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Flow-induced segregation in confined multicomponent suspensions: effects of particle size and rigidity

  • Amit Kumar (a1), Rafael G. Henríquez Rivera (a1) and Michael D. Graham (a1)


The effects of particle size and rigidity on segregation behaviour in confined simple shear flow of binary suspensions of fluid-filled elastic capsules are investigated in a model system that resembles blood. We study this problem with direct simulations as well as with a master equation model that incorporates two key sources of wall-normal particle transport: wall-induced migration and hydrodynamic pair collisions. The simulation results indicate that, in a mixture of large and small particles with equal capillary numbers, the small particles marginate, while the large particles antimarginate in their respective dilute suspensions. Here margination refers to localization of particles near walls, while antimargination refers to the opposite. In a mixture of particles with equal size and unequal capillary number, the stiffer particles marginate while the flexible particles antimarginate. The master equation model traces the origins of the segregation behaviour to the size and rigidity dependence of the wall-induced migration velocity and of the cross-stream particle displacements in various types of collisions. In particular, segregation by rigidity, especially at low volume fractions, is driven in large part by heterogeneous collisions, in which the stiff particle undergoes larger displacement. In contrast, segregation by size is driven mostly by the larger wall-induced migration velocity of larger particles. Additionally, a non-local drift-diffusion equation is derived from the master equation model, which provides further insights into the segregation behaviour.


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Abbitt, K. B. & Nash, G. B. 2003 Rheological properties of the blood influencing selectin-mediated adhesion of flowing leukocytes. Am. J. Physiol. Heart Circ. Physiol. 285 (1), H229H240.
Barbee, J. H. & Cokelet, G. R. 1971 The Fahraeus effect. Microvasc. Res. 3 (1), 616.
Barthes-Biesel, D. 2011 Modelling the motion of capsules in flow. Curr. Opin. Colloid Interface Sci. 16, 312.
Barthes-Biesel, D. & Chhim, V. 1981 The constitutive equation of a dilute suspension of spherical microcapsules. Intl J. Multiphase Flow 7 (5), 493505.
Barthes-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211222.
Beale, J. T. & Lai, M. C. 2001 A method for computing nearly singular integrals. SIAM J. Numer. Anal. 38 (6), 19021925.
Bird, G. A. 1978 Monte Carlo simulation of gas flows. Annu. Rev. Fluid Mech. 10 (1), 1131.
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press.
Charrier, J. M., Shrivastava, S. & Wu, R. 1989 Free and constrained inflation of elastic membranes in relation to thermoforming: non-axisymmetric problems. J. Strain Anal. Engng Design 24, 5574.
Crowl, L. & Fogelson, A. L. 2011 Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions. J. Fluid Mech. 676, 348375.
Da Cunha, F. R. & Hinch, E. J. 1996 Shear-induced dispersion in a dilute suspension of rough spheres. J. Fluid Mech. 309 (1), 211223.
Drazer, G., Koplik, J., Khusid, B. & Acrivos, A. 2002 Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions. J. Fluid Mech. 460, 307335.
Eckstein, E. C. & Belgacem, F. 1991 Model of platelet transport in flowing blood with drift and diffusion terms. Biophys. J. 60, 5369.
Fedosov, D. A., Fornleitner, J. & Gompper, G. 2012 Margination of white blood cells in microcapillary flow. Phys. Rev. Lett. 108 (2), 028104.
Firrell, J. C. & Lipowsky, H. H. 1989 Leukocyte margination and deformation in mesenteric venules of rat. Am. J. Physiol. Heart Circ. Physiol. 256 (6), H1667H1674.
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19, 023301.
Freund, J. B. & Shapiro, B. 2012 Transport of particles by magnetic forces and cellular blood flow in a model microvessel. Phys. Fluids 24, 051904.
Fung, Y. C. 1996 Biodynamics: Circulation. Springer.
Gardiner, C. W. 2004 Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences. Springer.
Glenister, F. K., Coppel, R. L., Cowman, A. F., Mohandas, N. & Cooke, B. M. 2002 Contribution of parasite proteins to altered mechanical properties of malaria-infected red blood cells. Blood 99 (3), 10601063.
