Particle squeezing in narrow confinements

  • Zhifeng Zhang
  • Jie Xu
  • Corina Drapaca


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.


Droplets Cells Particles Narrow confinements Soft matter Chip design Fluid mechanics Chemical engineering 



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


  1. Abkarian M, Faivre M, Horton R, Smistrup K, Best-Popescu CA, Stone HA (2008) Cellular-scale hydrodynamics. Biomed Mater 3:034011CrossRefGoogle Scholar
  2. Aceto N et al (2014) Circulating tumor cell clusters are oligoclonal precursors of breast cancer metastasis. Cell 158:1110–1122CrossRefGoogle Scholar
  3. 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 9:034106CrossRefGoogle Scholar
  4. Ahmed R, Jones T (2007) Optimized liquid DEP droplet dispensing. J Micromech Microeng 17:1052CrossRefGoogle Scholar
  5. Ahmmed SM, Bithi SS, Pore AA, Mubtasim N, Schuster C, Gollahon LS, Vanapalli SA (2018a) Multi-sample deformability cytometry of cancer cells. APL Bioeng 2:032002CrossRefGoogle Scholar
  6. Ahmmed SM, Suteria NS, Garbin V, Vanapalli SA (2018b) Hydrodynamic mobility of confined polymeric particles, vesicles, and cancer cells in a square microchannel. Biomicrofluidics 12:014114CrossRefGoogle Scholar
  7. Alix-Panabières C, Pantel K (2014) Technologies for detection of circulating tumor cells: facts and vision. Lab Chip 14:57–62CrossRefGoogle Scholar
  8. Anselmo A, Mitragotri S (2016) Designing drug-delivery nanoparticles. Chem Eng Prog 112: 52–57Google Scholar
  9. Aoki T, Ohashi T, Matsumoto T, Sato M (1997) The pipette aspiration applied to the local stiffness measurement of soft tissues. Ann Biomed Eng 25:581–587CrossRefGoogle Scholar
  10. Arata JP, Alexeev A (2009) Designing microfluidic channel that separates elastic particles upon stiffness. Soft Matter 5:2721–2724CrossRefGoogle Scholar
  11. 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 20160559Google Scholar
  12. Au SH et al (2016) Clusters of circulating tumor cells traverse capillary-sized vessels. Proc Natl Acad Sci 113:4947–4952CrossRefGoogle Scholar
  13. Ayan B et al (2017) A new aspiration-assisted bioprinting method for tissue fabrication. Paper presented at the Symposium on Biomaterials Science, New Jersey, USAGoogle Scholar
  14. Bächer C, Schrack L, Gekle S (2017) Clustering of microscopic particles in constricted blood flow. Phys Rev Fluids 2:013102CrossRefGoogle Scholar
  15. Barakat JM, Shaqfeh ESG (2018) The steady motion of a closely fitting vesicle in a tube. J Fluid Mech 835:721–761MathSciNetCrossRefGoogle Scholar
  16. Barthès-Biesel D (2012) Microhydrodynamics and complex fluids. CRC Press, Boco RatonzbMATHCrossRefGoogle Scholar
  17. 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 96:6199–6212CrossRefGoogle Scholar
  18. Benet E, Vernerey F (2016) Mechanics and stability of vesicles and droplets in confined spaces. Phys Rev E 94:062613CrossRefGoogle Scholar
  19. Benet E, Badran A, Pellegrino J, Vernerey F (2017) The porous media’s effect on the permeation of elastic (soft) particles. J Membr Sci 535:10–19CrossRefGoogle Scholar
  20. Beresnev IA, Deng W (2010) Viscosity effects in vibratory mobilization of residual oil. Geophysics 75:N79–N85CrossRefGoogle Scholar
  21. 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 32Google Scholar
  22. Beresnev IA, Li W, Vigil RD (2009) Condition for break-up of non-wetting fluids in sinusoidally constricted capillary channels. Transp Porous Media 80:581–604CrossRefGoogle Scholar
  23. Beresnev I, Gaul W, Vigil RD (2011) Direct pore-level observation of permeability increase in two-phase flow by shaking. Geophys Res Lett 38:L20302CrossRefGoogle Scholar
  24. Berthier J, Brakke K (2012) The physics of microdroplets. Wiley, HobokenzbMATHCrossRefGoogle Scholar
  25. 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 transferGoogle Scholar
  26. 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 onGoogle Scholar
  27. 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 21:737–746CrossRefGoogle Scholar
  28. Blunt MJ (2001) Flow in porous media-pore-network models and multiphase flow. Curr Opin Colloid Interface Sci 6:197–207CrossRefGoogle Scholar
  29. Boukellal H, Selimovic S, Jia Y, Cristobal G, Fraden S (2009) Simple, robust storage of drops and fluids in a microfluidic device. Lab Chip 9:331–338CrossRefGoogle Scholar
  30. Bow H et al (2011) A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11:1065–1073CrossRefGoogle Scholar
  31. Brakke KA (1992) The surface evolver. Exp Math 1:141–165MathSciNetzbMATHCrossRefGoogle Scholar
  32. Brosseau Q, Vrignon J, Baret J-C (2014) Microfluidic dynamic interfacial tensiometry (µDIT). Soft Matter 10:3066–3076CrossRefGoogle Scholar
  33. Brouzes E et al (2009) Droplet microfluidic technology for single-cell high-throughput screening. Proc Natl Acad Sci 106:14195–14200CrossRefGoogle Scholar
  34. Byun S et al (2013) Characterizing deformability and surface friction of cancer cells. Proc Natl Acad Sci 110:7580–7585CrossRefGoogle Scholar
  35. 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 316:646–667MathSciNetCrossRefGoogle Scholar
  36. 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 14:3008–3013CrossRefGoogle Scholar
  37. Chen H, Zhang Z (2018) An inertia-deformability hybrid circulating tumor cell chip: design, clinical test, and numerical analysis. J Med Devices 12(4):041004CrossRefGoogle Scholar
  38. Chen J et al (2011) Classification of cell types using a microfluidic device for mechanical and electrical measurement on single cells. Lab Chip 11:3174–3181CrossRefGoogle Scholar
  39. Chen Y et al (2014) Rare cell isolation and analysis in microfluidics. Lab Chip 14:626–645CrossRefGoogle Scholar
  40. 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 7:610CrossRefGoogle Scholar
  41. Chen L, Wang KX, Doyle PS (2017b) Effect of internal architecture on microgel deformation in microfluidic constrictions. Soft Matter 13:1920–1928CrossRefGoogle Scholar
  42. Chiu J-J, Chien S (2011) Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives. Physiol Rev 91:327–387CrossRefGoogle Scholar
  43. 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 3:2037CrossRefGoogle Scholar
  44. Christafakis AN, Tsangaris S (2008) Two-phase flows of droplets in contractions and double bends. Eng Appl Comput Fluid Mech 2:299–308Google Scholar
  45. Chrysikopoulos CV, Vogler ET (2006) Acoustically enhanced ganglia dissolution and mobilization in a monolayer of glass beads. Transp Porous Media 64:103–121CrossRefGoogle Scholar
  46. 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 155:80–93zbMATHCrossRefGoogle Scholar
  47. Chung C, Lee M, Char K, Ahn KH, Lee SJ (2010) Droplet dynamics passing through obstructions in confined microchannel flow. Microfluid Nanofluid 9:1151–1163CrossRefGoogle Scholar
  48. 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 5:1229–1232CrossRefGoogle Scholar
  49. 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 12:20150415CrossRefGoogle Scholar
  50. Cottet G-H, Maitre E (2004) A level-set formulation of immersed boundary methods for fluid–structure interaction problems. CR Math 338:581–586MathSciNetzbMATHGoogle Scholar
  51. 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: 979CrossRefGoogle Scholar
  52. Darvishzadeh T, Priezjev NV (2012) Effects of crossflow velocity and transmembrane pressure on microfiltration of oil-in-water emulsions. J Membr Sci 423–424:468–476CrossRefGoogle Scholar
  53. Datta P, Ayan B, Ozbolat IT (2017) Bioprinting for vascular and vascularized tissue biofabrication. Acta Biomater 51:1–20CrossRefGoogle Scholar
  54. Dawson G, Häner E, Juel A (2015) Extreme deformation of capsules and bubbles flowing through a localised constriction. Proc IUTAM 16:22–32CrossRefGoogle Scholar
  55. 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 28:471–478CrossRefGoogle Scholar
  56. Dressaire E, Sauret A (2017) Clogging of microfluidic systems. Soft Matter 13:37–48CrossRefGoogle Scholar
