Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-55wx7 Total loading time: 0.274 Render date: 2021-02-27T21:54:39.207Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Pressure-driven flow of a vesicle through a square microchannel

Published online by Cambridge University Press:  27 December 2018

Joseph M. Barakat
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Shamim M. Ahmmed
Affiliation:
Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Siva A. Vanapalli
Affiliation:
Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Eric S. G. Shaqfeh
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
Corresponding
E-mail address:

Abstract

The relative velocity and extra pressure drop of a single vesicle flowing through a square microchannel are quantified via boundary element simulations, lubrication theory and microfluidic experiments. The vesicle is modelled as a fluid sac enclosed by an inextensible, fluidic membrane with a negligible bending stiffness. All results are parametrized in terms of the vesicle sphericity (i.e. the reduced volume) and flow confinement (i.e. the ratio of the vesicle radius to the channel hydraulic radius). Direct comparison is made to previous studies of vesicle flow through circular tubes, revealing several distinct features of the square-channel geometry. Firstly, fluid in the suspending medium bypasses the vesicle through the corners of the channel, which in turn reduces the dissipation created by the vesicle. Secondly, the absence of rotational symmetry about the channel axis permits surface circulation in the membrane (tank treading), which in turn reduces the vesicle’s speed. At very high confinement, both theory and experiment indicate that the vesicle’s speed can be reduced below the mean speed of the suspending fluid through this mechanism. Finally, the contact area for lubrication is greatly reduced in the square-duct geometry, which in turn weakens the stress singularity predicted by lubrication theory. This fact directly leads to a breakdown of the lubrication approximation at low flow confinement, as verified by comparison to boundary element simulations. Since the only distinct property assumed of the membrane is its ability to preserve surface area locally, it is expected that the results of this study are applicable to other types of soft particles with immobilized surfaces (e.g. Pickering droplets, gel beads and biological cells).

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.