Goldsmith, H. L. & Spain, S. 1984 Margination of leukocytes in blood flow through small tubes. Microvasc. Res. 27 (2), 204222.
Helsing, J. & Ojala, R. 2008 On the evaluation of layer potentials close to their sources. J. Comput. Phys. 227 (5), 28992921.
Hernandez-Ortiz, J. P., de Pablo, J. J. & Graham, M. D. 2007 Fast computation of many-particle hydrodynamic and electrostatic interactions in a confined geometry. Phys. Rev. Lett. 98, 140602.
Hou, H. W., Bhagat, A. A. S., Chong, A. G. L., Mao, P., Tan, K. S. W., Han, J. & Lim, C. T. 2010 Deformability based cell margination: a simple microfluidic design for malaria-infected erythrocyte separation. Lab on a Chip 10, 26052613.
Ivanov, M. S. & Gimelshein, S. F. 1998 Computational hypersonic rarefied flows. Annu. Rev. Fluid Mech. 30 (1), 469505.
Jain, A. & Munn, L. L. 2009 Blood cell interactions and segregation in flow. PLos ONE 4, e7104.
Kim, S., Ong, P. K., Yalcin, O., Intaglietta, M. & Johnson, P. C. 2009 The cell-free layer in microvascular blood flow. Biorheology 46 (3), 181189.
Klöckner, A., Barnett, A., Greengard, L. & O’Neil, M. 2013 Quadrature by expansion: a new method for the evaluation of layer potentials. J. Comput. Phys. 252, 332349.
Koura, K. 1986 Null-collision technique in the direct-simulation Monte Carlo method. Phys. Fluids 29, 35093511.
Kumar, A. & Graham, M. D. 2011 Segregation by membrane rigidity in flowing binary suspensions of elastic capsules. Phys. Rev. E 84, 066316.
Kumar, A. & Graham, M. D. 2012a Accelerated boundary integral method for multiphase flow in non-periodic geometries. J. Comput. Phys. 231, 66826713.
Kumar, A. & Graham, M. D. 2012b Margination and segregation in confined flows of blood and other multicomponent suspensions. Soft Matt. 8, 1053610548.
Kumar, A. & Graham, M. D. 2012c Mechanism of margination in confined flows of blood and other multicomponent suspensions. Phys. Rev. Lett. 109, 108102.
Kumar, A. & Higdon, J. J. L. 2010 Origins of the anomalous stress behaviour in charged colloidal suspensions under shear. Phys. Rev. E 82, 051401.
Lac, E., Morel, A. & Barthès-Biesel, D. 2007 Hydrodynamic interaction between two identical capsules in simple shear flow. J. Fluid Mech. 573, 149169.
Lipowsky, H. H. 2013 In vivo studies of blood rheology in the microcirculation in an in vitro world: past, present and future. Biorheology 50, 316.
Loomis, K., McNeeley, K. & Bellamkonda, R. V. 2010 Nanoparticles with targeting, triggered release, and imaging functionality for cancer applications. Soft Matt. 7 (3), 839856.
Lopez, M. & Graham, M. D. 2007 Shear-induced diffusion in dilute suspensions of spherical or nonspherical particles: effects of irreversibility and symmetry breaking. Phys. Fluids 19, 073602.
Lyon, M. K. & Leal, L. G. 1998 An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 2. Bidisperse systems. J. Fluid Mech. 363, 5777.
Ma, H. & Graham, M. D. 2005 Theory of shear-induced migration in dilute polymer solutions near solid boundaries. Phys. Fluids 17, 083103.
Meng, Q. & Higdon, J. J. L. 2008 Large scale dynamic simulation of plate-like particle suspensions. Part 2. Brownian simulation. J. Rheol. 52, 3765.
Metsi, E. 2000 Large scale simulation of bidisperse emulsions and foams. PhD thesis, University of Illinois at Urbana-Champaign.
Narsimhan, V., Zhao, H. & Shaqfeh, E. S. G. 2013 Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded Couette flow at zero Reynolds number. Phys. Fluids 25, 061901.
