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Particle squeezing in narrow confinements

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Abstract

Many lab-on-a-chip applications require processing of droplets, cells, and particles using narrow confinements. The physics governing the process of a particle squeezing through narrow confinement is complex. Various models and applications have been developed in this area in recent years. In the present paper, we review the physics, modeling approaches, and designs of narrow confinements for the control of deformable droplets, cells, and particles. This review highlights the interdisciplinary nature of the problem, since the experimental, analytical, and numerical methods used in studies of particle squeezing through narrow confinements come from various fields of science and technology.

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References

  • Abkarian M, Faivre M, Horton R, Smistrup K, Best-Popescu CA, Stone HA (2008) Cellular-scale hydrodynamics. Biomed Mater 3:034011

    Google Scholar 

  • Aceto N et al (2014) Circulating tumor cell clusters are oligoclonal precursors of breast cancer metastasis. Cell 158:1110–1122

    Google Scholar 

  • Aghaamoo M, Zhang Z, Chen X, Xu J (2015) Deformability-based circulating tumor cell separation with conical-shaped microfilters: concept, optimization, and design criteria. Biomicrofluidics 9:034106

    Google Scholar 

  • Ahmed R, Jones T (2007) Optimized liquid DEP droplet dispensing. J Micromech Microeng 17:1052

    Google Scholar 

  • Ahmmed SM, Bithi SS, Pore AA, Mubtasim N, Schuster C, Gollahon LS, Vanapalli SA (2018a) Multi-sample deformability cytometry of cancer cells. APL Bioeng 2:032002

    Google Scholar 

  • Ahmmed SM, Suteria NS, Garbin V, Vanapalli SA (2018b) Hydrodynamic mobility of confined polymeric particles, vesicles, and cancer cells in a square microchannel. Biomicrofluidics 12:014114

    Google Scholar 

  • Alix-Panabières C, Pantel K (2014) Technologies for detection of circulating tumor cells: facts and vision. Lab Chip 14:57–62

    Google Scholar 

  • Anselmo A, Mitragotri S (2016) Designing drug-delivery nanoparticles. Chem Eng Prog 112: 52–57

    Google Scholar 

  • Aoki T, Ohashi T, Matsumoto T, Sato M (1997) The pipette aspiration applied to the local stiffness measurement of soft tissues. Ann Biomed Eng 25:581–587

    Google Scholar 

  • Arata JP, Alexeev A (2009) Designing microfluidic channel that separates elastic particles upon stiffness. Soft Matter 5:2721–2724

    Google Scholar 

  • Argatov I, Mishuris G (2016) Pipette aspiration testing of soft tissues: the elastic half-space model revisited. In: Proc. R. Soc. A, vol 2193. The Royal Society, p 20160559

  • Au SH et al (2016) Clusters of circulating tumor cells traverse capillary-sized vessels. Proc Natl Acad Sci 113:4947–4952

    Google Scholar 

  • Ayan B et al (2017) A new aspiration-assisted bioprinting method for tissue fabrication. Paper presented at the Symposium on Biomaterials Science, New Jersey, USA

  • Bächer C, Schrack L, Gekle S (2017) Clustering of microscopic particles in constricted blood flow. Phys Rev Fluids 2:013102

    Google Scholar 

  • Barakat JM, Shaqfeh ESG (2018) The steady motion of a closely fitting vesicle in a tube. J Fluid Mech 835:721–761

    MathSciNet  Google Scholar 

  • Barthès-Biesel D (2012) Microhydrodynamics and complex fluids. CRC Press, Boco Raton

    MATH  Google Scholar 

  • Beckman S, Barbano D (2013) Effect of microfiltration concentration factor on serum protein removal from skim milk using spiral-wound polymeric membranes. J Dairy Sci 96:6199–6212

    Google Scholar 

  • Benet E, Vernerey F (2016) Mechanics and stability of vesicles and droplets in confined spaces. Phys Rev E 94:062613

    Google Scholar 

  • Benet E, Badran A, Pellegrino J, Vernerey F (2017) The porous media’s effect on the permeation of elastic (soft) particles. J Membr Sci 535:10–19

    Google Scholar 

  • Beresnev IA, Deng W (2010) Viscosity effects in vibratory mobilization of residual oil. Geophysics 75:N79–N85

    Google Scholar 

  • Beresnev IA, Vigil RD, Li W, Pennington WD, Turpening RM, Iassonov PP, Ewing RP (2005) Elastic waves push organic fluids from reservoir rock. Geophys Res Lett 32

  • Beresnev IA, Li W, Vigil RD (2009) Condition for break-up of non-wetting fluids in sinusoidally constricted capillary channels. Transp Porous Media 80:581–604

    Google Scholar 

  • Beresnev I, Gaul W, Vigil RD (2011) Direct pore-level observation of permeability increase in two-phase flow by shaking. Geophys Res Lett 38:L20302

    Google Scholar 

  • Berthier J, Brakke K (2012) The physics of microdroplets. Wiley, Hoboken

    MATH  Google Scholar 

  • Bindiganavale GS, Moon H, You SM, Amaya M (2012) Digital microfluidic device for hotspot cooling in ICS using electrowetting on dielectric. Paper presented at the ASME 2012 third international conference on micro/nanoscale heat and mass transfer

  • Bindiganavale G, You SM, Moon H (2014) Study of hotspot cooling using electrowetting on dielectric digital microfluidic system. Paper presented at the Micro Electro Mechanical Systems (MEMS), 2014 IEEE 27th International Conference on

  • Blakely AM, Manning KL, Tripathi A, Morgan JR (2015) Bio-pick, place, and perfuse: a new instrument for three-dimensional tissue engineering. Tissue Eng Part C Methods 21:737–746

