Hydrodynamic interaction between two red blood cells in simple shear flow: its impact on the rheology of a semi-dilute suspension. (English) Zbl 1311.76155
Summary: Blood is a suspension of red blood cells (RBCs) and its rheology is important when discussing the physiology of the cardiovascular system. In this study, we performed a numerical investigation of the rheological properties of an RBC suspension from the dilute to semi-dilute regime. RBCs were modelled as a capsule with a two-dimensional hyperelastic membrane. Large deformation of the thin membrane was calculated by a finite element method. Due to the small size of the RBC, fluid motion around the RBC was assumed to follow Stokes flow and was solved by a boundary element method. In the dilute limit, cell-cell interactions were omitted and the bulk stress of the suspension was calculated by the stresslet generated on a single RBC. Interestingly, the effective shear viscosity of the dilute suspension decreased with increasing viscosity of the internal liquid. In the semi-dilute regime, cells can be considered as showing pairwise interactions. The effective shear viscosity of the semi-dilute suspension shows a quadratic increase with respect to the volume fraction. These findings are important for understanding the complex phenomena of blood rheology.
MSC:
| 76Z05 | Physiological flows |
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74K15 | Membranes |
| 76T20 | Suspensions |
| 92C35 | Physiological flow |
References:
| [1] | Pries AR, Secomb TW (2003) Rheology of the microcirculation. Clin Hemorheol Microcirc 29:143-148 |
| [2] | Baskurt OK, Meiselman HJ (2003) Blood rheology and hemodynamics. Semin Thromb Hemost 29:435-450 · doi:10.1055/s-2003-44551 |
| [3] | Merrill EW, Cokelet GR, Gilliland ER (1963) The rheology of human blood measurment near and at zero shear rate. J Rheol 7:303-317 · doi:10.1122/1.548959 |
| [4] | Freund JB, Orescanin MM (2011) Cellular flow in a small blood vessel. J Fluid Mech 671:466-490 · Zbl 1225.76315 · doi:10.1017/S0022112010005835 |
| [5] | Pan W, Fedosov DA, Caswell B, Kamiadakis GE (2011) The motion of ellipsoidal particles immersed in a viscous fluid. Microvasc Res 82:163-179 · doi:10.1016/j.mvr.2011.05.006 |
| [6] | Zhao H, Isfahani AHG, Olson LK, Freund JB (2010) A spectral boundary integral method for flowing blood cells. J Comput Phys 229:3726-3744 · Zbl 1186.92013 · doi:10.1016/j.jcp.2010.01.024 |
| [7] | Batchelor GK (1970) The stress system in a suspension of force-free particles. J Fluid Mech 41:545-570 · Zbl 0193.25702 · doi:10.1017/S0022112070000745 |
| [8] | Batchelor GK, Green JT (1972) The determination of the bulk stress in a suspension of spherical particles to order \[c^2\] c2. J Fluid Mech 56:401-427 · Zbl 0246.76108 |
| [9] | Batchelor GK (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech 83:97-117 · doi:10.1017/S0022112077001062 |
| [10] | Barthés-Biesel, D.; Walter, J.; Salsac, AV; Pozrikidis, C. (ed.), Computational hydrodynamics of capsules and biological cells (2010), Cambridge · Zbl 1446.92003 |
| [11] | Pozrikidis C (1992) Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, Cambridge · Zbl 0772.76005 · doi:10.1017/CBO9780511624124 |
| [12] | Skalak R, Tozeren A, Zarda RP, Chien S (1973) Strain energy function of red blood cell membranes. Biophys J 13:245-264 · doi:10.1016/S0006-3495(73)85983-1 |
| [13] | Walter J, Salsac AV, Barthès-Biesel D (2011) Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shape. J Fluid Mech 676:318-347 · Zbl 1241.76127 · doi:10.1017/S0022112011000486 |
| [14] | Omori T, Imai Y, Yamaguchi T, Ishikawa T (2012) Reorientation of a non-spherical capsule in creeping shear flow. Phys Rev Lett 108:138102 · doi:10.1103/PhysRevLett.108.138102 |
| [15] | Omori T, Ishikawa T, Imai Y, Yamaguchi T (2013) Membrane tension of red blood cells pairwisely interacting in simple shear flow. J Biomech 46:548-553 · doi:10.1016/j.jbiomech.2012.09.017 |
| [16] | Omori T, Ishikawa T, Imai Y, Yamaguchi T (2013) Shear-induced diffusion of red blood cells in a semi-dilute suspension. J Fluid Mech 724:154-174 · Zbl 1287.76249 · doi:10.1017/jfm.2013.159 |
| [17] | Foessel E, Walter J, Salsac AV, Barthès-Biesel D (2011) Influence of internal viscosity on the deformation of a spherical capsule in a simple shear flow. J Fluid Mech 672:477-486 · Zbl 1225.74035 · doi:10.1017/S0022112011000280 |
| [18] | Pedley TJ (1980) The fluid mechanics of large blood vessels. Cambridge University Press, Cambridge · Zbl 0449.76100 · doi:10.1017/CBO9780511896996 |
| [19] | Evans EA, Fung YC (1972) Improved measurements of the erythrocyte geometry. Microvasc Res 4:335-347 · doi:10.1016/0026-2862(72)90069-6 |
| [20] | Jeffery GB (1922) The motion of ellipsoidal particles Immersed in a viscous fluid. Proc R Soc Lond A 102:161-179 · JFM 49.0748.02 · doi:10.1098/rspa.1922.0078 |
| [21] | Ramanujan S, Pozrikidis C (1998) Deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J Fluid Mech 361:117-143 · Zbl 0921.76058 · doi:10.1017/S0022112098008714 |
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