Nash, G. B., Watts, T., Thornton, C. & Barigou, M. 2008 Red cell aggregation as a factor influencing margination and adhesion of leukocytes and platelets. Clin. Hemorheol. Microcirc. 39 (1), 303310.
Pine, D. J., Gollub, J. P., Brady, J. F. & Leshansky, A. M. 2005 Chaos and threshold for irreversibility in sheared suspensions. Nature 438 (7070), 9971000.
Popel, A. S. & Johnson, P. C. 2005 Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37, 4369.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Pozrikidis, C. 2006 Interception of two spheroidal particles in shear flow. J. Non-Newtonian Fluid Mech. 136 (1), 5063.
Pranay, P., Henríquez-Rivera, R. G. & Graham, M. D. 2012 Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids. Phys. Fluids 24, 061902.
Rahimian, A., Lashuk, I., Veerapaneni, S., Chandramowlishwaran, A., Malhotra, D., Moon, L., Sampath, R., Shringarpure, A., Vetter, J. & Vuduc, R. et al. 2010a Petascale direct numerical simulation of blood flow on 200K cores and heterogeneous architectures. In Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 111. IEEE Computer Society.
Rahimian, A., Veerapaneni, S. K. & Biros, G. 2010b Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method. J. Comput. Phys. 229, 64666484.
Reasor, D. A., Mehrabadi, M., Ku, D. N. & Aidun, C. K. 2012 Determination of critical parameters in platelet margination. Ann. Biomed. Engng 41, 238249.
Semwogerere, D. & Weeks, E. R. 2008 Shear-induced particle migration in binary colloidal suspensions. Phys. Fluids 20, 043306.
Shauly, A., Wachs, A. & Nir, A. 1998 Shear-induced particle migration in a polydisperse concentrated suspension. J. Rheol. 42, 13291348.
Sherwood, J. D., Risso, F., Collé-Paillot, F., Edwards-Lévy, F. & Lévy, M. C. 2003 Rates of transport through a capsule membrane to attain Donnan equilibrium. J. Colloid Interface Sci. 263, 202212.
Shevkoplyas, S. S., Yoshida, T., Munn, L. L. & Bitensky, M. W. 2005 Biomimetic autoseparation of leukocytes from whole blood in a microfluidic device. Anal. Chem. 77, 933937.
Skalak, R., Ozkaya, N. & Skalak, T. C. 1989 Biofluid mechanics. Annu. Rev. Fluid Mech. 21, 167204.
Smart, J. R. & Leighton, D. T. 1991 Measurement of the drift of a droplet due to the presence of a plane. Phys. Fluids A 3, 2128.
Sun, C., Migliorini, C. & Munn, L. L. 2003 Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. Biophys. J. 85 (1), 208222.
Tan, J., Thomas, A. & Liu, Y. 2012 Influence of red blood cells on nanoparticle targeted delivery in microcirculation. Soft Matt. 8, 19341946.
Tangelder, G. J., Teirlinck, H. C., Slaaf, D. W. & Reneman, R. S. 1985 Distribution of blood platelets flowing in arterioles. Am. J. Physiol. Heart Circ. Physiol. 248 (3), H318H323.
Truskey, G. A., Yuan, F. & Katz, D. F. 2004 Transport Phenomena in Biological Systems. Prentice Hall.
Ying, L., Biros, G. & Zorin, D. 2006 A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. J. Comput. Phys. 219 (1), 247275.
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, 37263744.
Zhao, H. & Shaqfeh, E. S. G. 2011 Shear-induced platelet margination in a microchannel. Phys. Rev. E 83, 061924.
Zhao, H., Shaqfeh, E. S. G. & Narsimhan, V. 2012 Shear-induced particle migration and margination in a cellular suspension. Phys. Fluids 24 (1), 11902.
Zurita-Gotor, M., Blawzdziewicz, J. & Wajnryb, E. 2007 Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres. J. Fluid Mech. 592, 447470.
Zurita-Gotor, M., Blawzdziewicz, J. & Wajnryb, E. 2012 Layering instability in a confined suspension flow. Phys. Rev. Lett. 108 (6), 68301.
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