  57. Drury J, Dembo M (1999) Hydrodynamics of micropipette aspiration. Biophys J 76:110–128CrossRefGoogle Scholar
  58. Drury J, Dembo M (2001) Aspiration of human neutrophils: effects of shear thinning and cortical dissipation. Biophys J 81:3166–3177CrossRefGoogle Scholar
  59. Evans EA, Waugh R, Melnik L (1976) Elastic area compressibility modulus of red cell membrane. Biophys J 16:585–595CrossRefGoogle Scholar
  60. 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 335:225–231CrossRefGoogle Scholar
  61. Facchin S, Miled MA, Sawan M (2015) In-channel constriction valve for cerebrospinal fluid sampling. IEEE Trans Magn 51:1–4CrossRefGoogle Scholar
  62. Fai T, Kusters R, Harting J, Rycroft C, Mahadevan L (2017) Active elastohydrodynamics of vesicles in narrow, blind constrictions. arXiv preprint arXiv:170501765Google Scholar
  63. 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, USAGoogle Scholar
  64. 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 403:396–401CrossRefGoogle Scholar
  65. 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 4:6213CrossRefGoogle Scholar
  66. Frostad JM, Paul A, Leal LG (2016) Coalescence of droplets due to a constant force interaction in a quiescent viscous fluid. Phys Rev Fluids 1:033904CrossRefGoogle Scholar
  67. 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 16:3058–3064CrossRefGoogle Scholar
  68. Gencoglu A, Olney D, LaLonde A, Koppula K, Lapizco-Encinas B (2013) Particle manipulation in insulator based dielectrophoretic devices. J Nanotechnol Eng Med 4:021002–021002CrossRefGoogle Scholar
  69. Genovese D, Sprakel J (2011) Crystallization and intermittent dynamics in constricted microfluidic flows of dense suspensions. Soft Matter 7:3889–3896CrossRefGoogle Scholar
  70. Gounley J, Draeger EW, Randles A (2017) Numerical simulation of a compound capsule in a constricted microchannel. Proc Comput Sci 108:175–184CrossRefGoogle Scholar
  71. Guevorkian K, Colbert M-J, Durth M, Dufour S, Brochard-Wyart F (2010) Aspiration of biological viscoelastic drops. Phys Rev Lett 104:218101CrossRefGoogle Scholar
  72. Guilak F, Tedrow JR, Burgkart R (2000) Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun 269:781–786CrossRefGoogle Scholar
  73. 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, USAGoogle Scholar
  74. Guo Q, McFaul SM, Ma H (2011) Deterministic microfluidic ratchet based on the deformation of individual cells. Phys Rev E 83:051910CrossRefGoogle Scholar
  75. Guo Q, Park S, Ma H (2012) Microfluidic micropipette aspiration for measuring the deformability of single cells. Lab Chip 12:2687–2695CrossRefGoogle Scholar
  76. 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 16:645–654CrossRefGoogle Scholar
  77. Gupta A, Matharoo HS, Makkar D, Kumar R (2014) Droplet formation via squeezing mechanism in a microfluidic flow-focusing device. Comput Fluids 100:218–226CrossRefGoogle Scholar
  78. Haider MA, Guilak F (2002) An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem. J Biomech Eng 124:586–595CrossRefGoogle Scholar
  79. Han X et al (2015) CRISPR-Cas9 delivery to hard-to-transfect cells via membrane deformation. Sci Adv 1:e1500454CrossRefGoogle Scholar
  80. Harvie D, Cooper-White J, Davidson M (2008) Deformation of a viscoelastic droplet passing through a microfluidic contraction. J Nonnewton Fluid Mech 155:67–79zbMATHCrossRefGoogle Scholar
  81. 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 20:1–13CrossRefGoogle Scholar
  82. Hendrickson GR, Lyon LA (2010) Microgel translocation through pores under confinement. Angew Chem Int Ed 49:2193–2197CrossRefGoogle Scholar
  83. Herant M, Heinrich V, Dembo M (2005) Mechanics of neutrophil phagocytosis: behavior of the cortical tension. J Cell Sci 118:1789–1797CrossRefGoogle Scholar
  84. Hochmuth RM (2000) Micropipette aspiration of living cells. J Biomech 33:15–22CrossRefGoogle Scholar
  85. Hoelzle D, Varghese B, Chan C, Rowat A (2014) A microfluidic technique to probe cell deformability. J Vis Exp 91:e51474Google Scholar
  86. Hong B, Zu Y (2013) Detecting circulating tumor cells: current challenges and new trends. Theranostics 3:377–396CrossRefGoogle Scholar
  87. 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 705:176–194MathSciNetzbMATHCrossRefGoogle Scholar
  88. 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 8:119CrossRefGoogle Scholar
  89. Hua H, Shin J, Kim J (2014) Dynamics of a compound droplet in shear flow. Int J Heat Fluid Flow 50:63–71CrossRefGoogle Scholar
  90. Hui M-H, Blunt MJ (2000) Effects of wettability on three-phase flow in porous media. J Phys Chem B 104:3833–3845CrossRefGoogle Scholar
  91. 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 7:43134CrossRefGoogle Scholar
  92. Izbassarov D, Muradoglu M (2016) A computational study of two-phase viscoelastic systems in a capillary tube with a sudden contraction/expansion. Phys Fluids 28:012110CrossRefGoogle Scholar
  93. Kadivar E, Farrokhbin M (2017) A numerical procedure for scaling droplet deformation in a microfluidic expansion channel. Phys A 479:449–459MathSciNetCrossRefGoogle Scholar
  94. Kan H-C, Udaykumar H, Shyy W, Tran-Son-Tay R (1998) Hydrodynamics of a compound drop with application to leukocyte modeling. Phys Fluids 10:760–774CrossRefGoogle Scholar
  95. 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 55:1102A1108CrossRefGoogle Scholar
  96. 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 StationGoogle Scholar
  97. 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 139:1315–1326CrossRefGoogle Scholar
  98. Kim Y, Kim K, Park Y (2012) Measurement techniques for red blood cell deformability: recent advances. INTECH Open Access Publisher Rijeka, CroatiaGoogle Scholar
  99. Kim J, Lee H, Shin S (2015) Advances in the measurement of red blood cell deformability: a brief review. J Cell Biotechnol 1:63–79CrossRefGoogle Scholar
  100. Kollmannsperger A et al (2016) Live-cell protein labelling with nanometre precision by cell squeezing. Nat Commun 7:10372CrossRefGoogle Scholar
  101. Kong T, Wang L, Wyss HM, Shum HC (2014) Capillary micromechanics for core-shell particles. Soft Matter 10:3271–3276CrossRefGoogle Scholar
  102. Kusters R, van der Heijden T, Kaoui B, Harting J, Storm C (2014) Forced transport of deformable containers through narrow constrictions. Phys Rev E 90:033006CrossRefGoogle Scholar
  103. 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 CrossRefGoogle Scholar
  104. 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 109:26–34CrossRefGoogle Scholar
  105. 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 109:900–913CrossRefGoogle Scholar
  106. 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 10:7207–7217CrossRefGoogle Scholar
  107. 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 13:7644–7648CrossRefGoogle Scholar
  108. Lee MS (2010) Computational studies of droplet motion and deformation in a microfluidic channel with a constriction. Master Thesis, University of Maryland, College Park, USAGoogle Scholar
  109. Lee L, Liu A (2014) The application of micropipette aspiration in molecular mechanics of single cells. J Nanotechnol Eng Med 5:040902CrossRefGoogle Scholar
  110. 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 26:013003CrossRefGoogle Scholar
  111. Legait B (1983) Laminar flow of two phases through a capillary tube with variable square cross-section. J Colloid Interface Sci 96:28–38CrossRefGoogle Scholar
  112. 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 91:400–411CrossRefGoogle Scholar
  113. Leong FY, Li Q, Lim CT, Chiam K-H (2011) Modeling cell entry into a micro-channel. Biomech Model Mechanobiol 10:755–766CrossRefGoogle Scholar
  114. Li H (2010) Smart hydrogel modelling. Springer, BerlinGoogle Scholar
  115. 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 372:20130389MathSciNetzbMATHCrossRefGoogle Scholar
  116. Li Y, Sarıyer OS, Ramachandran A, Panyukov S, Rubinstein M, Kumacheva E (2015) Universal behavior of hydrogels confined to narrow capillaries. Sci Rep 5: 17017CrossRefGoogle Scholar
  117. 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 8:79CrossRefGoogle Scholar
  118. Liang M, Yang S, Miao T, Yu B (2015) Minimum applied pressure for a drop through an abruptly constricted capillary. Microfluid Nanofluidics 19:1–8CrossRefGoogle Scholar
  119. 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 7:034114CrossRefGoogle Scholar
  120. Liu F, KC P, Zhang G, Zhe J (2015) Microfluidic magnetic bead assay for cell detection. Anal Chem 88:711–717CrossRefGoogle Scholar
  121. Lorenceau É, Quéré D (2003) Drops impacting a sieve. J Colloid Interface Sci 263:244–249CrossRefGoogle Scholar
  122. Luo Z, Bai B (2017) Off-center motion of a trapped elastic capsule in a microfluidic channel with a narrow constriction. Soft Matter 13:8281–8292CrossRefGoogle Scholar
  123. Luo Z, Bai B (2018) Dynamics of capsules enclosing viscoelastic fluid in simple shear flow. J Fluid Mech 840:656–687MathSciNetCrossRefGoogle Scholar
  124. Luo Y et al (2014) A constriction channel based microfluidic system enabling continuous characterization of cellular instantaneous Young’s modulus. Sens Actuators B 202:1183–1189CrossRefGoogle Scholar
  125. Luo Z et al (2015) Deformation of a single mouse oocyte in a constricted microfluidic channel. Microfluid Nanofluidics 19:883–890CrossRefGoogle Scholar
  126. Marella S, Udaykumar H (2004) Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components. Phys Fluids 16:244–264zbMATHCrossRefGoogle Scholar
  127. Massenburg SS, Amstad E, Weitz DA (2016) Clogging in parallelized tapered microfluidic channels. Microfluid Nanofluid 20:1–5CrossRefGoogle Scholar
  128. 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 40:32–40CrossRefGoogle Scholar
  129. Middleman S (1995) Modeling axisymmetric flows: dynamics of films, jets, and drops. Academic Press, New YorkGoogle Scholar
  130. Mittal R, Simmons S, Najjar F (2003) Numerical study of pulsatile flow in a constricted channel. J Fluid Mech 485:337–378zbMATHCrossRefGoogle Scholar
  131. Mogensen K, Stenby EH (1998) A dynamic two-phase pore-scale model of imbibition. Transp Porous Media 32:299–327CrossRefGoogle Scholar
  132. 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 9:014114CrossRefGoogle Scholar
  133. Mulligan MK, Rothstein JP (2011) The effect of confinement-induced shear on drop deformation and breakup in microfluidic extensional flows. Phys Fluids 23:022004CrossRefGoogle Scholar
  134. Muradoglu M, Gokaltun S (2005) Implicit multigrid computations of buoyant drops through sinusoidal constrictions. J Appl Mech 71:857–865zbMATHCrossRefGoogle Scholar
  135. 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 15:159–167CrossRefGoogle Scholar
  136. Olbricht W, Leal L (1983) The creeping motion of immiscible drops through a converging/diverging tube. J Fluid Mech 134:329–355CrossRefGoogle Scholar
  137. Olgac U, Kayaalp AD, Muradoglu M (2006) Buoyancy-driven motion and breakup of viscous drops in constricted capillaries. Int J Multiph Flow 32:1055–1071zbMATHCrossRefGoogle Scholar
  138. 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 112:9822–9827Google Scholar
  139. Park S-Y, Dimitrakopoulos P (2013) Transient dynamics of an elastic capsule in a microfluidic constriction. Soft matter 9:8844–8855CrossRefGoogle Scholar
  140. Park S-Y, Nam Y (2017) Single-sided digital microfluidic (SDMF) devices for effective coolant delivery and enhanced two-phase cooling. Micromachines 8:3CrossRefGoogle Scholar
  141. Pawar A, Caggioni M, Ergun R, Hartel R, Spicer P (2011) Arrested coalescence in Pickering emulsions. Soft Matter 7:7710–7716CrossRefGoogle Scholar
  142. 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 13:5832–5841CrossRefGoogle Scholar
  143. Pegoraro C et al (2014) Translocation of flexible polymersomes across pores at the nanoscale. Biomaterials Science 2:680–692CrossRefGoogle Scholar
  144. 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 110:13356–13361Google Scholar
  145. 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 113:7804–7809CrossRefGoogle Scholar
  146. Pollack MG, Fair RB, Shenderov AD (2000) Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl Phys Lett 77:1725–1726CrossRefGoogle Scholar
  147. 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 6:8529CrossRefGoogle Scholar
  148. Ralf S, Martin B, Thomas P, Stephan H (2012) Droplet based microfluidics. Rep Prog Phys 75:016601CrossRefGoogle Scholar
  149. Ratcliffe T, Zinchenko AZ, Davis RH (2010) Buoyancy-induced squeezing of a deformable drop through an axisymmetric ring constriction. Phys Fluids 22:082101CrossRefGoogle Scholar
  150. 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 383:167–176CrossRefGoogle Scholar
  151. Ren X, Ghassemi P, Babahosseini H, Strobl JS, Agah M (2017) Single-cell mechanical characteristics analyzed by multiconstriction microfluidic channels. ACS Sens 2:290–299CrossRefGoogle Scholar
  152. Roca J, Carvalho M (2013) Flow of a drop through a constricted microcapillary. Comput Fluids 87:50–56MathSciNetzbMATHCrossRefGoogle Scholar
  153. 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 10:421–430CrossRefGoogle Scholar
  154. 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 14:1135–1141CrossRefGoogle Scholar
  155. Sarioglu AF et al (2015) A microfluidic device for label-free, physical capture of circulating tumor cell clusters. Nature methods 12:685CrossRefGoogle Scholar
  156. Schebarchov D, Hendy S (2011) Uptake and withdrawal of droplets from carbon nanotubes. Nanoscale 3:134–141CrossRefGoogle Scholar
  157. Sendekie ZB, Gaveau A, Lammertink RGH, Bacchin P (2016) Bacteria delay the jamming of particles at microchannel bottlenecks. Sci Rep 6:31471CrossRefGoogle Scholar
  158. Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163:489–528MathSciNetzbMATHCrossRefGoogle Scholar
  159. Sharei A et al (2013) A vector-free microfluidic platform for intracellular delivery. Proc Natl Acad Sci 110:2082–2087CrossRefGoogle Scholar
  160. 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 28:5010–5016CrossRefGoogle Scholar
  161. 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 100:14618–14622CrossRefGoogle Scholar
  162. Shen F, Pompano RR, Kastrup CJ, Ismagilov RF (2009) Confinement regulates complex biochemical networks: initiation of blood clotting by “diffusion acting”. Biophysical journal 97:2137–2145CrossRefGoogle Scholar
  163. Shirai A, Masuda S (2013) Numerical simulation of passage of a neutrophil through a rectangular channel with a moderate constriction. PLOS One 8:e59416CrossRefGoogle Scholar
  164. 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 45:974–980CrossRefGoogle Scholar
  165. 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 46:1198–1207CrossRefGoogle Scholar
  166. Shojaei-Baghini E, Zheng Y, Sun Y (2013) Automated micropipette aspiration of single cells. Ann Biomed Eng 41:1208–1216CrossRefGoogle Scholar
  167. Shou D, Fan J (2015) Structural optimization of porous media for fast and controlled capillary flows. Phys Rev E 91:053021MathSciNetCrossRefGoogle Scholar
  168. Shou D, Fan J (2018) Design of nanofibrous and microfibrous channels for fast capillary flow. Langmuir 34:1235–1241CrossRefGoogle Scholar
  169. Shou D, Ye L, Fan J, Fu K (2013) Optimal design of porous structures for the fastest liquid absorption. Langmuir 30:149–155CrossRefGoogle Scholar
  170. Shou D, Ye L, Fan J, Fu K, Mei M, Wang H, Chen Q (2014a) Geometry-induced asymmetric capillary flow. Langmuir 30:5448–5454CrossRefGoogle Scholar
  171. Shou D, Ye L, Fan J (2014b) The fastest capillary flow under gravity. Appl Phys Lett 104:231602CrossRefGoogle Scholar
  172. Shou D, Ye L, Fan J (2014c) Treelike networks accelerating capillary flow. Phys Rev E 89:053007CrossRefGoogle Scholar
  173. Sohrabi S, Tan J, Yunus DE, He R, Liu YJB (2018) Label-free sorting of soft microparticles using a bioinspired synthetic cilia array. Biomicrofluidics 12:042206CrossRefGoogle Scholar
  174. Stewart MP, Sharei A, Ding X, Sahay G, Langer R, Jensen KF (2016) In vitro and ex vivo strategies for intracellular delivery. Nature 538:183–192CrossRefGoogle Scholar
  175. 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 157:611–623CrossRefGoogle Scholar
  176. 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 102:157–163CrossRefGoogle Scholar
  177. Tan H (2016) Three-dimensional simulation of micrometer-sized droplet impact and penetration into the powder bed. Chem Eng Sci 153:93–107CrossRefGoogle Scholar
  178. 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 25:89–100CrossRefGoogle Scholar
  179. 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 232:502–514Google Scholar
  180. 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 22:082103CrossRefGoogle Scholar
  181. Thanh Hoang V, Lim J, Byon C, Min Park J (2017) Three-dimensional simulation of droplet dynamics in planar contraction microchannel. Chem Eng Sci 176:59–65CrossRefGoogle Scholar
  182. Theisen E, Vogel M, Lopez C, Hirsa A, Steen P (2007) Capillary dynamics of coupled spherical-cap droplets. J Fluid Mech 580:495–505MathSciNetzbMATHCrossRefGoogle Scholar
  183. 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 142:04015078CrossRefGoogle Scholar
  184. Tomaiuolo G, Simeone M, Martinelli V, Rotoli B, Guido S (2009) Red blood cell deformation in microconfined flow. Soft Matter 5:3736–3740CrossRefGoogle Scholar
  185. Tomita M et al (1999) E-CELL: software environment for whole-cell simulation. Bioinformatics 15:72–84CrossRefGoogle Scholar
  186. 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 30:653–674zbMATHCrossRefGoogle Scholar
  187. Tsai T, Miksis MJ (1994) Dynamics of a drop in a constricted capillary tube. J Fluid Mech 274:197–217MathSciNetzbMATHCrossRefGoogle Scholar
  188. 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 61:1187–1195CrossRefGoogle Scholar
  189. Van Hirtum A, Wu B, Gao H, Luo XJEJoM-BF (2017) Constricted channel flow with different cross-section shapes. Eur J Mech-B/Fluids 63:1–8MathSciNetzbMATHCrossRefGoogle Scholar
  190. Vazquez RM et al (2015) An optofluidic constriction chip for monitoring metastatic potential and drug response of cancer cells. Integr Biol 7:477–484CrossRefGoogle Scholar
  191. Vogel MJ, Ehrhard P, Steen PH (2005) The electroosmotic droplet switch: countering capillarity with electrokinetics. Proc Natl Acad Sci 102:11974–11979CrossRefGoogle Scholar
  192. 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 130:021012CrossRefGoogle Scholar
  193. Watson KE, Dovi WF, Conhaim RL (2012) Evidence for active control of perfusion within lung microvessels. J Appl Physiol 112:48–53CrossRefGoogle Scholar
  194. Wetzel ED, Tucker CL (2001) Droplet deformation in dispersions with unequal viscosities and zero interfacial tension. J Fluid Mech 426:199–228zbMATHCrossRefGoogle Scholar
  195. Wörner M (2012) Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications. Microfluid Nanofluid 12:841–886CrossRefGoogle Scholar
  196. Wu T, Feng JJ (2013) Simulation of malaria-infected red blood cells in microfluidic channels: passage and blockage. Biomicrofluidics 7:044115CrossRefGoogle Scholar
  197. 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 5:227–230CrossRefGoogle Scholar
  198. Wyss HM (2015) Cell mechanics: combining speed with precision. Biophys J 109:1997CrossRefGoogle Scholar
  199. Xiao L, Liu Y, Chen S, Fu B (2016) Numerical simulation of a single cell passing through a narrow slit. Biomech Model Mechanobiol 15:1655–1667CrossRefGoogle Scholar
  200. Xie Y et al (2016) Probing cell deformability via acoustically actuated bubbles. Small 12:902–910CrossRefGoogle Scholar
  201. Xu J, Attinger D (2008) Drop on demand in a microfluidic chip. J Micromech Microeng 18:065020CrossRefGoogle Scholar
  202. Xu K, Zhu P, Huh C, Balhoff MT (2015) Microfluidic investigation of nanoparticles’ role in mobilizing trapped oil droplets in porous media. Langmuir 31:13673–13679CrossRefGoogle Scholar
  203. 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 25:16739–16753CrossRefGoogle Scholar
  204. Xue C, Wang J, Zhao Y, Chen D, Yue W, Chen J (2015) Constriction channel based single-cell mechanical property characterization. Micromachines 6:1794–1804CrossRefGoogle Scholar
  205. Yap B, Kamm RD (2005) Mechanical deformation of neutrophils into narrow channels induces pseudopod projection and changes in biomechanical properties. J Appl Physiol 98:1930–1939CrossRefGoogle Scholar
  206. Yazdani A, Karniadakis GE (2016) Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction. Soft Matter 12:4339–4351CrossRefGoogle Scholar
  207. Ye T, Phan-Thien N, Lim CT (2016) Particle-based simulations of red blood cells—a review. J Biomech 49:2255–2266CrossRefGoogle Scholar
  208. 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 520:16–21CrossRefGoogle Scholar
  209. 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 3:024001CrossRefGoogle Scholar
  210. Zhang Z, Drapaca C (2016) A critical velocity of squeezing a droplet through a circular constriction: implications on ischemic stroke. Bull Am Phys Soc 61Google Scholar
  211. 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 14:2576–2584CrossRefGoogle Scholar
  212. 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 112:6068–6073Google Scholar
  213. Zhang Z, Chen X, Xu J (2015b) Entry effects of droplet in a micro confinement: Implications for deformation-based circulating tumor cell microfiltration. Biomicrofluidics 9:024108CrossRefGoogle Scholar
  214. 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 expositionGoogle Scholar
  215. 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 21:146CrossRefGoogle Scholar
  216. Zhang Z, Drapaca C, Chen X, Xu J (2017b) Droplet squeezing through a narrow constriction: minimum impulse and critical velocity. Phys Fluids 29:072102CrossRefGoogle Scholar
  217. 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. CrossRefGoogle Scholar
  218. Zhao Y et al (2015) Simultaneous characterization of instantaneous Young’s modulus and specific membrane capacitance of single cells using a microfluidic system. Sensors 15:2763–2773CrossRefGoogle Scholar
  219. Zhao Y et al (2016) Single-cell electrical phenotyping enabling the classification of mouse tumor samples. Sci Rep 6:19487CrossRefGoogle Scholar
  220. 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 488–491Google Scholar
  221. Zheng Y, Shojaei-Baghini E, Azad A, Wang C, Sun Y (2012) High-throughput biophysical measurement of human red blood cells. Lab Chip 12:2560–2567CrossRefGoogle Scholar
  222. Zhou C, Yue P, Feng JJ (2006) Formation of simple and compound drops in microfluidic devices. Phys Fluids 18:092105CrossRefGoogle Scholar
  223. Zhou C, Yue P, Feng JJ (2007) Simulation of neutrophil deformation and transport in capillaries using newtonian and viscoelastic drop models. Ann Biomed Eng 35:766–780CrossRefGoogle Scholar
  224. 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 34:102–109CrossRefGoogle Scholar
  225. Zinchenko AZ, Davis RH (2006) A boundary-integral study of a drop squeezing through interparticle constrictions. J Fluid Mech 564:227–266MathSciNetzbMATHCrossRefGoogle Scholar
  226. Zinchenko AZ, Davis RH (2008) Squeezing of a periodic emulsion through a cubic lattice of spheres. Phys Fluids 20:040803zbMATHCrossRefGoogle Scholar
  227. Zinchenko AZ, Davis RH (2017) Motion of deformable drops through porous media. Annu Rev Fluid Mech 49:71–90MathSciNetzbMATHCrossRefGoogle Scholar
  228. Zolfaghari H, Izbassarov D, Muradoglu M (2017) Simulations of viscoelastic two-phase flows in complex geometries. Comput Fluids 156:548–561MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Engineering Science and MechanicsThe Pennsylvania State UniversityState CollegeUSA
  2. 2.Department of Mechanical and Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

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