603-607.
69. Matas J.-P., Morris J.F., Guazzelli E. Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 2004, 515:171-195.
70. Eloot S., De Bisschop F., Verdonck P. Experimental evaluation of the migration of spherical particles in three-dimensional Poiseuille flow. Phys. Fluids 2004, 16:2282-2293.
71. Takemura F., Magnaudet J. Lateral migration of a small spherical buoyant particle in a wall-bounded linear shear flow. Phys. Fluids 2009, 21:083303.
72. Ho B.P., Leal L.G. Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 1974, 65:365-400.
73. Ishi K., Hasimoto H. Lateral migration of a spherical particle in flows in a circular tube. J. Phys. Soc. Jpn. 1980, 48:2144-2155.
74. Schonberg J.A., Hinch E.J. Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 1989, 203:517-524.
75. McLaughlin J.B. The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 1993, 246:249-265.
76. Asmolov E.S. The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 1999, 381:63-87.
77. Feng J., Hu H.H., Joseph D.D. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 1994, 277:271-301.
78. Yang B.H., Wang J., Joseph D.D., Hu H.H., Pan T.-W., Glowinski R. Migration of a sphere in tube flow. J. Fluid Mech. 2005, 540:109-131.
79. Chun B., Ladd A.J.C. Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys. Fluids 2006, 18:031704.
80. Shao X., Yu Z., Sun B. Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys. Fluids 2008, 20:103307.
81. Bhagat A.A.S., Kuntaegowdanahalli S.S., Papautsky I. Continuous particle separation in spiral microchannels using dean flows and differential migration. Lab Chip 2008, 8:1906-1914.
82. Di Carlo D. Inertial microfluidics. Lab Chip 2009, 9:3038-3046.
83. Bhagat A.A.S., Kuntaegowdanahalli S.S., Kaval N., Seliskar C.J., Papautsky I. Inertial microfluidics for sheath-less high-throughput flow cytometry. Biomed. Microdev. 2010, 12:187-195.
84. Amini H., Lee W., Di Carlo D. Inertial microfluidic physics. Lab Chip 2014, 14:2739-2761.
85. D'Avino G., Cicale G., Hulsen M.A., Greco F., Maffettone P.L. Effects of confinement on the motion of a single sphere in a sheared viscoelastic liquid. J. Non-Newtonian Fluid Mech. 2009, 157:101-107.
86. Bikard J., Menard P., Peuvrel-Disidier E., Budtova T. 3D numerical simulation of the behavior of a spherical particle suspended in a Newtonian fluid and submitted to a simple shear. Comp. Mater. Sci. 2006, 37:517-525.
87. N. Tonmukayakul, J.F. Morris, J. Bryant, M. Talbot, R. Schultz, R. Pipkin, Flow through apparatus for testing particle laden fluids and methods of making and using same, US Patent Number US8,024,962 (B2), 2010.
88. N. Tonmukayakul, J.F. Morris, R. Prud'homme, Method for estimating proppant transport and suspend ability of viscoelastic liquids, US Patent Application Publication Number US20110219856 (A1), 2011.
89. van den Brule B.H.A.A., Gheissary G. Effects of fluid elasticity on the static and dynamic settling of a spherical particle. J. Non-Newtonian Fluid Mech. 1993, 49:123-132.
90. Padhy S., Shaqfeh E.S.G., Iaccarino G., Morris J.F., Tonmukayakul N. Simulations of a sphere sedimenting in a viscoelastic fluid with cross shear flow. J. Non-Newtonian Fluid Mech. 2013, 197:48-60.
91. Padhy S., Rodriguez M., Shaqfeh E.S.G., Iaccarino G., Morris J.F., Tonmukayakul N. The effect of shear thinning and walls on the sedimentation of a sphere in an elastic fluid under orthogonal shear. J. Non-Newtonian Fluid Mech. 2013, 201:120-129.
92. Housiadas K.D., Tanner R.I. The drag of a freely sedimentating sphere in a sheared weakly viscoelastic fluid. J. Non-Newtonian Fluid Mech. 2012, 183-184:52-56.
93. Tanner R.I., Housiadas K.D., Qi F. Mechanism of drag increase on spheres in viscoelastic cross-shear flows. J. Non-Newtonian Fluid Mech. 2014, 203:51-53.
94. Huang P.Y., Feng J., Hu H.H., Joseph D.D. Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. J. Fluid Mech. 1997, 343:73-94.
95. D'Avino G., Tuccillo T., Hulsen M.A., Greco F., Maffettone P.L. Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow. Comput. Fluids 2010, 39:709-721.
96. D'Avino G., Maffettone P.L., Greco F., Hulsen M.A. Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J. Non-Newtonian Fluid Mech. 2010, 165:466-474.
97. Caserta S., D'Avino G., Greco F., Guido S., Maffettone P.L. Migration of a sphere in a viscoelastic fluid under planar shear flow: experiments and numerical predictions. Soft Matter 2010, 7:1100-1106.
98. Goldman A.J., Cox R.G., Brenner H. Slow viscous motion of a sphere parallel to a plane wall - II. Couette flow. Chem. Eng. Sci. 1967, 22:653-660.
99. Ho B.P., Leal L.G. Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech. 1976, 76:783-799.
100. Karnis A., Mason S.G. Particle motions in sheared suspensions. XIX. Viscoelastic media. Trans. Soc. Rheol. 1966, 10:571-592.
101. Lormand B.M., Phillips R.J. Sphere migration in oscillatory Couette flow of a viscoelastic fluid. J. Rheol. 2004, 48:551-570.
102. D'Avino G., Snijkers F., Pasquino R., Hulsen M.A., Greco F., Maffettone P.L., Vermant J. Migration of a sphere suspended in viscoelastic liquids in Couette flow: experiments and simulations. Rheol. Acta 2012, 51:215-234.
103. Highgate D.J., Whorlow R.W. End effects and particle migration effects in concentric cylinder rheometry. Rheol. Acta 1969, 8:142-151.
104. Chan P.C.-H., Leal L.G. A note on the motion of a spherical particle in a general quadratic flow of a second-order fluid. J. Fluid Mech. 1977, 82:549-559.
105. Jefri M.A., Zahed A.H. Elastic and viscous effects on particle migration in plane-Poiseuille flow. J. Rheol. 1989, 33:691-708.
106. Tehrani M.A. An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheol. 1996, 40:1057-1077.
107. Patankar N.A., Huang P.Y., Ko T., Joseph D.D. Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation. J. Fluid Mech. 2001, 438:67-100.
108. Ko T., Patankar N.A., Joseph D.D. Lift and multiple equilibrium positions of a single particle in Newtonian and Oldroyd-B fluids. Comput. Fluids 2006, 35:121-146.
109. Villone M.M., D'Avino G., Hulsen M.A., Greco F., Maffettone P.L. Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow. Comput. Fluids 2011, 42:82-91.
110. Sullivan M.T., Moore K., Stone H.A. Transverse instability of bubbles in viscoelastic channel flows. Phys. Rev. Lett. 2008, 101:244503.
111. Lee E.F., Koch D.L., Yoo Y.L. Cross-stream forces and velocities of fixed and freely suspended particles in viscoelastic Poiseuille flow: perturbation and numerical analyses. J. Non-Newtonian Fluid Mech. 2010, 165:1309-1327.
112. Villone M.M., D'Avino G., Hulsen M.A., Greco F., Maffettone P.L. Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow. J. Non-Newtonian Fluid Mech. 2011, 166:1396-1405.
113. D'Avino G., Romeo G., Villone M.M., Greco F., Netti P.A., Maffettone P.L. Single-line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. Lab Chip 2012, 12:1638-1645.
114. Romeo G., D'Avino G., Greco F., Netti P.A., Maffettone P.L. Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions. Lab Chip 2013, 13:2802-2807.
115. Seo K.W., Byeon H.J., Huh H.K., Lee S.J. Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids. RCS Adv. 2014, 4:3512-3520.
116. Xue S.C., Phan-Thien N., Tanner R.I. Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method. J. Non-Newtonian Fluid. Mech. 1995, 59:191-213.
117. Debbaut B., Avalosse T., Dooley J., Hughes K. On the development of secondary motions in straight channels induced by the second normal stress difference: experiments and simulations. J. Non-Newtonian Fluid. Mech. 1997, 69:255-271.
118. Debbaut B., Dooley J. Secondary motions in straight and tapered channels: experiments and three-dimensional finite element simulation with a multimode differential viscoelastic model. J. Rheol. 1999, 43:1525-1545.
119. Villone M.M., D'Avino G., Hulsen M.A., Greco F., Maffettone P.L. Particle motion in square channel flow of a viscoelastic liquid: migration vs. secondary flows. J. Non-Newtonian Fluid Mech. 2013, 195:1-8.
120. Lim H., Nam J., Shin S. Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow. Microfluid. Nanofluid. 2014, 17:683-692.
121. Leshansky A.M., Bransky A., Korin N., Dinnar U. Tunable nonlinear viscoelastic focusing in a microfluidic device. Phys. Rev. Lett. 2007, 98:234501.
122. Kang K., Lee S.S., Hyun K., Lee S.J., Kim J.M. DNA-based highly tunable particle focuser. Nat. Commun. 2013, 4:2567-2574.
123. Yang S., Kim J.Y., Lee S.J., Lee S.S., Kim J.M. Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. Lab Chip 2011, 11:266-273.
124. Cha S., Shin T., Lee S.S., Shim W., Lee G., Lee S.J., Kim Y., Kim J.M. Cell stretching measurement utilizing viscoelastic particle focusing. Anal. Chem. 2012, 84:10471-10477.
125. Lee D.J., Brenner H., Youn J.R., Song Y.S. Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci. Rep. 2013, 3:3258-3265.
126. Del Giudice F., Romeo G., D'Avino G., Greco F., Netti P.A., Maffettone P.L. Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel. Lab Chip 2013, 13:4263-4271.
127. Seo K.W., Kang Y.J., Lee S.J. Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids. Phys. Fluids 2014, 26:063301.
128. Lim E.J., Ober T.J., Edd J.F., Desai S.P., Neal D., Bong K., Doyle P.S., McKinley G.H., Toner M. Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat. Commun. 2014, 4120.
129. Yang S., Lee S.S., Ahn S.W., Kang K., Shim W., Lee G., Hyun K., Kim J.M. Deformability-selective particle entrainment and separation in a rectangular microchannel using medium viscoelasticity. Soft Matter 2012, 8:5011-5019.
130. Kim J.Y., Ahn S.W., Lee S.S., Kim J.M. Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow. Lab Chip 2012, 12:2807-2814.
131. Nam J., Lim H., Kim D., Jung H., Shin S. Continuous separation of microparticles in a microfluidic channel via the elasto-inertial effect of non-Newtonian fluid. Lab Chip 2012, 12:1347-1354.
132. Riddle M.J.C., Narvaez C., Bird R.B. Interactions between two spheres falling along their line of centers in a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 1977, 2:23-35.
133. Bird R.B., Armstrong R.C., Hassager O. Dynamics of Polymeric Liquids 1987, John Wiley & Sons, New York.
134. Bush M.B. On the stagnation flow behind a sphere in a shear-thinning viscoelastic fluid. J. Non-Newtonian Fluid Mech. 1994, 55:229-247.
135. Arigo M.T., McKinley G.H. An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid. Rheol. Acta 1998, 37:307-327.
136. Harlen O.G. The negative wake behind a sphere sedimenting through a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 2002, 108:411-430.
137. Gheissary G., van den Brule B.H.A.A. Unexpected phenomena observed in particle settling in non-Newtonian media. J. Non-Newtonian Fluid Mech. 1996, 67:1-18.
138. Joseph D.D., Liu Y.J., Poletto M., Feng J. Aggregation and dispersion of spheres falling in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 1994, 54:45-86.
139. Daugan S., Talini L., Herzhaft B., Allain C. Aggregation of particles settling in shear-thinning fluids. Part 1. Two-particle aggregation. Eur. Phys. J. E 2002, 7:73-81.
140. Yu Z., Wachs A., Peysson Y. Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J. Non-Newtonian Fluid Mech. 2006, 136:126-139.
141. Phillips R.J. Dynamic simulation of hydrodynamically interacting spheres in a quiescent second-order fluid. J. Fluid Mech. 1996, 315:345-365.
142. Phillips R.J., Talini L. Chaining of weakly interacting particles suspended in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 2007, 147:175-188.
143. Ardekani A.M., Rangel R.H., Joseph D.D. Two spheres in a free stream of a second-order fluid. Phys. Fluids 2008, 20:063101.
144. Feng J., Huang P.Y., Joseph D.D. Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 1996, 63:63-88.
145. Singh P., Joseph D.D., Hesla T.I., Glowinski R., Pan T.-W. A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flow. J. Non-Newtonian Fluid Mech. 2000, 91:165-188.
146. Shao X.M., Yu Z.S. Sedimentation of circular particles in Oldroyd-B fluid. J. Hydrodynamics 2004, 16:254-259.
147. Binous H., Phillips R.J. Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells. J. Non-Newtonian Fluid Mech. 1999, 83:93-130.
148. Lee S.W., Ryu S.H., Kim C. Studies on the axisymmetric sphere-sphere interaction problem in Newtonian and non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 2003, 110:1-25.
149. Verneuil E., Phillips R.J., Talini L. Axisymmetric two-sphere sedimentation in a shear thinning viscoelastic fluid: particle interactions and induced fluid velocity fields. J. Rheol. 2007, 51:1343-1359.
150. Eisenberg D.A., Klink I.M., Phillips R.J. Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: sphere-wall and sphere-sphere interactions. J. Rheol. 2013, 57:857-880.
151. Yu Z., Phan-Thien N., Fan Y., Tanner R.I. Viscoelastic mobility problem of a system of particles. J. Non-Newtonian Fluid Mech. 2002, 104:87-124.
152. Hao J., Pan T.-W., Glowinski R., Joseph D.D. A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach. J. Non-Newtonian Fluid Mech. 2009, 156:95-111.
153. Gumulya M.M., Horsley R.R., Pareek V., Lichti D.D. The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres. Chem. Eng. Sci. 2011, 66:5822-5831.
154. Bot E.T.G., Hulsen M.A., van den Brule B.H.A.A. The motion of two spheres falling along their line of centres in a Boger fluid. J. Non-Newtonian Fluid Mech. 1998, 79:191-212.
155. Batchelor G.K., Green J.T. The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 1972, 56:375-400.
156. Darabaner C.L., Mason S.G. Particle motions in sheared suspensions. XXII. Interactions of rigid spheres (experimental). Rheol. Acta 1967, 2:273-284.
157. Choi Y., Hulsen M.A., Meijer H.E.H. An extended finite element method for the simulation of particulate viscoelastic flows. J. Non-Newtonian Fluid Mech. 2010, 165:607-624.
158. Yoon S., Walkley M.A., Harlen O.G. Two particle interactions in a confined viscoelastic fluid under shear. J. Non-Newtonian Fluid Mech. 2012, 185-186:39-48.
159. Snijkers F., Pasquino R., Vermant J. Hydrodynamic interactions between two equally sized spheres in viscoelastic fluids in shear flow. Langmuir 2013, 29:5701-5713.
160. D'Avino G., Hulsen M.A., Maffettone P.L. Dynamics of pairs and triplets of particles in a viscoelastic fluid flowing in a cylindrical channel. Comput. Fluids 2013, 86:45-55.
161. Janssen P.J.A., Baron M.D., Anderson P.D., Blawzdziewicz J., Loewenberg M., Wajnryb E. Collective dynamics of confined rigid spheres and deformable drops. Soft Matter 2012, 8:3495-3506.
162. Daugan S., Talini L., Herzhaft B., Allain C. Aggregation of particles settling in shear-thinning fluids. Part 2. Three-particle aggregation. Eur. Phys. J. E 2002, 9:55-62.
163. Choi Y.J., Hulsen M.A. Alignment of particles in a confined shear flow of a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 2012, 175-176:89-103.
164. Tee S.-Y., Mucha P.J., Cipelletti L., Manley S., Brenner M.P., Segre P.N., Weitz D.A. Nonuniversal velocity fluctuations of sedimenting particles. Phys. Rev. Lett. 2002, 89:054501.
165. Bergougnoux L., Ghicini S., Guazzelli E., Hinch J. Spreading fronts and fluctuations in sedimentation. Phys. Fluids 2003, 15:1875.
