Viscoelastic fluid naturally has both viscous and elastic properties. Therefore, there are two sources of nonlinear effects, namely inertial and elastic nonlinearities. The existence of elastic nonlinearity brings about various interesting flow phenomena in viscoelastic fluid flow, especially in microfluidics where the inertial nonlinearity can be negligible while the elastic nonlinearity can dominate the flow. Specifically, purely elasticity-induced instability and turbulence can occur in microchannels when the elastic nonlinearity is strong enough. Recently, those intriguing properties of viscoelastic fluid flow have motivated lots of researches on taking viscoelastic fluid as working fluid in different types of microfluidic devices, such as micro-mixers, micro heat exchangers, logic microfluidic circuits and particle manipulation. This paper aims to provide a state-of-the-art review of the nonlinear effect of viscoelastic fluids and its applications in the aforementioned microfluidic fields, which may provide a useful guidance for the researchers who are interested in this area.
WeissenbergK. A continuum theory of rheological phenomena. Nature1947; 159: 310–311.
8.
DavidFJ. Open channel siphon with viscoelastic fluids. Nature1966; 212: 754–756.
9.
MerringtonAC. Flow of visco-elastic materials in capillaries. Nature1943; 152: 663.
10.
KayeA. A bouncing liquid stream. Nature1963; 197: 1001–1002.
11.
Toms BA. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In: The 1st international congress on rheology, Amsterdam, The Netherlands, September 1948, pp.135–141.
12.
BirdRBCurtissCFArmstrongRC, et al.Dynamics of polymer liquids: vol. 2: Kinetic theory, New York: John Wiley and Sons Inc, 1987.
13.
LiXLiFCaiW, et al.Very-low-Re chaotic motions of viscoelastic fluid and its unique applications in microfluidic devices: a review. Exp Therm Fluid Sci2012; 39: 16.
14.
ArndtKFLechnerMD. Polymer solids and polymer melts–mechanical and thermomechanical properties of polymers, Heidelberg: Springer, 2014.
15.
Arndt KF, Jipa S, Krahl F, et al. Polymer solids and polymer melts -- definitions and physical properties I. In: Arndt KF and Lechner MD (eds) Numerical data and functional relationships in science and technology. Group VIII, Advanced materials and technologies. Volume 6, Polymers. Heidelberg: Springer, 2013.
16.
Dealy JM and Larson RG. Structure and rheology of molten polymers—from structure to flow behavior and back again. 2nd ed. Munich: Hanser, 2018.
17.
EveraersRSukumaranSKGrestGS, et al.Rheology and microscopic topology of entangled polymeric liquids. Science2004; 303: 823–826.
18.
JönssonBLindmanBHolmbergK, et al.Surfactants and polymers in aqueous solution, 2nd ed. Hoboken, NJ: John Wiley & Sons, Ltd, 2002.
19.
LiFCYuBWeiJJ, et al.Turbulent drag reduction by surfactant additives, Singapore: John Wiley & Sons Singapore Pte. Ltd, 2012.
20.
EzrahiSTuvalEAserinA. Properties, main applications and perspectives of worm micelles. Adv Colloid Interface Sci2006; 128: 77–102.
21.
OliveiraMSNAlvesMAPinhoFT. Microfluidic flows of viscoelastic fluids. transport and mixing in laminar flows, Hoboken, NJ: John Wiley & Sons, Ltd, 2010.
22.
GroismanASteinbergV. Elastic turbulence in a polymer solution flow. Nature2000; 405: 53–55.
23.
CaiWHLiYYZhangHN, et al.An efficient micro-mixer by elastic instabilities of viscoelastic fluids: Mixing performance and mechanistic analysis. Int J Heat Fluid Flow2018; 74: 130–143.
24.
LiDYLiXBZhangHN, et al.Efficient heat transfer enhancement by elastic turbulence with polymer solution in a curved microchannel. Microfluid Nanofluid2017; 21: 13.
25.
GroismanAEnzelbergerMQuakeSR. Microfluidic memory and control devices. Science2003; 300: 4.
26.
BayarehMAshaniMNUsefianA. Active and passive micromixers: a comprehensive review. Chem Eng Process2020; 147: 19.