    Google Scholar 

  • Blunt MJ (2001) Flow in porous media-pore-network models and multiphase flow. Curr Opin Colloid Interface Sci 6:197–207

    Google Scholar 

  • Boukellal H, Selimovic S, Jia Y, Cristobal G, Fraden S (2009) Simple, robust storage of drops and fluids in a microfluidic device. Lab Chip 9:331–338

    Google Scholar 

  • Bow H et al (2011) A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11:1065–1073

    Google Scholar 

  • Brakke KA (1992) The surface evolver. Exp Math 1:141–165

    MathSciNet  MATH  Google Scholar 

  • Brosseau Q, Vrignon J, Baret J-C (2014) Microfluidic dynamic interfacial tensiometry (µDIT). Soft Matter 10:3066–3076

    Google Scholar 

  • Brouzes E et al (2009) Droplet microfluidic technology for single-cell high-throughput screening. Proc Natl Acad Sci 106:14195–14200

    Google Scholar 

  • Byun S et al (2013) Characterizing deformability and surface friction of cancer cells. Proc Natl Acad Sci 110:7580–7585

    Google Scholar 

  • Casquero H, Bona-Casas C, Gomez H (2017) NURBS-based numerical proxies for red blood cells and circulating tumor cells in microscale blood flow. Comput Methods Appl Mech Eng 316:646–667

    MathSciNet  Google Scholar 

  • Chang C-L, Jalal SI, Huang W, Mahmood A, Matei DE, Savran CA (2014) High-throughput immunomagnetic cell detection using a microaperture chip system. IEEE Sens J 14:3008–3013

    Google Scholar 

  • Chen H, Zhang Z (2018) An inertia-deformability hybrid circulating tumor cell chip: design, clinical test, and numerical analysis. J Med Devices 12(4):041004

    Google Scholar 

  • Chen J et al (2011) Classification of cell types using a microfluidic device for mechanical and electrical measurement on single cells. Lab Chip 11:3174–3181

    Google Scholar 

  • Chen Y et al (2014) Rare cell isolation and analysis in microfluidics. Lab Chip 14:626–645

    Google Scholar 

  • Chen H, Cao B, Sun B, Cao Y, Yang K, Lin Y-S, Chen H (2017a) Highly-sensitive capture of circulating tumor cells using micro-ellipse filters. Sci Rep 7:610

    Google Scholar 

  • Chen L, Wang KX, Doyle PS (2017b) Effect of internal architecture on microgel deformation in microfluidic constrictions. Soft Matter 13:1920–1928

    Google Scholar 

  • Chiu J-J, Chien S (2011) Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives. Physiol Rev 91:327–387

    Google Scholar 

  • Choi D, Lee H, Im DJ, Kang IS, Lim G, Kim DS, Kang KH (2013) Spontaneous electrical charging of droplets by conventional pipetting. Scientific Reports 3:2037

    Google Scholar 

  • Christafakis AN, Tsangaris S (2008) Two-phase flows of droplets in contractions and double bends. Eng Appl Comput Fluid Mech 2:299–308

    Google Scholar 

  • Chrysikopoulos CV, Vogler ET (2006) Acoustically enhanced ganglia dissolution and mobilization in a monolayer of glass beads. Transp Porous Media 64:103–121

    Google Scholar 

  • Chung C, Hulsen MA, Kim JM, Ahn KH, Lee SJ (2008) Numerical study on the effect of viscoelasticity on drop deformation in simple shear and 5: 1: 5 planar contraction/expansion microchannel. J Nonnewton Fluid Mech 155:80–93

    MATH  Google Scholar 

  • Chung C, Lee M, Char K, Ahn KH, Lee SJ (2010) Droplet dynamics passing through obstructions in confined microchannel flow. Microfluid Nanofluid 9:1151–1163

    Google Scholar 

  • Clark S, Haubert K, Beebe DJ, Ferguson E, Wheeler M (2005) Reduction of polyspermic penetration using biomimetic microfluidic technology during in vitro fertilization. Lab Chip 5:1229–1232

    Google Scholar 

  • Comanns P, Buchberger G, Buchsbaum A, Baumgartner R, Kogler A, Bauer S, Baumgartner W (2015) Directional, passive liquid transport: the Texas horned lizard as a model for a biomimetic ‘liquid diode’. J R Soc Interface 12:20150415

    Google Scholar 

  • Cottet G-H, Maitre E (2004) A level-set formulation of immersed boundary methods for fluid–structure interaction problems. CR Math 338:581–586

    MathSciNet  MATH  Google Scholar 

  • Danielczok JG, Terriac E, Hertz L, Petkova-Kirova P, Lautenschläger F, Laschke MW, Kaestner L (2017) Red blood cell passage of small capillaries is associated with transient Ca2+-mediated adaptations. Front Physiol 8: 979

    Google Scholar 

  • Darvishzadeh T, Priezjev NV (2012) Effects of crossflow velocity and transmembrane pressure on microfiltration of oil-in-water emulsions. J Membr Sci 423–424:468–476

    Google Scholar 

  • Datta P, Ayan B, Ozbolat IT (2017) Bioprinting for vascular and vascularized tissue biofabrication. Acta Biomater 51:1–20

    Google Scholar 

  • Dawson G, Häner E, Juel A (2015) Extreme deformation of capsules and bubbles flowing through a localised constriction. Proc IUTAM 16:22–32

    Google Scholar 

  • Dixon MW, Dearnley MK, Hanssen E, Gilberger T, Tilley L (2012) Shape-shifting gametocytes: how and why does P. falciparum go banana-shaped? Trends Parasitol 28:471–478

    Google Scholar 

  • Dressaire E, Sauret A (2017) Clogging of microfluidic systems. Soft Matter 13:37–48

