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Numerical Simulation of Red Blood Cell Suspensions Behind a Moving Interface in a Capillary

Published online by Cambridge University Press:  09 August 2018

Shihai Zhao*
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204, USA.
Tsorng-Whay Pan*
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204, USA.
*
*Corresponding author.Email address:[email protected]
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Abstract

Computational modeling and simulation are presented on the motion of red blood cells behind a moving interface in a capillary. The methodology is based on an immersed boundary method and the skeleton structure of the red blood cell (RBC) membrane is modeled as a spring network. As by the nature of the problem, the computational domain is moving with either a designated RBC or an interface in an infinitely long two-dimensional channel with an undisturbed flow field in front of the computational domain. The tanking-treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation purpose. We then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary, which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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References

[1] Chang, H.-C., Zhou, R., Capillary penetration failure of blood suspensions, J. Colloid Interface Sci. 287 (2005), pp. 647656.Google Scholar
[2] Zhou, R., Gordon, J., Palmer, A.F., Chang, H.-C., Role of erythrocyte deformability during capillary wetting, Biotechnology and Bioengineering 93 (2006), pp. 201211.Google ScholarPubMed
[3] Cristini, V., Kassab, G.S., Computer odeling of red blood cell rheology in the microcirculation: a brief overview., Ann. Biomed. Eng. 33 (2005), pp. 17241727.Google Scholar
[4] Pozrikidis, C., Modeling and simulation of capsules and biological cells. Chapman & Hall/CRC: Boca Raton, 2003.Google Scholar
[5] Peskin, C.S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220252.Google Scholar
[6] Peskin, C.S., The immersed boundary method, Acta Numer., 11 (2002), pp. 479517.Google Scholar
[7] Peskin, C.S., McQueen, D.M., Modeling prosthetic heart valves for numerical analysis of blood flow in the heart, J. Comput. Phys., 37 (1980), pp. 11332.Google Scholar
[8] Eggleton, C., Popel, A., Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10 (1998), pp. 18341845.Google Scholar
[9] Bagchi, P., Johnson, P., Popel, A., Computational Fluid Dynamic Simulation of Aggregation of Deformable Cells in a Shear Flow, J. Biomech. Eng., 127 (2005), pp. 10701080.Google Scholar
[10] Bagchi, P., Mesoscale simulation of blood flow in small vessels, Biophys. J., 92 (2007), pp. 18581877.Google Scholar
[11] Zhang, J., Johnson, J., Popel, A.S., Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows, Microvasc. Res., 77 (2009), pp. 265272.Google Scholar
[12] Crowl, L.M., Fogelson, A.L., Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells, Int. J. Numer. Meth. Biomed. Engng., 26 (2010), pp. 471487.Google Scholar
[13] Kaoui, B., Harting, J., Misbah, C., Two-dimensional vesicle dynamics under shear flow: Effect of confinement, Phys. Rev. E, 83 (2011), 066319.Google Scholar
[14] Kim, Y., Lai, M.-C., Numerical study of viscosity and inertial effects on tank-treading and tumbling motions of vesicles under shear flow, Phys. Rev. E, 86 (2012), 066321.Google Scholar
[15] Shi, L., Pan, T.-W., Glowinski, R., Deformation of a single blood cell in bounded Poiseuille flows, Phys. Rev. E, 85 (2012), 016307.Google Scholar
[16] Shi, L., Pan, T.-W., Glowinski, R., Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows, Phys. Rev. E, 86 (2012), 056308.Google Scholar
[17] Shi, L., Pan, T.-W., Glowinski, R., Numerical simulation of lateral migration of red blood cells in Poiseuille flows, Int. J. Numer. Methods Fluids, 68 (2012), pp. 13931408.Google Scholar
[18] Tsubota, K., Wada, S., Yamaguchi, T., Simulation study on effects of hematocrit on blood flow properties using particle method, J. Biomech. Sci. Eng., 1 (2006), pp. 159170.Google Scholar
[19] Fedosov, D. A., Caswell, B., Karniadakis, G. E., A multiscale red blood cell model with accurate mechanics, rheology, and dynamics, Biophysical journal, 98 (2010), pp. 22152225.Google Scholar
[20] Wang, T., Pan, T.-W., Xing, Z., Glowinski, R., Numerical simulation of rheology of red blood cell rouleaux in microchannels, Phys. Rev. E, 79 (2009), 041916.CrossRefGoogle ScholarPubMed
[21] Alexeev, A., Verberg, R., Balazs, A.C., Modeling the interactions between deformable capsules rolling on a compliant surface, Soft Matter 2 (2006), pp. 499509.Google Scholar
[22] Glowinski, R., Finite element methods for incompressible viscous flow, in Handbook of Numerical Analysis, Vol. IX, Ciarlet, PG and Lions, JL (Eds.). North-Holland, Amsterdam (2003), pp. 71176.Google Scholar
[23] Chorin, A.J., Hughes, T.J.R., Mccracken, M.F., Marsden, J.E., Product formulas and numerical algorithms, Comm. Pure Appl. Math., 31 (1978), pp. 205256.Google Scholar
[24] Dean, E.J., Glowinski, R., A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow, C.R. Acad. Sc. Paris, Série 1, 325 (1997), pp. 783791.Google Scholar
[25] Dean, E.J., Glowinski, R., Pan, T.-W., A wave equation approach to the numerical simulation of incompressible viscous fluid flow modeled by the NavierStokes equations, in Mathematical and Numerical Aspects of Wave Propagation, JA, De Santo (Ed.). SIAM: Philadelphia (1998), pp. 6574.Google Scholar
[26] Hu, H.H., Joseph, D.D., Crochet, M.J., Direct simulation of fluid particle motions, Theoret. Comput. Fluid Dynamics 3 (1992), pp. 285306.Google Scholar
[27] Pan, T.-W., Glowinski, R., Galdi, G.P., Direct simulation of the motion of a settling ellipsoid in Newtonian fluid, J. Comput. Applied Math., 149 (2002), pp. 7182.Google Scholar