27.
LiSNZhangHNChengJP, et al.A state-of-the-art overview on the developing trend of heat transfer enhancement by single-phase flow at micro scale. Int J Heat Mass Transf2019; 143: 34.
28.
CaiGZXueLZhangHL, et al.A review on micromixers. Micromachines2017; 8: 27.
29.
LuXYLiuCHuGQ, et al.Particle manipulations in non-Newtonian microfluidics: a review. J Colloid Interface Sci2017; 500: 182–201.
30.
VaithianathanTCollinsLR. Numerical approach to simulating turbulent flow of a viscoelastic polymer solution. J Comput Phys (USA)2003; 187: 1–21.
31.
VaithianathanTRobertABrasseurJG, et al.An improved algorithm for simulating three-dimensional, viscoelastic turbulence. J Non-Newton Fluid Mech2006; 140: 3–22.
32.
BirdRBWiestJM. Constitutive equations for polymeric liquid. Ann Rev Fluid Mech1995; 27: 169–193.
33.
Bird RB, Armstrong RC and Hassager O. Dynamics of polymeric liquids: vol. 1, Fluid mechanics. 2nd ed. New York: Wiley, 1987.
34.
LarsonRG. The structure and rheology of complex fluids, Oxford: Oxford University Press, 1998.
35.
Oliveira MSN, Alves MA and Pinho FT. Microfluidic flows of viscoelastic fluids. In: Grigoriev R (ed) Transport and mixing in laminar flows: from microfluidics to oceanic currents. Weinheim: Wiley-VCH, 2012.
36.
ZhangHNLiDYLiXB, et al.Numerical simulation of heat transfer process of viscoelastic fluid flow at high Weissenberg number by log-conformation reformulation. J Fluids Eng-Transact ASME2017, pp. 139: 091402.
37.
ZhangHNLiFCCaoY, et al.Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow. Chin Phys B2013; 22: 8.
38.
RemsLKawaleDLeeLJ, et al.Flow of DNA in micro/nanofluidics: from fundamentals to applications. Biomicrofluidics2016; 10: 27.
39.
DelaplaceGThakurRKBouvierL, et al.Dimensional analysis for planetary mixer: mixing time and Reynolds numbers. Chem Eng Sci2007; 62: 1442–1447.
40.
DealyJM. Weissenberg and Deborah numbers – their definition and use. Rheol Bull2010; 79: 14–18.
41.
PooleRJ. The Deborah and Weissenberg numbers. Br Soc Rheol Rheol Bull2012; 53: 32–39.
42.
Raiyleigh L. On the stability, or instability, of certain fluid motions. Proceedings London Mathematical Society 1880; 11: 57–70.
43.
LarsonRGShaqfehESGMullerSJ. A purely elastic instability in Taylor-Couette flow. J Fluid Mech1990; 218: 573–600.
McKinleyGHOztekinAByarsJA, et al.Self-similar spiral instabilities in elastic flows between a cone and a plate. J Fluid Mech1995; 285: 123–164.
46.
ByarsJAOztekinABrownRA, et al.Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks. J Fluid Mech1994; 271: 173–218.
47.
LarsonRG. Instabilities in viscoelastic flows. Rheologica Acta1992; 31: 213–263.
48.
ShaqfehESG. Purely elastic instabilities in viscometric flows. Ann Rev1996, pp. 28: 129–185. .
49.
McKinleyGHPakdelPOztekinA. Rheological and geometric scaling of purely elastic flow instabilities. J Non-Newton Fluid Mech1996; 67: 19–47.
BonnDIngremeauFAmaroucheneY, et al.Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions. Phys Rev E2011; 84: 5.
52.
PanLMorozovAWagnerC, et al.Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys Rev Lett2013; 110: 5.
53.
HawardSJ. Microfluidic extensional rheometry using stagnation point flow. Biomicrofluidics2016; 10: 26.
54.
ArratiaPEThomasCCDiorioJ, et al.Elastic instabilities of polymer solutions in cross-channel flow. Phys Rev Lett2006; 96: 4.
55.