    Google Scholar 

  • Drury J, Dembo M (1999) Hydrodynamics of micropipette aspiration. Biophys J 76:110–128

    Google Scholar 

  • Drury J, Dembo M (2001) Aspiration of human neutrophils: effects of shear thinning and cortical dissipation. Biophys J 81:3166–3177

    Google Scholar 

  • Evans EA, Waugh R, Melnik L (1976) Elastic area compressibility modulus of red cell membrane. Biophys J 16:585–595

    Google Scholar 

  • Fabbri F et al (2013) Detection and recovery of circulating colon cancer cells using a dielectrophoresis-based device: KRAS mutation status in pure CTCs. Cancer Lett 335:225–231

    Google Scholar 

  • Facchin S, Miled MA, Sawan M (2015) In-channel constriction valve for cerebrospinal fluid sampling. IEEE Trans Magn 51:1–4

    Google Scholar 

  • Fai T, Kusters R, Harting J, Rycroft C, Mahadevan L (2017) Active elastohydrodynamics of vesicles in narrow, blind constrictions. arXiv preprint arXiv:170501765

  • Fang Z, Zhang Z, Chen X, Xu J (2014) Inertial microfluidic spiral CTCs filter with micropillars. Paper presented at the 36th EMBS special topic conference on healthcare innovation & point-of-care technologies, Seattle, WA, USA

  • Fenton B, Wilson D, Cokelet G (1985) Analysis of the effects of measured white blood cell entrance times on hemodynamics in a computer model of a microvascular bed. Pflügers Arch 403:396–401

    Google Scholar 

  • Fischer-Friedrich E, Hyman AA, Jülicher F, Müller DJ, Helenius J (2014) Quantification of surface tension and internal pressure generated by single mitotic cells. Sci Rep 4:6213

    Google Scholar 

  • Frostad JM, Paul A, Leal LG (2016) Coalescence of droplets due to a constant force interaction in a quiescent viscous fluid. Phys Rev Fluids 1:033904

    Google Scholar 

  • Gai Y, Khor JW, Tang S (2016) Confinement and viscosity ratio effect on droplet break-up in a concentrated emulsion flowing through a narrow constriction. Lab Chip 16:3058–3064

    Google Scholar 

  • Gencoglu A, Olney D, LaLonde A, Koppula K, Lapizco-Encinas B (2013) Particle manipulation in insulator based dielectrophoretic devices. J Nanotechnol Eng Med 4:021002–021002

    Google Scholar 

  • Genovese D, Sprakel J (2011) Crystallization and intermittent dynamics in constricted microfluidic flows of dense suspensions. Soft Matter 7:3889–3896

    Google Scholar 

  • Gounley J, Draeger EW, Randles A (2017) Numerical simulation of a compound capsule in a constricted microchannel. Proc Comput Sci 108:175–184

    Google Scholar 

  • Guevorkian K, Colbert M-J, Durth M, Dufour S, Brochard-Wyart F (2010) Aspiration of biological viscoelastic drops. Phys Rev Lett 104:218101

    Google Scholar 

  • Guilak F, Tedrow JR, Burgkart R (2000) Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun 269:781–786

    Google Scholar 

  • Guo Q, Ma H (2011) Microfluidic device for measuring the stiffness of single cells. In: 15th International Conference on Miniaturized Systems for Chemistry and Life Sciences, 2–6 October 2011, Seattle, Washington, USA

  • Guo Q, McFaul SM, Ma H (2011) Deterministic microfluidic ratchet based on the deformation of individual cells. Phys Rev E 83:051910

    Google Scholar 

  • Guo Q, Park S, Ma H (2012) Microfluidic micropipette aspiration for measuring the deformability of single cells. Lab Chip 12:2687–2695

    Google Scholar 

  • Guo Q, Duffy SP, Matthews K, Deng X, Santoso AT, Islamzada E, Ma H (2016) Deformability based sorting of red blood cells improves diagnostic sensitivity for malaria caused by Plasmodium falciparum. Lab Chip 16:645–654

    Google Scholar 

  • Gupta A, Matharoo HS, Makkar D, Kumar R (2014) Droplet formation via squeezing mechanism in a microfluidic flow-focusing device. Comput Fluids 100:218–226

    Google Scholar 

  • Haider MA, Guilak F (2002) An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem. J Biomech Eng 124:586–595

    Google Scholar 

  • Han X et al (2015) CRISPR-Cas9 delivery to hard-to-transfect cells via membrane deformation. Sci Adv 1:e1500454

    Google Scholar 

  • Harvie D, Cooper-White J, Davidson M (2008) Deformation of a viscoelastic droplet passing through a microfluidic contraction. J Nonnewton Fluid Mech 155:67–79

    MATH  Google Scholar 

  • Hassanzadeh A, Pourmahmoud N, Dadvand A (2017) Numerical simulation of motion and deformation of healthy and sick red blood cell through a constricted vessel using hybrid lattice Boltzmann-immersed boundary method. Comput Methods Biomech Biomed Eng 20:1–13

    Google Scholar 

  • Hendrickson GR, Lyon LA (2010) Microgel translocation through pores under confinement. Angew Chem Int Ed 49:2193–2197

    Google Scholar 

  • Herant M, Heinrich V, Dembo M (2005) Mechanics of neutrophil phagocytosis: behavior of the cortical tension. J Cell Sci 118:1789–1797

    Google Scholar 

  • Hochmuth RM (2000) Micropipette aspiration of living cells. J Biomech 33:15–22

    Google Scholar 

  • Hoelzle D, Varghese B, Chan C, Rowat A (2014) A microfluidic technique to probe cell deformability. J Vis Exp 91:e51474

    Google Scholar 

  • Hong B, Zu Y (2013) Detecting circulating tumor cells: current challenges and new trends. Theranostics 3:377–396

