Skip to main content
×
×
Home

Spheres in the vicinity of a bifurcation: elucidating the Zweifach–Fung effect

  • V. DOYEUX (a1), T. PODGORSKI (a1), S. PEPONAS (a1), M. ISMAIL (a1) and G. COUPIER (a1)...
Abstract

The problem of the splitting of a suspension in bifurcating channels divided into two branches of non-equal flow rates is addressed. As has long been observed, in particular in blood flow studies, the volume fraction of particles generally increases in the high-flow-rate branch and decreases in the low-flow-rate branch. In the literature, this phenomenon is sometimes interpreted as the result of some attraction of the particles towards this high-flow-rate branch. In this paper, we focus on the existence of such an attraction through microfluidic experiments and two-dimensional simulations and show clearly that such an attraction does not occur but is, on the contrary, directed towards the low-flow-rate branch. Arguments for this attraction are given and a discussion on the sometimes misleading arguments found in the literature is given. Finally, the enrichment of particles in the high-flow-rate branch is shown to be mainly a consequence of the initial distribution in the inlet branch, which shows necessarily some depletion near the walls.

Copyright
Corresponding author
Email address for correspondence: gwennou.coupier@ujf-grenoble.fr
References
Hide All
Abkarian, M., Faivre, M. & Viallat, A. 2007 Swinging of red blood cells under shear flow. Phys. Rev. Lett. 98, 188302.
Abkarian, M., Lartigue, C. & Viallat, A. 2002 Tank treading and unbinding of deformable vesicles in shear flow: determination of the lift force. Phys. Rev. Lett. 88, 068103.
Angelova, M. I., Soleau, S., Meleard, P., Faucon, J. F. & Bothorel, P. 1992 Preparation of giant vesicles by external AC electric fields: kinetics and applications. Prog. Colloid. Polym. Sci. 89, 127131.
Asmolov, E. S. 2002 The inertial lift on a small particle in a weak-shear parabolic flow. Phys. Fluids 14, 1528.
Audet, D. M. & Olbricht, W. L. 1987 The motion of model cells at capillary bifurcations. Microvasc. Res. 33, 377396.
Bagchi, P. 2007 Mesoscale simulation of blood flow in small vessels. Biophys. J. 92, 18581877.
Balvin, M., Sohn, E., Iracki, T., Drazer, G. & Frechette, J. 2009 Directional locking and the role of irreversible interactions in deterministic hydrodynamics separations in microfluidic devices. Phys. Rev. Lett. 103, 078301.
Barber, J. O., Alberding, J. P., Restrepo, J. M. & Secomb, T. W. 2008 Simulated two-dimensional red blood cell motion, deformation, and partitioning in microvessel bifurcations. Ann. Biomech. Engng 36, 16901698.
Beaucourt, J., Rioual, F., Séon, T., Biben, T. & Misbah, C. 2004 Steady to unsteady dynamics of a vesicle in a flow. Phys. Rev. E 69, 011906.
Biben, T., Farutin, A. & Misbah, C. 2011 Numerical study of 3D vesicles under flow: discovery of new peculiar behaviors. Phys. Rev. E (in press) arXiv:0912.4702.
Bugliarello, G. & Hsiao, G. C. C. 1964 Phase separation in suspensions flowing through bifurcations: a simplified hemodynamic model. Science 143, 469471.
Callens, N., Minetti, C., Coupier, G., Mader, M.-A., Dubois, F., Misbah, C. & Podgorski, T. 2008 Hydrodynamic lift of vesicles under shear flow in microgravity. Europhys. Lett. 83, 24002.
Carr, R. T. & Wickham, L. L. 1990 Plasma skimming in serial microvascular bifurcations. Microvasc. Res. 40, 179190.
Chesnutt, J. K. W. & Marshall, J. S. 2009 Effect of particle collisions and aggregation on red blood cell passage through a bifurcation. Microvasc. Res. 78, 301313.
Chien, S., Tvetenstrand, C. D., Epstein, M. A. & Schmid-Schonbein, G. W. 1985 Model studies on distributions of blood cells at microvascular bifurcations. Am. J. Physiol. Heart Circ. Physiol. 248, H568H576.
Coupier, G., Kaoui, B., Podgorski, T. & Misbah, C. 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20, 111702.
Danker, G. & Misbah, C. 2007 Rheology of a dilute suspension of vesicles. Phys. Rev. Lett. 98, 088104.
Danker, G., Vlahovska, P. M. & Misbah, C. 2009 Vesicles in Poiseuille flow. Phys. Rev. Lett. 102, 148102.
Davis, J. A., Inglis, D. W., Morton, K. J., Lawrence, D. A., Huang, L. R., Chou, S. Y., Sturm, J. C. & Austin, R. H. 2006 Deterministic hydrodynamics: taking blood apart. Proc. Natl Acad. Sci. USA 103, 1477914784.