References

Abkarian, M., Faivre, M. & Stone, H. A. 2006 High-speed microfluidic differential manometer for cellular-scale hydrodynamics. Proc. Natl Acad. Sci. USA 103 (3), 538542.CrossRefGoogle ScholarPubMed
Ahmmed, S. M., Suteria, N. S., Garbin, V. & Vanapalli, S. A. 2018 Hydrodynamic mobility of confined polymeric particles, vesicles and cancer cells in a square microchannel. Biomicrofluidics 12 (1), 014114.CrossRefGoogle Scholar
Angelova, M. I., Soléau, S., Méléard, P. & Faucon, F. 1992 Preparation of giant vesicles by external AC electric fields: kinetics and applications. Prog. Colloid. Polym. Sci. 89, 127131.CrossRefGoogle Scholar
Barakat, J. M.2018 Microhydrodynamics of vesicles in channel flow. PhD thesis, Stanford University.Google Scholar
Barakat, J. M. & Shaqfeh, E. S. G. 2018a Stokes flow of vesicles in a circular tube. J. Fluid Mech. 851, 606635.CrossRefGoogle Scholar
Barakat, J. M. & Shaqfeh, E. S. G. 2018b The steady motion of a closely fitting vesicle in a tube. J. Fluid Mech. 835, 721761.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Brenner, H. 1970 Pressure drop due to the motion of neutrally buoyant particles in duct flows. J. Fluid Mech. 10 (4), 641660.CrossRefGoogle Scholar
Brenner, H. 1971 Pressure drop due to the motion of neutrally buoyant particles in duct flows. Part II. Spherical droplets and bubbles. Ind. Engng Chem. Fundam. 10 (4), 537543.CrossRefGoogle Scholar
Brenner, H. & Happel, J. 1958 Slow viscous flow past a sphere in a cylindrical tube. J. Fluid Mech. 4 (2), 195213.CrossRefGoogle Scholar
Bruinsma, R. 1996 Rheology and shape transitions of vesicles under capillary flow. Physica A 234 (1–2), 249270.CrossRefGoogle Scholar
Byun, S., Son, S., Amodei, D., Cermak, N., Shaw, J., Kang, J. H., Hecht, V. C., Winslow, M. M., Jacks, T., Mallick, P. & Manalis, S. R. 2013 Characterizing deformability and surface friction of cancer cells. Proc. Natl Acad. Sci. USA 110 (19), 75807585.CrossRefGoogle ScholarPubMed
Chen, T. C. & Skalak, R. 1970 Stokes flow in a cylindrical tube containing a line of spheroidal particles. Appl. Sci. Res. 22 (1), 403441.CrossRefGoogle Scholar
Dahl, J. B., Lin, J. M. G., Muller, S. J. & Kumar, S. 2015 Microfluidic strategies for understanding the mechanics of cells and cell-mimetic systems. Annu. Rev. Chem. Biomol. Engng 6, 293317.CrossRefGoogle ScholarPubMed
Dahl, J. B., Narsimhan, V., Gouveia, B., Kumar, S., Shaqfeh, E. S. G. & Muller, S. 2016 Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow. Soft Matt. 12, 37873796.CrossRefGoogle ScholarPubMed
Evans, E. & Needham, D. 1986 Giant vesicle bilayers composed of mixtures of lipids, cholesterol and polypeptides: thermomechanical and (mutual) adherence properties. Faraday Disc. Chem. Soc. 81, 267280.CrossRefGoogle Scholar
Evans, E. & Needham, D. 1987 Physical properties of surfactant bilayer membranes: thermal transitions, elasticity, rigidity, cohesion and colloidal interactions. J. Phys. Chem. 91 (16), 42194228.CrossRefGoogle Scholar
Evans, E. & Yeung, A. 1994 Hidden dynamics in rapid changes of bilayer shape. Chem. Phys. Lipids. 73, 3956.CrossRefGoogle Scholar
Goldsmith, H. L. & Mason, S. G. 1962 The flow of suspensions through tubes. Part I. Single spheres, rods, and discs. J. Colloid Sci. 17 (5), 448476.CrossRefGoogle Scholar
Goldsmith, H. L. & Skalak, R. 1975 Hemodynamics. Annu. Rev. Fluid Mech. 7 (1), 213247.CrossRefGoogle Scholar
Groisman, A., Enzelberger, M. & Quake, S. R. 2003 Microfluidic memory and control devices. Science 300 (5621), 955958.CrossRefGoogle ScholarPubMed
Halpern, D. & Secomb, T. W. 1989 The squeezing of red blood cells through capillaries with near-minimal diameters. J. Fluid Mech. 203, 381400.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5 (2), 317328.CrossRefGoogle Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28c (11), 693703.CrossRefGoogle Scholar
Hochmuth, R. M. & Sutera, S. P. 1970 Spherical caps in low Reynolds-number tube flow. Chem. Engng Sci. 25 (4), 593604.CrossRefGoogle Scholar
Khan, Z. S., Kamyabi, N., Hussain, F. & Vanapalli, S. A. 2017 Passage times and friction due to flow of confined cancer cells, drops, and deformable particles in a microfluidic channel. Conv. Sci. Phys. Onc. 3 (2), 024001.Google Scholar
Khan, Z. S. & Vanapalli, S. A. 2013 Probing the mechanical properties of brain cancer cells using a microfluidic cell squeezer device. Biomicrofluidics 7 (1), 011806.CrossRefGoogle ScholarPubMed
Kreyszig, E. 1959 Differential Geometry. Dover.CrossRefGoogle Scholar
Lighthill, M. J. 1968 Pressure-forcing of tightly fitting pellets along fluid-filled elastic tubes. J. Fluid Mech. 34 (1), 113143.CrossRefGoogle Scholar
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395419.CrossRefGoogle Scholar
Marmottant, P. & Hilgenfeldt, S. 2003 Controlled vesicle deformation and lysis by single oscillating bubbles. Nature 423 (6936), 153156.CrossRefGoogle ScholarPubMed
O’Neill, M. E. & Stewartson, K. 1967 On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech. 27, 705724.CrossRefGoogle Scholar