    Google Scholar 

  • Hu X, Salsac A, Barthès-Biesel D (2012) Flow of a spherical capsule in a pore with circular or square cross-section. J Fluid Mech 705:176–194

    MathSciNet  MATH  Google Scholar 

  • Hu Q, Ren Y, Liu W, Chen X, Tao Y, Jiang H (2017) Fluid flow and mixing induced by AC continuous electrowetting of liquid metal droplet. Micromachines 8:119

    Google Scholar 

  • Hua H, Shin J, Kim J (2014) Dynamics of a compound droplet in shear flow. Int J Heat Fluid Flow 50:63–71

    Google Scholar 

  • Hui M-H, Blunt MJ (2000) Effects of wettability on three-phase flow in porous media. J Phys Chem B 104:3833–3845

    Google Scholar 

  • Ito H et al (2017) Mechanical diagnosis of human erythrocytes by ultra-high speed manipulation unraveled critical time window for global cytoskeletal remodeling. Scientific Reports 7:43134

    Google Scholar 

  • Izbassarov D, Muradoglu M (2016) A computational study of two-phase viscoelastic systems in a capillary tube with a sudden contraction/expansion. Phys Fluids 28:012110

    Google Scholar 

  • Kadivar E, Farrokhbin M (2017) A numerical procedure for scaling droplet deformation in a microfluidic expansion channel. Phys A 479:449–459

    MathSciNet  Google Scholar 

  • Kan H-C, Udaykumar H, Shyy W, Tran-Son-Tay R (1998) Hydrodynamics of a compound drop with application to leukocyte modeling. Phys Fluids 10:760–774

    Google Scholar 

  • Khalifat N, Beaune G, Nagarajan U, Winnik FM, Brochard-Wyart F (2016) Soft matter physics: Tools and mechanical models for living cellular aggregates. Jpn J Appl Phys 55:1102A1108

    Google Scholar 

  • Khambhampati TK (2013) A comparative study between Newtonian and non-Newtonian models in a stenosis of a carotid artery. Master Thesis. Texas A&M University, College Station

    Google Scholar 

  • Kim M-Y, Oskarsson T, Acharyya S, Nguyen DX, Zhang XH-F, Norton L, Massague J (2009) Tumor self-seeding by circulating cancer cells. Cell 139:1315–1326

    Google Scholar 

  • Kim Y, Kim K, Park Y (2012) Measurement techniques for red blood cell deformability: recent advances. INTECH Open Access Publisher Rijeka, Croatia

    Google Scholar 

  • Kim J, Lee H, Shin S (2015) Advances in the measurement of red blood cell deformability: a brief review. J Cell Biotechnol 1:63–79

    Google Scholar 

  • Kollmannsperger A et al (2016) Live-cell protein labelling with nanometre precision by cell squeezing. Nat Commun 7:10372

    Google Scholar 

  • Kong T, Wang L, Wyss HM, Shum HC (2014) Capillary micromechanics for core-shell particles. Soft Matter 10:3271–3276

    Google Scholar 

  • Kusters R, van der Heijden T, Kaoui B, Harting J, Storm C (2014) Forced transport of deformable containers through narrow constrictions. Phys Rev E 90:033006

    Google Scholar 

  • Lagny TJ, Bassereau P (2015) Bioinspired membrane-based systems for a physical approach of cell organization and dynamics: usefulness and limitations. Interface Focus 5:20150038 

    Google Scholar 

  • Lange JR, Steinwachs J, Kolb T, Lautscham LA, Harder I, Whyte G, Fabry B (2015) Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties. Biophys J 109:26–34

    Google Scholar 

  • Lautscham LA et al (2015) Migration in confined 3D environments is determined by a combination of adhesiveness, nuclear volume, contractility, and cell stiffness. Biophys J 109:900–913

    Google Scholar 

  • Lazaro GR, Hernandez-Machado A, Pagonabarraga I (2014) Rheology of red blood cells under flow in highly confined microchannels. II. Effect of focusing and confinement. Soft Matter 10:7207–7217

    Google Scholar 

  • Le Goff A, Kaoui B, Kurzawa G, Haszon B, Salsac A-V (2017) Squeezing bio-capsules into a constriction: deformation till break-up. Soft Matter 13:7644–7648

    Google Scholar 

  • Lee MS (2010) Computational studies of droplet motion and deformation in a microfluidic channel with a constriction. Master Thesis, University of Maryland, College Park, USA

  • Lee L, Liu A (2014) The application of micropipette aspiration in molecular mechanics of single cells. J Nanotechnol Eng Med 5:040902

    Google Scholar 

  • Lee G-H, Kim S-H, Ahn K, Lee S-H, Park JY (2015) Separation and sorting of cells in microsystems using physical principles. J Micromech Microeng 26:013003

    Google Scholar 

  • Legait B (1983) Laminar flow of two phases through a capillary tube with variable square cross-section. J Colloid Interface Sci 96:28–38

    Google Scholar 

  • Legait B, Sourieau P, Combarnous M (1983) Inertia, viscosity, and capillary forces during two-phase flow in a constricted capillary tube. J Colloid Interface Sci 91:400–411

    Google Scholar 

  • Leong FY, Li Q, Lim CT, Chiam K-H (2011) Modeling cell entry into a micro-channel. Biomech Model Mechanobiol 10:755–766

    Google Scholar 

  • Li H (2010) Smart hydrogel modelling. Springer, Berlin

    Google Scholar 

  • Li X, Peng Z, Lei H, Dao M, Karniadakis GE (2014) Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Philos Trans R Soc Lond A Math Phys Eng Sci 372:20130389