166. Allen E., Uhlherr P. Nonhomogeneous sedimentation in viscoelastic fluids. J. Rheol. 1989, 33:627-638.
167. Bobroff S., Phillips R. Nuclear magnetic resonance imaging investigation of sedimentation of concentrated suspensions in non-Newtonian fluids. J. Rheol. 1998, 42:1419-1436.
168. Daugan S., Talini L., Herzhaft B., Peysson Y., Allain C. Sedimentation of suspensions in shear-thinning fluids. Oil Gas Sci. Technol. Rev. IFP 2004, 59:71-80.
169. Mora S., Talini L., Allain C. Structuring sedimentation in a shear-thinning fluid. Phys. Rev. Lett. 2005, 95:088301.
170. Philips R.J. Structural instability in the sedimentation of particulate suspensions through viscoelastic fluids. J. Non-Newtonian Fluid Mech. 2010, 165:479-488.
171. Vishnampet R., Saintillan D. Concentration instability of sedimenting spheres in a second-order fluid. Phys. Fluids 2012, 24:073302.
172. Michele J., Patzold R., Donis R. Alignment and aggregation effects in suspensions of spheres in non-Newtonian media. Rheol. Acta 1977, 16:317-321.
173. Giesekus H. Particle movement in flows of non-Newtonian fluids. Z. Angew. Math. Mech. 1978, 58:T26-T37.
174. Petit L., Noetinger B. Shear-induced structures in macroscopic dispersions. Rheol. Acta 1988, 27:437-441.
175. Lyon M.K., Mead D.W., Elliott R.E., Leal L.G. Structure formation in moderately concentrated viscoelastic suspensions in simple shear flow. J. Rheol. 2001, 45:881-890.
176. Highgate D.J. Particle migration in cone-plate viscometry of suspensions. Nature 1966, 211:1390-1391.
177. Won D., Kim C. Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow. J. Non-Newtonian Fluid Mech. 2004, 117:141-146.
178. Scirocco R., Vermant J., Mewis J. Effect of the viscoelasticity of the suspending fluid on structure formation in suspensions. J. Non-Newtonian Fluid Mech. 2004, 117:183-192.
179. Pasquino R., Snijkers F., Grizzuti N., Vermant J. The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions. Rheol. Acta 2010, 49:993-1001.
180. Pasquino R., Panariello D., Grizzuti N. Migration and alignment of spherical particles in sheared viscoelastic suspensions: a quantitative determination of the flow-induced self-assembly kinetics. J. Colloid Interface Sci. 2013, 394:49-54.
181. Pasquino R., D'Avino G., Maffettone P.L., Greco F., Grizzuti N. Migration and chaining of noncolloidal spheres suspended in a sheared viscoelastic medium: experiments and numerical simulations. J. Non-Newtonian Fluid Mech. 2014, 203:1-8.
182. Mirsepassi A., Rajaram B., Mohraz A., Dunn-Rankin D. Particle chaining and chain dynamics in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 2012, 179:1-8.
183. Van Loon S., Fransaer J., Clasen C., Vermant J. String formation in sheared suspensions in rheologically complex media: the essential role of shear thinning. J. Rheol. 2014, 58:237-254.
184. Pasquino R., Snijkers F., Grizzuti N., Vermant J. Directed self-assembly of spheres into a two-dimensional colloidal crystal by viscoelastic stresses. Langmuir 2010, 26:3016-3019.
185. Hwang W.R., Hulsen M.A. Structure formation of non-colloidal particles in viscoelastic fluids subjected to simple shear flow. Macromol. Mater. Eng. 2011, 296:321-330.
186. Santos de Oliveira I.S., van den Noort A., Padding J.T., den Otter W.K., Briels W.J. Alignment of particles in sheared viscoelastic fluids. J. Chem. Phys. 2011, 135:104902.
187. Santos de Oliveira I.S., den Otter W.K., Briels W.J. The origin of flow-induced alignment of spherical colloids in shear-thinning viscoelastic fluids. J. Chem. Phys. 2012, 137:204908-1-204908-9.
188. H. Giesekus, Some new results in suspension rheology, in: F. Wendt (Ed.), Lect. Ser. 1981-1988, Non-Newt. Flows, Von Karman Inst. for Fluid Dynamics, Rhode Saint Genese, Belgium, 1981.
189. Santos de Oliveira I.S., den Otter W.K., Briels W.J. Alignment and segregation of bidisperse colloids in a shear-thinning viscoelastic fluid under shear flow. EPL 2013, 101:28002-1-28002-6.
190. Villone M.M., Hulsen M.A., Anderson P.D., Maffettone P.L. Simulations of deformable systems in fluids under shear flow using an arbitrary Lagrangian Eulerian technique. Comput. Fluids 2014, 90:88-100.
191. Villone M.M., Greco F., Hulsen M.A., Maffettone P.L. Simulations of an elastic particle in Newtonian and viscoelastic fluids subjected to confined shear flow. J. Non-Newtonian Fluid Mech. 2014, 210:47-55.
192. Greco F. Drop deformation for non-Newtonian fluids in slow flows. J. Non-Newtonian Fluid Mech. 2002, 107:111-131.
193. Lauga E. Life at high Deborah number. EPL 2009, 86:64001.
194. Purcell E.M. Life at low Reynolds number. Am. J. Phys. 1977, 45:3-11.
195. Keim N.C., Garcia M., Arratia P.E. Fluid elasticity can enable propulsion at low Reynolds number. Phys. Fluids 2012, 24:081703.
196. Pak O.S., Zhu L., Brandt L., Lauga E. Micropropulsion and microrheology in complex fluids via symmetry breaking. Phys. Fluids 2012, 24:103102.
197. Lauga E. Propulsion in a viscoelastic fluid. Phys. Fluids 2007, 19:083104.
198. Fu H.C., Powers T.R., Wolgemuth C.W. Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 2007, 99:258101.
199. Fu H.C., Wolgemuth C.W., Powers T.R. Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 2009, 21:033102.
200. Teran J., Fauci L., Shelley M. Viscoelastic fluid response can increase the speed and efficiency of a free swimmer. Phys. Rev. Lett. 2010, 104:038101.
201. Elfring G.J., Pak O.S., Lauga E. Two-dimensional flagellar synchronization in viscoelastic fluids. J. Fluid Mech. 2010, 646:505-515.
202. Chrispell J.C., Fauci L.J., Shelley M. An actuated elastic sheet interacting with passive and active structures in a viscoelastic fluid. Phys. Fluids 2013, 25:013103.
203. Elfring G.J., Lauga E. Hydrodynamic phase locking of swimming microorganisms. Phys. Rev. Lett. 2009, 103:088101.
204. Blake J.R. A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 1971, 46:199-208.
205. Zhu L., Do-Quang M., Lauga E., Brandt L. Locomotion by tangential deformation in a polymeric fluid. Phys. Rev. E 2011, 83:011901.
206. Zhu L., Lauga E., Brandt L. Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 2012, 24:051902.
207. Shen X.N., Arratia P.E. Undulatory swimming in viscoelastic fluids. Phys. Rev. Lett. 2011, 106:208101.
208. Liu B., Powers T.R., Breuer K.S. Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl. Acad. Sci. USA 2011, 108:19516-19520.
209. Espinosa-Garcia J., Lauga E., Zenit R. Fluid elasticity increases the locomotion of flexible swimmers. Phys. Fluids 2013, 25:031701.
210. Spagnolie S.E., Liu B., Powers T.R. Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes. Phys. Rev. Lett. 2013, 111:068101.
211. Dasgupta M., Liu B., Fu H.C., Berhanu M., Breuer K.S., Powers T.R., Kudrolli A. Speed of a swimming sheet in Newtonian and viscoelastic fluids. Phys. Rev. E 2013, 87:013015.
212. Ardekani A.M., Gore E. Emergence of a limit cycle for swimming microorganisms in a vortical flow of a viscoelastic fluid. Phys. Rev. E 2012, 85:056309.
213. Uspal W.E., Eral H.B., Doyle P.S. Engineering particle trajectories in microfluidic flows using particle shape. Nat. Commun. 2013, 4:2666.
214. Gao T., Hu H.H., Ponte Castaneda P. Shape dynamics and rheology of soft elastic particles in a shear flow. Phys. Rev. Lett. 2012, 108:058302.
215. Zhu L., Lauga E., Brandt L. Low-Reynolds-number swimming in a capillary tube. J. Fluid Mech. 2013, 726:285-311.