Pommella, A., Brooks, N. J., Seddon, J. M. & Garbin, V. 2015 Selective flow-induced vesicle rupture to sort by membrane mechanical properties. Sci. Rep. 5 (1), 13163.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Pries, A. R., Neuhaus, D. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Physiol. 263 (6), H1770H1778.Google ScholarPubMed
Quéguiner, C. & Barthès-Biesel, D. 1997 Axisymmetric motion of capsules through cylindrical channels. J. Fluid Mech. 348, 349376.CrossRefGoogle Scholar
Ratulowski, J. & Chang, H. C. 1989 Transport of gas bubbles in capillaries. Phys. Fluids A 1 (1), 16421655.CrossRefGoogle Scholar
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2005 A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: the sedimentation of fibers. Phys. Fluids 17 (3), 3301.CrossRefGoogle Scholar
Savin, T., Bandi, M. M. & Mahadevan, L. 2016 Pressure-driven occlusive flow of a confined red blood cell. Soft Matt. 12 (2), 562573.CrossRefGoogle ScholarPubMed
Secomb, T. W., Skalak, R., Oozkaya, N. & Gross, J. F. 1986 Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163, 405423.CrossRefGoogle Scholar
Sharei, A., Zoldan, J., Adamo, A., Sim, W. Y., Cho, N., Jackson, E., Mao, S., Schneider, S., Han, M.-J., Lytton-Jean, A., Basto, P. A., Jhunjhunwala, S., Lee, J., Heller, D. A., Kang, J. W., Hartoularos, G. C., Kim, K.-S., Anderson, D. G., Langer, R. & Jensen, K. F. 2013 A vector-free microfluidic platform for intracellular delivery. Proc. Natl Acad. Sci. USA 110 (6), 20822087.CrossRefGoogle ScholarPubMed
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245264.CrossRefGoogle ScholarPubMed
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77 (3), 9771026.CrossRefGoogle Scholar
Sutera, S. P. & Skalak, R. 1993 The history of Poiseuille’s law. Annu. Rev. Fluid Mech. 25 (1), 120.CrossRefGoogle Scholar
Tözeren, H. & Skalak, R. 1978 The steady flow of closely fitting incompressible elastic spheres in a tube. J. Fluid Mech. 87 (1), 116.CrossRefGoogle Scholar
Trozzo, R., Boedec, G., Leonetti, M. & Jaeger, M. 2015 Axisymmetric boundary element method for vesicles in a capillary. J. Comput. Phys. 289, 6282.CrossRefGoogle Scholar
Tullock, D. L., Phan, T. N. & Graham, A. L. 1992 Boundary element simulations of spheres settling in circular, square and triangular conduits. Rheol. Acta 31 (2), 139150.CrossRefGoogle Scholar
Vanapalli, S. A., Banpurkar, A. G., van den Ende, D., Duits, M. H. G. & Mugele, F. 2009 Hydrodynamic resistance of single confined moving drops in rectangular microchannels. Lab on a Chip 9 (7), 982990.CrossRefGoogle ScholarPubMed
Vanapalli, S. A., Van den Ende, D., Duits, M. H. G. & Mugele, F. 2007 Scaling of interface displacement in a microfluidic comparator. Appl. Phys. Lett. 90 (1), 114109.CrossRefGoogle Scholar
Vitkova, V., Mader, M. & Podgorski, T. 2004 Deformation of vesicles flowing through capillaries. Europhys. Lett. 68 (3), 398404.CrossRefGoogle Scholar
Vuong, S. M. & Anna, S. L. 2012 Tuning bubbly structures in microchannels. Biomicrofluidics 6 (2), 022004.CrossRefGoogle ScholarPubMed
Wang, H. & Skalak, R. 1969 Viscous flow in a cylindrical tube containing a line of spherical particles. J. Fluid Mech. 38, 7596.CrossRefGoogle Scholar
White, F. M. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.Google Scholar
Wong, H., Morris, S. & Radke, C. J. 1992 Three-dimensional menisci in polygonal capillaries. J. Colloid Interface Sci. 148 (2), 317336.CrossRefGoogle Scholar
Wong, H., Radke, C. J. & Morris, S. 1995a The motion of long bubbles in polygonal capillaries. Part 1. Thin films. J. Fluid Mech. 292, 7194.CrossRefGoogle Scholar
Wong, H., Radke, C. J. & Morris, S. 1995b The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow. J. Fluid Mech. 292, 95110.CrossRefGoogle Scholar
Xia, Y. & Whitesides, G. M. 1998 Soft lithography. Annu. Rev. Mater. Sci. 28, 153184.CrossRefGoogle Scholar
Zhao, H., Isfahani, A. H. G., Olson, L. N. & Freund, J. B. 2010 A spectral boundary integral method for flowing blood cells. J. Comput. Phys. 229 (1), 37263744.CrossRefGoogle Scholar
Zhao, H. & Shaqfeh, E. S. G. 2013 The dynamics of a non-dilute vesicle suspension in a simple shear flow. J. Fluid Mech. 725, 709731.CrossRefGoogle Scholar
Zhao, H., Spann, A. P. & Shaqfeh, E. S. G. 2011 The dynamics of a vesicle in a wall-bound shear flow. Phys. Fluids 23, 121901.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 33
Total number of PDF views: 407 *
View data table for this chart

* Views captured on Cambridge Core between 27th December 2018 - 27th February 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Pressure-driven flow of a vesicle through a square microchannel
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Pressure-driven flow of a vesicle through a square microchannel
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Pressure-driven flow of a vesicle through a square microchannel
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *