Abstract
Particles suspended in diluted viscoelastic fluids migrate in the transverse direction of the fluid flow towards equilibrium locations determined by spatial normal stress distributions across the cross-section of microfluidic channels. Polymer solutions with a negative first normal stress difference exhibit unexpected fluid behaviors such as material contraction after die extrusion and filament compression of semiflexible biopolymer gels in abrupt shear flow. The lateral particle migration was investigated in a hydroxypropyl cellulose (HPC) viscoelastic fluid with a negative first normal-stress difference. Unlike common viscoelastic fluids with positive normal stress differences, double-line particle focusing was identified in a microfluidic channel, which was caused by the negative first normal stress difference. More importantly, unique particle migration with different-sized particles in a microchannel was observed in which bigger particles were double-line focused along the channel walls while smaller particles were single-line focused at the center. A new particle focusing mechanism was suggested to demonstrate this unique double line focusing behavior of particles in the viscoelastic fluids.
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References
Acad JEANY (1984) Optical properties of hydroxypropyl cellulose. Macromolecules 17:1512–1520. https://doi.org/10.1021/ma00138a016
Ahn SW, Lee SS, Lee SJ, Kim JM (2015) Microfluidic particle separator utilizing sheathless elasto-inertial focusing. Chem Eng Sci 126:237–243. https://doi.org/10.1016/j.ces.2014.12.019
Barnes HA (1989) An introduction to rheology. Elsevier, Amsterdam
Cartas-Ayala MA, Raafat M, Karnik R (2013) Self-sorting of deformable particles in an asynchronous logic microfluidic circuit. Small 9:375–381. https://doi.org/10.1002/smll.201201422
Cha S, Shin T, Lee SS et al (2012) Cell stretching measurement utilizing viscoelastic particle focusing. Anal Chem 84:10471–10477. https://doi.org/10.1021/ac302763n
D’Avino G, Romeo G, Villone MM et al (2012) Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. Lab Chip 12:1638. https://doi.org/10.1039/c2lc21154h
Del Giudice F, Romeo G, D’Avino G et al (2013) Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel. Lab Chip 13:4263–4271. https://doi.org/10.1039/c3lc50679g
Del Giudice F, D’Avino G, Greco F et al (2015a) Effect of fluid rheology on particle migration in a square-shaped microchannel. Microfluid Nanofluidics 19:95–104. https://doi.org/10.1007/s10404-015-1552-x
Del Giudice F, D’Avino G, Greco F et al (2015b) Rheometry-on-a-chip: measuring the relaxation time of a viscoelastic liquid through particle migration in microchannel flows. Lab Chip 15:783–792. https://doi.org/10.1039/C4LC01157K
Eom Y, Jung D, Hwang SS, Kim B (2016) Characteristic dynamic rheological responses of nematic poly(p-phenylene terephthalamide) and cholesteric hydroxypropyl cellulose phases. Polym J 48:869–874. https://doi.org/10.1038/pj.2016.46
Fried F, Leal CR, Godinho MH, Martins AF (1994) The first normal stress difference and viscosity in shear of liquid crystalline solutions of hydroxypropylcellulose: new experimental data and theory. Polym Adv Technol 5:596–599. https://doi.org/10.1002/pat.1994.220050922
Guan G, Wu L, Bhagat AA et al (2013) Spiral microchannel with rectangular and trapezoidal cross-sections for size based particle separation. Sci Rep 3:1475. https://doi.org/10.1038/srep01475
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. https://doi.org/10.1017/S002211207600089X
Hoekstra H, Vermant J, Mewis J, Narayanan T (2002) Rheology and structure of suspensions in liquid crystalline hydroxypropylcellulose solutions. Langmuir 18:5695–5703. https://doi.org/10.1021/la020097y
Hongladarom K, Secakusuma V, Burghardt WR (1994) Relation between molecular orientation and rheology in lyotropic hydroxypropylcellulose solutions. J Rheol (N Y N Y) 38:1505–1523. https://doi.org/10.1122/1.550556
Howard MP, Panagiotopoulos AZ, Nikoubashman A (2015) Inertial and viscoelastic forces on rigid colloids in microfluidic channels. J Chem Phys. https://doi.org/10.1063/1.4922323
Huang PY, Feng J, Hu HH, Joseph DD (1997) Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. J Fluid Mech 343:S0022112097005764. https://doi.org/10.1017/S0022112097005764
Janmey PA, McCormick ME, Rammensee S et al (2007) Negative normal stress in semiflexible biopolymer gels. Nat Mater 6:48–51. https://doi.org/10.1038/nmat1810
Kang AR, Ahn SW, Lee SJ et al (2011) Medium viscoelastic effect on particle segregation in concentrated suspensions under rectangular microchannel flows. Korea Aust Rheol J 23:247–254. https://doi.org/10.1007/s13367-011-0030-6
Kang K, Lee SS, Hyun K et al (2013) DNA-based highly tunable particle focuser. Nat Commun 4:2567. https://doi.org/10.1038/ncomms3567
Kharchenko SB, Douglas JF, Obrzut J et al (2004) Flow-induced properties of nanotube-filled polymer materials. Nat Mater 3:564–568. https://doi.org/10.1038/nmat1183
Kim B, Kim JM (2016) Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel. Biomicrofluidics. https://doi.org/10.1063/1.4944628
Kim J, Kim JY, Kim Y et al (2017) Shape measurement of ellipsoidal particles in a cross-slot microchannel utilizing viscoelastic particle focusing. Anal Chem 89:8662–8666. https://doi.org/10.1021/acs.analchem.7b02559
Kiss G, Porter RS (1980) Rheology of concentrated solutions of helical polypeptides. J Polym Sci Polym Phys Ed 18:361–388. https://doi.org/10.1002/pol.1980.180180217
Korneeva EV, Shtennikova IN, Shibaev VP et al (1990) Conformational properties of hydroxypropylcellulose !. Hydrodynamic properties and equilibrium rigidity of its macromolecules. Eur Polym J 26:781–785
Kulichikhin VG, Makarova VV, Tolstykh MY et al (2011) Structural evolution of liquid-crystalline solutions of hydroxypropyl cellulose and hydroxypropyl cellulose-based nanocomposites during flow. Polym Sci Ser A 53:748–764. https://doi.org/10.1134/S0965545x11090070 doi
Larson RG (1990) Arrested Tumbling in shearing flows of liquid crystal polymers. Macromolecules. https://doi.org/10.1021/ma00219a020
Lee DJ, Brenner H, Youn JR, Song YS (2013) Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci Rep 3:3258. https://doi.org/10.1038/srep03258
Leshansky AM, Bransky A, Korin N, Dinnar U (2007) Tunable nonlinear viscoelastic “focusing” in a microfluidic device. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.98.234501
Li G, McKinley GH, Ardekani AM (2015) Dynamics of particle migration in channel flow of viscoelastic fluids. J Fluid Mech 785:486–505. https://doi.org/10.1017/jfm.2015.619
Li D, Lu X, Xuan X (2016) Viscoelastic separation of particles by size in straight rectangular microchannels: a parametric study for a refined understanding. Anal Chem. https://doi.org/10.1021/acs.analchem.6b03501
Lim EJ, Ober TJ, Edd JF et al (2014a) Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat Commun 5:4120. https://doi.org/10.1038/ncomms5120
Lim H, Nam J, Shin S (2014b) Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow. Microfluid Nanofluidics 17:683–692. https://doi.org/10.1007/s10404-014-1353-7
Lin-Gibson S, Pathak JA, Grulke EA et al (2004) Elastic Flow Instability in nanotube suspensions. Phys Rev Lett 92:048302. https://doi.org/10.1103/PhysRevLett.92.048302
Liu C, Xue C, Hu G (2015) Sheathless separation of particles and cells by viscoelastic effects in straight rectangular microchannels. Proc Eng 126:721–724. https://doi.org/10.1016/j.proeng.2015.11.278
Lu X, Xuan X (2015) Elasto-inertial pinched flow fractionation for continuous shape-based particle separation. Anal Chem 87:11523–11530. https://doi.org/10.1021/acs.analchem.5b03321
Lu X, Zhu L, Hua R, Xuan X (2015) Continuous sheath-free separation of particles by shape in viscoelastic fluids. Appl Phys Lett. https://doi.org/10.1063/1.4939267
Martins AF, Leal CR, Godinho MH, Fried F (2001) The influence of polymer molecular weight on the first normal-stress difference and shear-viscosity of LC solutions of hydroxypropylcellulose. Mol Cryst Liq Cryst 362:305–312. https://doi.org/10.1080/10587250108025777 doi
Miller MJ, Christiansen EB (1972) The stress state of elastic fluids in viscometric flow. AIChE J 18:600–608. https://doi.org/10.1002/aic.690180321
Morrison F (2001) Understanding rheology. Oxford Univ Press, Oxford. https://doi.org/10.3933/ApplRheol-12-233
Nam J, Lim H, Kim D et al (2012) Continuous separation of microparticles in a microfluidic channel via the elasto-inertial effect of non-Newtonian fluid. Lab Chip. https://doi.org/10.1039/c2lc21304d
Nam J, Tan JKS, Khoo BL et al (2015) Hybrid capillary-inserted microfluidic device for sheathless particle focusing and separation in viscoelastic flow. Biomicrofluidics 9:064117. https://doi.org/10.1063/1.4938389
Pasquali M (2004) Swell properties and swift processing. Nat Mater 3:509–510. https://doi.org/10.1038/nmat1188
Phillies GDJ, O’Connell R, Whitford P, Streletzky KA (2003) Mode structure of diffusive transport in hydroxypropyl cellulose: Water. J Chem Phys 119:9903–9913. https://doi.org/10.1063/1.1615968
Procedures E (1990) Conformational properties of hydroxypropylcellulose–ii. flow birefringence and optical anisotropy of hydroxypropylcellulose macromolecules. Eur Polym J 26:787–790
Romeo G, D’Avino G, Greco F et al (2013) Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions. Lab Chip 13:2802. https://doi.org/10.1039/c3lc50257k
Shaw MT, MacKnight WJ (2005) Introduction to polymer viscoelasticity, 3rd edn. John Wiley & Sons, Hoboken, United States
Tian F, Zhang W, Cai L et al (2017) Microfluidic co-flow of Newtonian and viscoelastic fluids for high-resolution separation of microparticles. Lab Chip. https://doi.org/10.1039/C7LC00671C
Villone MM, D’Avino G, Hulsen MA et al (2011) Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow. J Nonnewton Fluid Mech 166:1396–1405. https://doi.org/10.1016/j.jnnfm.2011.09.003
Villone MM, D’Avino G, Hulsen MA et al (2013) Particle motion in square channel flow of a viscoelastic liquid: migration vs. secondary flows. J Nonnewton Fluid Mech 195:1–8. https://doi.org/10.1016/j.jnnfm.2012.12.006
Yang S, Kim JY, Lee SJ et al (2011) Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. Lab Chip 11:266–273. https://doi.org/10.1039/c0lc00102c
Yang SH, Lee DJ, Youn JR, Song YS (2017) Multiple-line particle focusing under viscoelastic flow in a microfluidic device. Anal Chem 89:3639–3647. https://doi.org/10.1021/acs.analchem.6b05052
Young Kim J, Won Ahn S, Sik Lee S, Min Kim J (2012) Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow. Lab Chip 12:2807. https://doi.org/10.1039/c2lc40147a
Yuan D, Zhang J, Yan S et al (2015) Dean-flow-coupled elasto-inertial three-dimensional particle focusing under viscoelastic flow in a straight channel with asymmetrical expansion–contraction cavity arrays. Biomicrofluidics. https://doi.org/10.1063/1.4927494
Acknowledgements
The authors acknowledge the support from the soft chemical materials research center for organic–inorganic multi-dimensional structure, which is funded by Gyeonggi Regional Research center Program (GRRC Dankook 2016-B03). Also, it was supported by the Industrial Strategic Technology Development Program, which is funded by the Ministry of Trade, Industry and Energy (MI, Korea) [10052641]. The authors are grateful for these supports.
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This article is part of the topical collection “Particle motion in non-Newtonian microfluidics” guest edited by Xiangchun Xuan and Gaetano D’Avino.
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Yang, S.H., Lee, D.J., Youn, J.R. et al. Double-line particle focusing induced by negative normal stress difference in a microfluidic channel. Microfluid Nanofluid 23, 21 (2019). https://doi.org/10.1007/s10404-018-2179-5
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DOI: https://doi.org/10.1007/s10404-018-2179-5