Poole RJ, Alves MM, Afonso AM, et al. Purely elastic instabilities in a microfluidic cross-slot geometry. In: The Society of Rheology 79th Annual Meeting, Salt Lake City, USA, 7--11 October 2007.
SousaPCPinhoFTOliveiraMSN, et al.Purely elastic flow instabilities in microscale cross-slot devices. Soft Matter2015; 11: 8856–8862.
58.
GroismanASteinbergV. Elastic turbulence in curvilinear flows of polymer solutions. New J Phys2004; 6: 48.
59.
BertiSBistagninoABoffettaG, et al.Two-dimensional elastic turbulence. Phys Rev E2008; 77: 4.
60.
BurgheleaTSegreESteinbergV. Elastic turbulence in von Karman swirling flow between two disks. Phys Fluids2007; 19: 26.
61.
BurgheleaTSegreESteinbergV. Role of elastic stress in statistical and scaling properties of elastic turbulence. Phys Rev Lett2006; 96: 4.
62.
CaiWHLiXBZhangHN, et al.Viscoelastic fluid dynamics (in Chinese), Beijing: The Science Publishing Company, 2016.
63.
LeeCYChangCLWangYN, et al.Microfluidic mixing: a review. Int J Mol Sci2011; 12: 3263–3287.
64.
NguyenNTWuZG. Micromixers – a review. J Micromech Microeng2005; 15: R1–R16.
65.
NouriDZabihi-HesariAPassandideh-FardM. Rapid mixing in micromixers using magnetic field. Sens Actuator A-Phys2017; 255: 79–86.
66.
OrbaySOzcelikALataJ, et al.Mixing high-viscosity fluids via acoustically driven bubbles. J Micromech Microeng2017; 27: 6.
67.
WuYPRenYKTaoY, et al.A novel micromixer based on the alternating current-flow field effect transistor. Lab Chip2017; 17: 186–197.
68.
SuhYKKangS. A review on mixing in microfluidics. Micromachines2010; 1: 82–111.
69.
MansurEAYeMXWangYD, et al.A state-of-the-art review of mixing in microfluidic mixers. Chin J Chem Eng2008; 16: 503–516.
70.
LeeCYWangWTLiuCC, et al.Passive mixers in microfluidic systems: a review. Chem Eng J2016; 288: 146–160.
71.
KleinstreuerC. Microfluidics and nanofluidics: theory and selected applications, Hoboken, NJ: John Wiley & Sons, Inc., 2013.
72.
GroismanASteinbergV. Efficient mixing at low Reynolds numbers using polymer additives. Nature2001; 410: 905–908.
73.
Tatsumi K, Takeda Y, Suga K, et al. Turbulence characteristics and mixing performances of viscoelastic fluid flow in a serpentine microchannel. In: Journal of Physics: Conference Series 2011 (Vol. 318, No. 9, p. 092020). IOP Publishing Ltd.
74.
GanHYLamYCNguyenNT, et al.Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number. Microfluid Nanofluid2007; 3: 101–108.
75.
LiFCKinoshitaHLiXB, et al.Creation of very-low-Reynolds-number chaotic fluid motions in microchannels using viscoelastic surfactant solution. Exp Therm Fluid Sci2010; 34: 8.
76.
LiXBOishiMOshimaM, et al.Measuring elasticity-induced unstable flow structures in a curved microchannel using confocal micro particle image velocimetry. Exp Therm Fluid Sci2016; 75: 118–128.
77.
XuJLGanYHZhangDC, et al.Microscale heat transfer enhancement using thermal boundary layer redeveloping concept. Int J Heat Mass Transf2005; 48: 1662–1674.
78.
HajmohammadiMRAlipourPParsaH. Microfluidic effects on the heat transfer enhancement and optimal design of microchannels heat sinks. Int J Heat Mass Transf2018; 126: 808–815.
79.
Steinke ME and Kandlikar SG. Single-phase liquid heat transfer in plain and enhanced microchannels. New York, NY: American Society of Mechanical Engineers, 2006, pp.943–951.
80.
Li DY. Study on elastic turbulence and heat transfer enhancement of viscoelastic fluid flow in curvy microchannel. PhD Thesis, Harbin Institute of Technology, China, 2017.
81.
YiPAwangRARoweWST, et al.PDMS nanocomposites for heat transfer enhancement in microfluidic platforms. Lab Chip2014; 14: 3419–3426.
82.
LiXBLiFCCaiWH, et al.Very-low-Re chaotic motions of viscoelastic fluid and its unique applications in microfluidic devices: a review. Exp Therm Fluid Sci2012; 39: 1–16.
83.
AbedWMWhalleyRDDennisDJC, et al.Experimental investigation of the impact of elastic turbulence on heat transfer in a serpentine channel. J Non-Newton Fluid Mech2016; 231: 68–78.
84.
LiDYLiXBZhangHN, et al.Measuring heat transfer performance of viscoelastic fluid flow in curved microchannel using Ti-Pt film temperature sensor. Exp Therm Fluid Sci2016; 77: 226–233.
LiDYZhangHNChengJP, et al.Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel. Microfluid Nanofluid2017; 21: 16.
87.
TaoWQGuo ZY and WangBX. Field synergy principle for enhancing convective heat transfer-its extension and numerical verifications. Int J Heat Mass Transf2002; 45: 3849–3856.
88.
Nolan KP, Agarwal A, Lei SH, et al. Mixing enhancement due to viscoelastic instability in serpentine microchannels at very large weissenberg numbers. In: 2016 15th IEEE intersociety conference on thermal and thermomechanical phenomena in electronic systems. New York: IEEE, 2016, pp.301–306.
89.
ThorsenTRobertsRWArnoldFH, et al.Dynamic pattern formation in a vesicle-generating microfluidic device. Phys Rev Lett2001; 86: 4163–4166.
90.
BeebeDJMooreJSBauerJM, et al.Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature2000; 404: 588–590.
91.
GroismanAQuakeSR. A microfluidic rectifier: anisotropic flow resistance at low Reynolds numbers. Phys Rev Lett2004; 92: 4.
92.
NguyenNTLamYCHoSS, et al.Improvement of rectification effects in diffuser/nozzle structures with viscoelastic fluids. Biomicrofluidics2008; 2: 14.
93.
SousaPCPinhoFTOliveiraMSN, et al.Efficient microfluidic rectifiers for viscoelastic fluid flow. J Non-Newton Fluid Mech2010; 165: 652–671.
94.
GroismanAQuakeSR. A microfluidic rectifier: anisotropic flow resistance at low Reynolds numbers. Phys Rev Lett2004; 92: 4.
95.
SousaPCPinhoFTOliveiraMSN, et al.High performance microfluidic rectifiers for viscoelastic fluid flow. RSC Adv2012; 2: 920–929.
96.
JensenKESzaboPOkkelsF, et al.Experimental characterisation of a novel viscoelastic rectifier design. Biomicrofluidics2012; 6: 8.
97.
SoleRMosesMForrestS. Liquid brains, solid brains. Philos Trans R Soc B-Biol Sci2019; 374: 6.
98.
XuanXCZhuJJChurchC. Particle focusing in microfluidic devices. Microfluid Nanofluid2010; 9: 1–16.
PrattEDHuangCHawkinsBG, et al.Rare cell capture in microfluidic devices. Chem Eng Sci2011; 66: 1508–1522.
101.
NilssonJEvanderMHammarstromB, et al.Review of cell and particle trapping in microfluidic systems. Anal Chim Acta2009; 649: 141–157.
102.
KarimiAYazdiSArdekaniAM. Hydrodynamic mechanisms of cell and particle trapping in microfluidics. Biomicrofluidics2013; 7: 23.
103.
ZhouYNMaZCTayebiM, et al.Submicron particle focusing and exosome sorting by wavy microchannel structures within viscoelastic fluids. Anal Chem2019; 91: 4577–4584.
104.
RaffieeAHArdekaniAMDabiriS. Numerical investigation of elasto-inertial particle focusing patterns in viscoelastic microfluidic devices. J Non-Newton Fluid Mech2019; 272: 10.
105.
SongHYLeeSHSalehiyanR, et al.Relationship between particle focusing and dimensionless numbers in elasto-inertial focusing. Rheologica Acta2016; 55: 889–900.
106.
NamJNamgungBLimCT, et al.Microfluidic device for sheathless particle focusing and separation using a viscoelastic fluid. J Chromatogr A2015; 1406: 244–250.
107.
LiYKZhangHNLiYY, et al.Dynamic control of particle separation in deterministic lateral displacement separator with viscoelastic fluids. Sci Rep2018; 8: 9.
108.
LiuCXueCDChenXD, et al.Size-based separation of particles and cells utilizing viscoelastic effects in straight microchannels. Anal Chem2015; 87: 6041–6048.
109.
HuhDGuWKamotaniY, et al.Microfluidics for flow cytometric analysis of cells and particles. Physiol Meas2005; 26: R73–R98.
110.
GodinJChenCHChoSH, et al.Microfluidics and photonics for Bio-System-on-a-Chip: a review of advancements in technology towards a microfluidic flow cytometry chip. J Biophotonics2008; 1: 355–376.
111.
KulrattanarakTvan der SmanRGMSchroenC, et al.Classification and evaluation of microfluidic devices for continuous suspension fractionation. Adv Colloid Interface Sci2008; 142: 53–66.
SeoKWByeonHJHuhHK, et al.Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids. RSC Adv2014; 4: 3512–3520.
114.
DannhauserDRossiDCausaF, et al.Optical signature of erythrocytes by light scattering in microfluidic flows. Lab Chip2015; 15: 3278–3285.
115.
D'AvinoGRomeoGVilloneMM, et al.Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. Lab Chip2012; 12: 1638–1645.
LiDLuXYXuanXC. Viscoelastic separation of particles by size in straight rectangular microchannels: a parametric study for a refined understanding. Anal Chem2016; 88: 12303–12309.
118.
YangSKimJYLeeSJ, et al.Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. Lab Chip2011; 11: 266–273.
119.
Del GiudiceFRomeoGD'AvinoG, et al.Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel. Lab Chip2013; 13: 4263–4271.
120.
Del GiudiceFD'AvinoGGrecoF, et al.Effect of fluid rheology on particle migration in a square-shaped microchannel. Microfluid Nanofluid2015; 19: 95–104.
121.
KimBKimJM. Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel. Biomicrofluidics2016; 10: 11.
122.
LeeDJBrennerHYounJR, et al.Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci Rep2013; 3: 8.
123.
XiangNZhangXJDaiQ, et al.Fundamentals of elasto-inertial particle focusing in curved microfluidic channels. Lab Chip2016; 16: 2626–2635.
124.
YuanDZhangJYanS, et al.Dean-flow-coupled elasto-inertial three-dimensional particle focusing under viscoelastic flow in a straight channel with asymmetrical expansion-contraction cavity arrays. Biomicrofluidics2015; 9: 13.
125.
YuanDZhaoQYanS, et al.Recent progress of particle migration in viscoelastic fluids. Lab Chip2018; 18: 551–567.
126.
VilloneMMD'AvinoGHulsenMA, et al.Particle motion in square channel flow of a viscoelastic liquid: Migration vs. secondary flows. J Non-Newton Fluid Mech2013; 195: 1–8.
127.
KimJYAhnSWLeeSS, et al.Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow. Lab Chip2012; 12: 2807–2814.
128.
SajeeshPSenAK. Particle separation and sorting in microfluidic devices: a review. Microfluid Nanofluid2014; 17: 1–52.
129.
ShieldsCWReyesCDLopezGP. Microfluidic cell sorting: a review of the advances in the separation of cells from debulking to rare cell isolation. Lab Chip2015; 15: 1230–1249.
130.
LeeGHKimSHAhnK, et al.Separation and sorting of cells in microsystems using physical principles. J Micromech Microeng2016; 26: 15.
131.
Al-FaqheriWThioTHGQasaimehMA, et al.Particle/cell separation on microfluidic platforms based on centrifugation effect: a review. Microfluid Nanofluid2017; 21: 23.
132.
YanSZhangJYuanD, et al.Hybrid microfluidics combined with active and passive approaches for continuous cell separation. Electrophoresis2017; 38: 238–249.