Dellimore, J. W., Dunlop, M. J. & Canham, P. B. 1983 Ratio of cells and plasma in blood flowing past branches in small plastic channels. Am. J. Physiol. Heart Circ. Physiol. 244, H635H643.
Deschamps, J., Kantsler, V., Segre, E. & Steinberg, V. 2009 Dynamics of a vesicle in general flow. Proc. Natl Acad. Sci. USA 106, 11444.
Ditchfield, R. & Olbricht, W. L. 1996 Effects of particle concentration on the partitioning of suspensions at small divergent bifurcations. J. Biomech. Engng 118, 287294.
Dupire, J., Abkarian, M. & Viallat, A. 2010 Chaotic dynamics of red blood cells in a sinusoidal flow. Phys. Rev. Lett. 104, 168101.
El-Kareh, A. W. & Secomb, T. W. 2000 A model for red blood cell motion in bifurcating microvessels. Intl J. Multiphase Flow 26, 15451564.
Eloot, S., De Bisschop, F. & Verdonck, P. 2004 Experimental evaluation of the migration of spherical particles in three-dimensional Poiseuille flow. Phys. Fluids 16, 22822293.
Enden, G. & Popel, A. S. 1992 A numerical study of the shape of the surface separating flow into branches in microvascular bifurcations. J. Biomech. Engng 114, 398405.
Engl, W., Roche, M., Colin, A., Panizza, P. & Ajdari, A. 2005 Droplet traffic at a simple junction at low capillary numbers. Phys. Rev. Lett. 95, 208304.
Fan, R., Vermesh, O., Srivastava, A., Yen, B., Qin, L., Ahmad, H., Kwong, G. A., Liu, C.-C., Gould, J., Hood, L. & Heath, J. R. 2008 Integrated barcode chips for rapid, multiplexed analysis of proteins in microliter quantities of blood. Nature Biotech. 26, 13731378.
Farutin, A., Biben, T. & Misbah, C. 2010 Analytical progress in the theory of vesicles under linear flow. Phys. Rev. E 81, 061904.
Fenton, B. M., Carr, R. T. & Cokelet, G. R. 1985 Nonuniform red cell distribution in 20 to 100 μm bifurcations. Microvasc. Res. 29, 103126.
Frechette, J. & Drazer, G. 2009 Directional locking and deterministic separation in periodic arrays. J. Fluid Mech. 627, 379401.
Fung, Y. C. 1973 Stochastic flow in capillary blood vessels. Microvasc. Res. 5, 3448.
Fung, Y. C. 1993 Biomechanics: Mechanical Properties of Living Tissues. Springer.
Ghigliotti, G., Biben, T. & Misbah, C. 2010 Rheology of a dilute two-dimensional suspension of vesicles. J. Fluid Mech. 653, 489518.
Girault, V. & Raviart, P.A. 1986 Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms. Springer.
Griggs, A. J., Zinchenko, A. Z. & Davis, R. H. 2007 Low-Reynolds-number motion of a deformable drop between two parallel plane walls. Intl J. Multiphase Flow 33, 182206.
Guibert, R., Fonta, C. & Plouraboue, F. 2010 A new approach to model confined suspensions flows in complex networks: application to blood flow. Trans. Porous Med. 83, 171194.
Hecht, F. & Pironneau, O. 2010 A finite element software for PDEs: freeFEM++. Available at: http://www.freefem.org/.
Inglis, D. W. 2009 Efficient microfluidic particle separation arrays. Appl. Phys. Lett. 94, 013510.
Jäggi, R. D., Sandoz, R. & Effenhauser, C. S. 2007 Microfluidic depletion of red blood cells from whole blood in high-aspect-ratio microchannels. Microfluid Nanofluid 3, 4753.
Janela, J., Lefebvre, A. & Maury, B. 2005 A penalty method for the simulation of fluid-rigid body interaction. In ESAIM: Proc (ed. Cancès, E. & Gerbeau, J.-F.), vol. 14, pp. 115123. ESAIM.
Jousse, F., Farr, R., Link, D. R., Fuerstman, M. J. & Garstecki, P. 2006 Bifurcation of droplet flows within capillaries. Phys. Rev. E 74, 036311.
Kantsler, V., Segre, E. & Steinberg, V. 2008 Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow. Europhys. Lett. 82, 58005.
Kaoui, B., Coupier, G., Misbah, C. & Podgorski, T. 2009 Lateral migration of vesicles in microchannels: effects of walls and shear gradient. Houille Blanche 5, 112119.
Kaoui, B., Ristow, G., Cantat, I., Misbah, C. & Zimmermann, W. 2008 Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow. Phys. Rev. E 77, 021903.
Kersaudy-Kerhoas, M., Dhariwal, R., Desmulliez, M. P. Y. & Jouvet, L. 2010 Hydrodynamic blood plasma separation in microfluidic channels. Microfluid Nanofluid 8, 105114.