    MathSciNet  MATH  Google Scholar 

  • Li Y, Sarıyer OS, Ramachandran A, Panyukov S, Rubinstein M, Kumacheva E (2015) Universal behavior of hydrogels confined to narrow capillaries. Sci Rep 5: 17017

    Google Scholar 

  • Li H, Chen J, Du W, Xia Y, Wang D, Zhao G, Chu J (2017) The optimization of a microfluidic CTC filtering chip by simulation. Micromachines 8:79

    Google Scholar 

  • Liang M, Yang S, Miao T, Yu B (2015) Minimum applied pressure for a drop through an abruptly constricted capillary. Microfluid Nanofluidics 19:1–8

    Google Scholar 

  • Lin BK, McFaul SM, Jin C, Black PC, Ma H (2013) Highly selective biomechanical separation of cancer cells from leukocytes using microfluidic ratchets and hydrodynamic concentrator. Biomicrofluidics 7:034114

    Google Scholar 

  • Liu F, KC P, Zhang G, Zhe J (2015) Microfluidic magnetic bead assay for cell detection. Anal Chem 88:711–717

    Google Scholar 

  • Lorenceau É, Quéré D (2003) Drops impacting a sieve. J Colloid Interface Sci 263:244–249

    Google Scholar 

  • Luo Z, Bai B (2017) Off-center motion of a trapped elastic capsule in a microfluidic channel with a narrow constriction. Soft Matter 13:8281–8292

    Google Scholar 

  • Luo Z, Bai B (2018) Dynamics of capsules enclosing viscoelastic fluid in simple shear flow. J Fluid Mech 840:656–687

    MathSciNet  Google Scholar 

  • Luo Y et al (2014) A constriction channel based microfluidic system enabling continuous characterization of cellular instantaneous Young’s modulus. Sens Actuators B 202:1183–1189

    Google Scholar 

  • Luo Z et al (2015) Deformation of a single mouse oocyte in a constricted microfluidic channel. Microfluid Nanofluidics 19:883–890

    Google Scholar 

  • Marella S, Udaykumar H (2004) Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components. Phys Fluids 16:244–264

    MATH  Google Scholar 

  • Massenburg SS, Amstad E, Weitz DA (2016) Clogging in parallelized tapered microfluidic channels. Microfluid Nanofluid 20:1–5

    Google Scholar 

  • McGregor AL, Hsia C-R, Lammerding J (2016) Squish and squeeze—the nucleus as a physical barrier during migration in confined environments. Curr Opin Cell Biol 40:32–40

    Google Scholar 

  • Middleman S (1995) Modeling axisymmetric flows: dynamics of films, jets, and drops. Academic Press, New York

    Google Scholar 

  • Mittal R, Simmons S, Najjar F (2003) Numerical study of pulsatile flow in a constricted channel. J Fluid Mech 485:337–378

    MATH  Google Scholar 

  • Mogensen K, Stenby EH (1998) A dynamic two-phase pore-scale model of imbibition. Transp Porous Media 32:299–327

    Google Scholar 

  • Monzawa T, Kaneko M, Tsai C-HD, Sakuma S, Arai F (2015) On-chip actuation transmitter for enhancing the dynamic response of cell manipulation using a macro-scale pump. Biomicrofluidics 9:014114

    Google Scholar 

  • Mulligan MK, Rothstein JP (2011) The effect of confinement-induced shear on drop deformation and breakup in microfluidic extensional flows. Phys Fluids 23:022004

    Google Scholar 

  • Muradoglu M, Gokaltun S (2005) Implicit multigrid computations of buoyant drops through sinusoidal constrictions. J Appl Mech 71:857–865

    MATH  Google Scholar 

  • Myrand-Lapierre M-E, Deng X, Ang RR, Matthews K, Santoso AT, Ma H (2015) Multiplexed fluidic plunger mechanism for the measurement of red blood cell deformability. Lab Chip 15:159–167

    Google Scholar 

  • Olbricht W, Leal L (1983) The creeping motion of immiscible drops through a converging/diverging tube. J Fluid Mech 134:329–355

    Google Scholar 

  • Olgac U, Kayaalp AD, Muradoglu M (2006) Buoyancy-driven motion and breakup of viscous drops in constricted capillaries. Int J Multiph Flow 32:1055–1071

    MATH  Google Scholar 

  • Pak OS, Young Y-N, Marple GR, Veerapaneni S, Stone HA (2015) Gating of a mechanosensitive channel due to cellular flows. Proc Natl Acad Sci 112:9822–9827

    Google Scholar 

  • Park S-Y, Dimitrakopoulos P (2013) Transient dynamics of an elastic capsule in a microfluidic constriction. Soft matter 9:8844–8855

    Google Scholar 

  • Park S-Y, Nam Y (2017) Single-sided digital microfluidic (SDMF) devices for effective coolant delivery and enhanced two-phase cooling. Micromachines 8:3

    Google Scholar 

  • Pawar A, Caggioni M, Ergun R, Hartel R, Spicer P (2011) Arrested coalescence in Pickering emulsions. Soft Matter 7:7710–7716

    Google Scholar 

  • Peco C, Chen W, Liu Y, Bandi M, Dolbow JE, Fried E (2017) Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers. Soft matter 13:5832–5841

    Google Scholar 

  • Pegoraro C et al (2014) Translocation of flexible polymersomes across pores at the nanoscale. Biomaterials Science 2:680–692

    Google Scholar 

  • Peng Z, Li X, Pivkin IV, Dao M, Karniadakis GE, Suresh S (2013) Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc Natl Acad Sci 110:13356–13361

    Google Scholar 

  • Pivkin I, Peng Z, Karniadakis G, Buffet P, Dao M, Suresh S (2016) Biomechanics of red blood cells in human spleen and consequences for physiology and disease. Proc Natl Acad Sci 113:7804–7809

    Google Scholar 

  • Pollack MG, Fair RB, Shenderov AD (2000) Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl Phys Lett 77:1725–1726

    Google Scholar 

  • Prévost C, Zhao H, Manzi J, Lemichez E, Lappalainen P, Callan-Jones A, Bassereau P (2015) IRSp53 senses negative membrane curvature and phase separates along membrane tubules. Nat Commun 6:8529

    Google Scholar 

  • Ralf S, Martin B, Thomas P, Stephan H (2012) Droplet based microfluidics. Rep Prog Phys 75:016601

    Google Scholar 

  • Ratcliffe T, Zinchenko AZ, Davis RH (2010) Buoyancy-induced squeezing of a deformable drop through an axisymmetric ring constriction. Phys Fluids 22:082101

    Google Scholar 

  • Ratcliffe T, Zinchenko A, Davis R (2012) Simulations of gravity-induced trapping of a deformable drop in a three-dimensional constriction. J Colloid Interface Sci 383:167–176

    Google Scholar 

  • Ren X, Ghassemi P, Babahosseini H, Strobl JS, Agah M (2017) Single-cell mechanical characteristics analyzed by multiconstriction microfluidic channels. ACS Sens 2:290–299

    Google Scholar 

  • Roca J, Carvalho M (2013) Flow of a drop through a constricted microcapillary. Comput Fluids 87:50–56

    MathSciNet  MATH  Google Scholar 

  • Rosenfeld L, Fan L, Chen Y, Swoboda R, Tang S (2014) Break-up of droplets in a concentrated emulsion flowing through a narrow constriction. Soft Matter 10:421–430

    Google Scholar 

  • Sakuma S, Kuroda K, Tsai C-HD, Fukui W, Arai F, Kaneko M (2014) Red blood cell fatigue evaluation based on the close-encountering point between extensibility and recoverability. Lab Chip 14:1135–1141

    Google Scholar 

  • Sarioglu AF et al (2015) A microfluidic device for label-free, physical capture of circulating tumor cell clusters. Nature methods 12:685

    Google Scholar 

  • Schebarchov D, Hendy S (2011) Uptake and withdrawal of droplets from carbon nanotubes. Nanoscale 3:134–141

    Google Scholar 

  • Sendekie ZB, Gaveau A, Lammertink RGH, Bacchin P (2016) Bacteria delay the jamming of particles at microchannel bottlenecks. Sci Rep 6:31471

    Google Scholar 

  • Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163:489–528

    MathSciNet  MATH  Google Scholar 

  • Sharei A et al (2013) A vector-free microfluidic platform for intracellular delivery. Proc Natl Acad Sci 110:2082–2087

    Google Scholar 

  • She S, Xu C, Yin X, Tong W, Gao C (2012) Shape deformation and recovery of multilayer microcapsules after being squeezed through a microchannel. Langmuir 28:5010–5016

    Google Scholar 

  • Shelby JP, White J, Ganesan K, Rathod PK, Chiu DT (2003) A microfluidic model for single-cell capillary obstruction by Plasmodium falciparum-infected erythrocytes. Proc Natl Acad Sci 100:14618–14622

    Google Scholar 

  • Shen F, Pompano RR, Kastrup CJ, Ismagilov RF (2009) Confinement regulates complex biochemical networks: initiation of blood clotting by “diffusion acting”. Biophysical journal 97:2137–2145

    Google Scholar 

  • Shirai A, Masuda S (2013) Numerical simulation of passage of a neutrophil through a rectangular channel with a moderate constriction. PLOS One 8:e59416

    Google Scholar 

  • Shirai A, Fujita R, Hayase T (2002) Transit characteristics of a neutrophil passing through a circular constriction in a cylindrical capillary vessel. JSME Int J Ser C Mech Syst Mach Elem Manuf 45:974–980

    Google Scholar 

  • Shirai A, Fujita R, Hayase T (2003) Transit characteristics of a neutrophil passing through two moderate constrictions in a cylindrical capillary vessel. JSME Int J Ser C Mech Syst Mach Elem Manuf 46:1198–1207

    Google Scholar 

  • Shojaei-Baghini E, Zheng Y, Sun Y (2013) Automated micropipette aspiration of single cells. Ann Biomed Eng 41:1208–1216

    Google Scholar 

  • Shou D, Fan J (2015) Structural optimization of porous media for fast and controlled capillary flows. Phys Rev E 91:053021

    MathSciNet  Google Scholar 

  • Shou D, Fan J (2018) Design of nanofibrous and microfibrous channels for fast capillary flow. Langmuir 34:1235–1241

    Google Scholar 

  • Shou D, Ye L, Fan J, Fu K (2013) Optimal design of porous structures for the fastest liquid absorption. Langmuir 30:149–155

    Google Scholar 

  • Shou D, Ye L, Fan J, Fu K, Mei M, Wang H, Chen Q (2014a) Geometry-induced asymmetric capillary flow. Langmuir 30:5448–5454

    Google Scholar 

  • Shou D, Ye L, Fan J (2014b) The fastest capillary flow under gravity. Appl Phys Lett 104:231602

    Google Scholar 

  • Shou D, Ye L, Fan J (2014c) Treelike networks accelerating capillary flow. Phys Rev E 89:053007

    Google Scholar 

  • Sohrabi S, Tan J, Yunus DE, He R, Liu YJB (2018) Label-free sorting of soft microparticles using a bioinspired synthetic cilia array. Biomicrofluidics 12:042206

    Google Scholar 

  • Stewart MP, Sharei A, Ding X, Sahay G, Langer R, Jensen KF (2016) In vitro and ex vivo strategies for intracellular delivery. Nature 538:183–192

    Google Scholar 

  • Stroka KM, Jiang H, Chen S-H, Tong Z, Wirtz D, Sun SX, Konstantopoulos K (2014) Water permeation drives tumor cell migration in confined microenvironments. Cell 157:611–623

    Google Scholar 

  • Sun N, Li X, Wang Z, Li Y, Pei R (2018) High-purity capture of CTCs based on micro-beads enhanced isolation by size of epithelial tumor cells (ISET) method. Biosens Bioelectr 102:157–163

    Google Scholar 

  • Tan H (2016) Three-dimensional simulation of micrometer-sized droplet impact and penetration into the powder bed. Chem Eng Sci 153:93–107

    Google Scholar 

  • Tan J, Sinno TR, Diamond SL (2018a) A parallel fluid–solid coupling model using LAMMPS and Palabos based on the immersed boundary method. J Comput Sci 25:89–100

    Google Scholar 

  • Tan J, Sohrabi S, He R, Liu Y (2018b) Numerical simulation of cell squeezing through a micropore by the immersed boundary method. Proc Inst Mech Eng Part C J Mech Eng Sci 232:502–514

    Google Scholar 

  • Tasoglu S, Kaynak G, Szeri AJ, Demirci U, Muradoglu M (2010) Impact of a compound droplet on a flat surface: a model for single cell epitaxy. Phys Fluids 22:082103

    Google Scholar 

  • Thanh Hoang V, Lim J, Byon C, Min Park J (2017) Three-dimensional simulation of droplet dynamics in planar contraction microchannel. Chem Eng Sci 176:59–65

    Google Scholar 

  • Theisen E, Vogel M, Lopez C, Hirsa A, Steen P (2007) Capillary dynamics of coupled spherical-cap droplets. J Fluid Mech 580:495–505

    MathSciNet  MATH  Google Scholar 

  • To HD, Scheuermann A, Galindo-Torres SA (2015) Probability of transportation of loose particles in suffusion assessment by self-filtration criteria. J Geotech Geoenviron Eng 142:04015078

    Google Scholar 

  • Tomaiuolo G, Simeone M, Martinelli V, Rotoli B, Guido S (2009) Red blood cell deformation in microconfined flow. Soft Matter 5:3736–3740

    Google Scholar 

  • Tomita M et al (1999) E-CELL: software environment for whole-cell simulation. Bioinformatics 15:72–84

    Google Scholar 

  • Toose EM, Geurts BJ, Kuerten JGM (1999) A 2D boundary element method for simulating the deformation of axisymmetric compound non-Newtonian drops. Int J Numer Meth Fluids 30:653–674

    MATH  Google Scholar 

  • Tsai T, Miksis MJ (1994) Dynamics of a drop in a constricted capillary tube. J Fluid Mech 274:197–217

    MathSciNet  MATH  Google Scholar 

  • Tsai C-HD, Sakuma S, Arai F, Kaneko M (2014) A new dimensionless index for evaluating cell stiffness-based deformability in microchannel. Biomed Eng IEEE Trans 61:1187–1195

    Google Scholar 

  • Van Hirtum A, Wu B, Gao H, Luo XJEJoM-BF (2017) Constricted channel flow with different cross-section shapes. Eur J Mech-B/Fluids 63:1–8

    MathSciNet  MATH  Google Scholar 

  • Vazquez RM et al (2015) An optofluidic constriction chip for monitoring metastatic potential and drug response of cancer cells. Integr Biol 7:477–484

    Google Scholar 

  • Vogel MJ, Ehrhard P, Steen PH (2005) The electroosmotic droplet switch: countering capillarity with electrokinetics. Proc Natl Acad Sci 102:11974–11979

    Google Scholar 

  • Wang W, Huang Y, Grujicic M, Chrisey DB (2008) Study of impact-induced mechanical effects in cell direct writing using smooth particle hydrodynamic method. J Manuf Sci Eng 130:021012

    Google Scholar 

  • Watson KE, Dovi WF, Conhaim RL (2012) Evidence for active control of perfusion within lung microvessels. J Appl Physiol 112:48–53

    Google Scholar 

  • Wetzel ED, Tucker CL (2001) Droplet deformation in dispersions with unequal viscosities and zero interfacial tension. J Fluid Mech 426:199–228

    MATH  Google Scholar 

  • Wörner M (2012) Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications. Microfluid Nanofluid 12:841–886

    Google Scholar 

  • Wu T, Feng JJ (2013) Simulation of malaria-infected red blood cells in microfluidic channels: passage and blockage. Biomicrofluidics 7:044115

    Google Scholar 

  • Wu T, Guo Q, Ma H, Feng JJ (2015) The critical pressure for driving a red blood cell through a contracting microfluidic channel. Theor Appl Mech Lett 5:227–230

    Google Scholar 

  • Wyss HM (2015) Cell mechanics: combining speed with precision. Biophys J 109:1997

    Google Scholar 

  • Xiao L, Liu Y, Chen S, Fu B (2016) Numerical simulation of a single cell passing through a narrow slit. Biomech Model Mechanobiol 15:1655–1667

    Google Scholar 

  • Xie Y et al (2016) Probing cell deformability via acoustically actuated bubbles. Small 12:902–910

    Google Scholar 

  • Xu J, Attinger D (2008) Drop on demand in a microfluidic chip. J Micromech Microeng 18:065020

    Google Scholar 

  • Xu K, Zhu P, Huh C, Balhoff MT (2015) Microfluidic investigation of nanoparticles’ role in mobilizing trapped oil droplets in porous media. Langmuir 31:13673–13679

    Google Scholar 

  • Xu B et al (2017) Arch-like microsorters with multi-modal and clogging-improved filtering functions by using femtosecond laser multifocal parallel microfabrication. Opt Express 25:16739–16753

    Google Scholar 

  • Xue C, Wang J, Zhao Y, Chen D, Yue W, Chen J (2015) Constriction channel based single-cell mechanical property characterization. Micromachines 6:1794–1804

    Google Scholar 

  • Yap B, Kamm RD (2005) Mechanical deformation of neutrophils into narrow channels induces pseudopod projection and changes in biomechanical properties. J Appl Physiol 98:1930–1939

    Google Scholar 

  • Yazdani A, Karniadakis GE (2016) Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction. Soft Matter 12:4339–4351

    Google Scholar 

  • Ye T, Phan-Thien N, Lim CT (2016) Particle-based simulations of red blood cells—a review. J Biomech 49:2255–2266

    Google Scholar 

  • Yoshino T, Tanaka T, Nakamura S, Negishi R, Shionoiri N, Hosokawa M, Matsunaga T (2017) Evaluation of cancer cell deformability by microcavity array. Anal Biochem 520:16–21

    Google Scholar 

  • Zeina K, Nabiollah K, Fazle H, Siva V (2017) Passage times and friction due to flow of confined cancer cells, drops, and deformable particles in a microfluidic channel. Converg Sci Phys Oncol 3:024001

    Google Scholar 

  • Zhang Z, Drapaca C (2016) A critical velocity of squeezing a droplet through a circular constriction: implications on ischemic stroke. Bull Am Phys Soc 61

  • Zhang Z, Xu J, Hong B, Chen X (2014) The effects of 3D channel geometry on CTC passing pressure–towards deformability-based cancer cell separation. Lab Chip 14:2576–2584

    Google Scholar 

  • Zhang Y et al (2015a) Multiple stiffening effects of nanoscale knobs on human red blood cells infected with Plasmodium falciparum malaria parasite. Proc Natl Acad Sci 112:6068–6073

    Google Scholar 

  • Zhang Z, Chen X, Xu J (2015b) Entry effects of droplet in a micro confinement: Implications for deformation-based circulating tumor cell microfiltration. Biomicrofluidics 9:024108

    Google Scholar 

  • Zhang Z, Xu J, Chen X (2015c) Compound Droplet Modelling of Circulating Tumor Cell Microfiltration. Paper presented at the ASME 2015 international mechanical engineering congress and exposition

  • Zhang X, Chen X, Tan H (2017a) On the thin-film-dominated passing pressure of cancer cell squeezing through a microfluidic CTC chip. Microfluid Nanofluid 21:146

    Google Scholar 

  • Zhang Z, Drapaca C, Chen X, Xu J (2017b) Droplet squeezing through a narrow constriction: minimum impulse and critical velocity. Phys Fluids 29:072102

    Google Scholar 

  • Zhang X, Hashem MA, Chen X, Tan H (2018) On passing a non-Newtonian circulating tumor cell (CTC) through a deformation-based microfluidic chip. Theor Comput Fluid Dyn. https://doi.org/10.1007/s00162-018-0475-z

    Article  Google Scholar 

  • Zhao Y et al (2015) Simultaneous characterization of instantaneous Young’s modulus and specific membrane capacitance of single cells using a microfluidic system. Sensors 15:2763–2773

    Google Scholar 

  • Zhao Y et al (2016) Single-cell electrical phenotyping enabling the classification of mouse tumor samples. Sci Rep 6:19487

    Google Scholar 

  • Zhao C, Ma W, Yu X, Su H, Zhang Z, Zohar Y, Lee Y-K (2017) The capillary number effect on cell viability in Microfluidic Elasto-Filtration devices for viable circulating tumor cell isolation. In: Solid-state sensors, actuators and microsystems (TRANSDUCERS), 2017 19th international conference on (2017). IEEE, pp 488–491

  • Zheng Y, Shojaei-Baghini E, Azad A, Wang C, Sun Y (2012) High-throughput biophysical measurement of human red blood cells. Lab Chip 12:2560–2567

    Google Scholar 

  • Zhou C, Yue P, Feng JJ (2006) Formation of simple and compound drops in microfluidic devices. Phys Fluids 18:092105

    Google Scholar 

  • Zhou C, Yue P, Feng JJ (2007) Simulation of neutrophil deformation and transport in capillaries using newtonian and viscoelastic drop models. Ann Biomed Eng 35:766–780

    Google Scholar 

  • Zhou C, Yue P, Feng JJ (2008) Deformation of a compound drop through a contraction in a pressure-driven pipe flow. Int J Multiph Flow 34:102–109

    Google Scholar 

  • Zinchenko AZ, Davis RH (2006) A boundary-integral study of a drop squeezing through interparticle constrictions. J Fluid Mech 564:227–266

    MathSciNet  MATH  Google Scholar 

  • Zinchenko AZ, Davis RH (2008) Squeezing of a periodic emulsion through a cubic lattice of spheres. Phys Fluids 20:040803

    MATH  Google Scholar 

  • Zinchenko AZ, Davis RH (2017) Motion of deformable drops through porous media. Annu Rev Fluid Mech 49:71–90

    MathSciNet  MATH  Google Scholar 

  • Zolfaghari H, Izbassarov D, Muradoglu M (2017) Simulations of viscoelastic two-phase flows in complex geometries. Comput Fluids 156:548–561

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

Zhifeng Zhang thanks the support of Harvey & Geraldine Brush Fellowship and Max & Joan Schlienger Scholarship awarded by College of Engineering, the Pennsylvania State University.

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  1. Engineering Science and Mechanics, The Pennsylvania State University, State College, PA, 16802, USA

    Zhifeng Zhang & Corina Drapaca

  2. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Jie Xu

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Zhang, Z., Xu, J. & Drapaca, C. Particle squeezing in narrow confinements. Microfluid Nanofluid 22, 120 (2018). https://doi.org/10.1007/s10404-018-2129-2

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