Kim, Y. W. & Yoo, J. Y. 2008 The lateral migration of neutrally-buoyant spheres transported through square microchannels. J. Micromech. Microengng 18, 065015.
Lefebvre, A. 2007 Fluid–particle simulations with FreeFem++. In ESAIM: Proc., vol. 18, pp. 120132. ESAIM.
Maury, B. 2009 Numerical analysis of a finite element/volume penalty method. SIAM J. Numer. Anal. 47 (2), 11261148.
Mayrovitz, H. N. & Roy, J. 1983 Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am. J. Physiol. 255, H1031H1038.
McWhirter, J. L., Noguchi, H. & Gompper, G. 2009 Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc. Natl Acad. Sci. USA 106, 60396043.
Mortazavi, S. & Tryggvason, G. 2000 A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid. Mech. 411, 325350.
Noguchi, H. 2010 Dynamic modes of red blood cells in oscillatory shear flow. Phys. Rev. E 81, 061920.
Obrist, D., Weber, B., Buck, A. & Jenny, P. 2010 Red blood cell distribution in simplified capillary networks. Phil. Trans. R. Soc. Lond. A 368, 28972918.
Olla, P. 1997 The lift on a tank-treading ellipsoidal cell in a shear flow. J. Phys. II Paris 7, 15331540.
Pamme, N. 2007 Continuous flow separations in microfluidic devices. Lab Chip 7, 16441659.
Peyla, P. 2007 A deformable object in a microfluidic configuration: a numerical study. Europhys. Lett. 80, 34001.
Podgorski, T., Callens, N., Minetti, C., Coupier, G., Dubois, F. & Misbah, C. 2010 Dynamics of vesicle suspensions in shear flow between walls. Microgravity Sci. Technol. 23, 263270.
Pries, A. R., Ley, K., Claassen, M. & Gaethgens, P. 1989 Red cell distribution at microvascular bifurcations. Microvasc. Res. 38, 81101.
Pries, A. R., Secomb, T. W. & Gaethgens, P. 1996 Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res. 32, 654667.
Risso, F., Collé-Paillot, F. & Zagzoule, M. 2006 Experimental investigation of a bioartificial capsule flowing in a narrow tube. J. Fluid. Mech. 547, 149173.
Roberts, B. W. & Olbricht, W. L. 2003 Flow-induced particulate separations. AIChE J. 49, 28422849.
Roberts, B. W. & Olbricht, W. L. 2006 The distribution of freely suspended particles at microfluidic bifurcations. AIChE J. 52, 199206.
Schindler, M. & Ajdari, A. 2008 Droplet traffic in microfluidic networks: a simple model for understanding and designing. Phys. Rev. Lett. 100, 044501.
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in a Poiseuille flow. J. Fluid Mech. 203, 517524.
Secomb, T. W., Styp-Rekowska, B. & Pries, A. R. 2007 Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann. Biomed. Engng 35, 755765.
Sessoms, D. A., Belloul, M., Engl, W., Roche, M., Courbin, L. & Panizza, P. 2009 Droplet motion in microfluidic networks: hydrodynamic interactions and pressure-drop measurements. Phys. Rev. E 80, 016317.
Svanes, K. & Zweifach, B. W. 1968 Variations in small blood vessel hematocrits produced in hypothermic rats by micro-occlusion. Microvasc. Res. 1, 210220.
Tanaka, H. & Araki, T. 2000 Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics. Phys. Rev. Lett. 85 (6), 13381341.
Vitkova, V., Mader, M.-A., Polack, B., Misbah, C. & Podgorski, T. 2008 Micro–macro link in rheology of erythrocyte and vesicle suspensions. Biophys. J. 95, 3335.
Vlahovska, P. M., Podgorski, T. & Misbah, C. 2009 Vesicles and red blood cells in flow: from individual dynamics to rheology. C. R. Physique 10, 775789.
White, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.
Yang, S., Ündar, A. & Zahn, J. D. 2006 A microfluidic device for continuous, real time blood plasma separation. Lab Chip 6, 871880.
Yang, S. & Zahn, J. D. 2004 Particle separation in microfluidic channels using flow rate control. In Proc. ASME Conf. International Mechanical Engineering Exp Fluids Engineering (IMECE), Anaheim, CA.
Yen, R. T. & Fung, Y. C. 1978 Effect of velocity distribution on red cell distribution in capillary blood vessels. Am. J. Physiol. Heart Circ. Physiol. 235, H251H257.
Yoo, J. Y. & Kim, Y. W. 2010 Two-phase flow laden with spherical particles in a microcapillary. Intl J. Multiphase Flow 36, 460466.
Zheng, S., Liu, J.-Q. & Tai, Y.-C. 2008 Streamline-based microfluidic devices for erythrocytes and leukocytes separation. J. Microelectromech. Syst. 17, 10291038.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed