Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T04:49:18.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Shear-induced diffusion of red blood cells in a semi-dilute suspension

Published online by Cambridge University Press:  29 April 2013

T. Omori ,
T. Ishikawa ,
Y. Imai  and
T. Yamaguchi
T. Omori*
Affiliation:
Department of Biomedical Engineering, Tohoku University, Sendai 980-8579, Miyagi, Japan
T. Ishikawa
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, Sendai 980-8579, Miyagi, Japan
Y. Imai
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, Sendai 980-8579, Miyagi, Japan
T. Yamaguchi
Affiliation:
Department of Biomedical Engineering, Tohoku University, Sendai 980-8579, Miyagi, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The diffusion of red blood cells (RBCs) in blood is important to the physiology and pathology of the cardiovascular system. In this study, we investigate flow-induced diffusion of RBCs in a semi-dilute system by calculating the pairwise interactions between RBCs in simple shear flow. A capsule with a hyperelastic membrane was used to model an RBC. Its deformation was resolved using the finite element method, whereas fluid motion inside and outside the RBC was solved using the boundary element method. The results show that shear-induced RBC diffusion is significantly anisotropic, i.e. the velocity gradient direction component is larger than the vorticity direction. We also found that the motion of RBCs during the interaction is strongly dependent on the viscosity ratio of the internal to external fluid, and the diffusivity decreases monotonically as the viscosity ratio increases. The scaling argument also suggests that the diffusivity is proportional to the shear rate and haematocrit, if the suspension is in a semi-dilute environment and the capillary number is invariant. These fundamental findings are useful to understand transport phenomena in blood flow.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 724 , 10 June 2013 , pp. 154 - 174
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barthés-Biesel, D. & Rallison, J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251–267.Google Scholar
Barthés-Biesel, D., Walter, J. & Salsac, A. V. 2010 Computational hydrodynamics of capsules and biological cells. In Flow-Induced Deformation of Artificial Capsules. Taylor & Francis.Google Scholar
Batchelor, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97–117.Google Scholar
Batchelor, G. K. & Green, J. T. 1972a The determination of the bulk stress in a suspension of spherical particles to order ${c}^{2} $ . J. Fluid Mech. 56, 401–427.Google Scholar
Batchelor, G. K. & Green, J. T. 1972b The hydrodynamic interaction of two small freely moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.CrossRefGoogle Scholar
Chaffey, C. E. & Brenner, H. 1967 A second-order theory for shear deformation of drops. J. Colloid Interface Sci. 24, 258–269.Google Scholar
Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322, 549–560.CrossRefGoogle Scholar
Evans, E. A. & Fung, Y. C. 1972 Improved measurements of the erythrocyte geometry. Microvasc. Res. 4, 335–347.Google Scholar
Foessel, E., Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Influence of internal viscosity on the deformation of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 472–486.CrossRefGoogle Scholar
Goldsmith, H. L. & Karino, T. 1977 Microscope considerations: the motions of individual particles. Ann. N.Y. Acad Sci. 1283, 241–255.Google Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28, 693–703.Google Scholar
Hochmuth, R. M. & Waugh, R. E. 1987 Erythrocyte membrane elasticity and viscosity. Annu. Rev. Physiol. 49, 209–219.CrossRefGoogle ScholarPubMed
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.Google Scholar
Ishikawa, T. & Yamaguchi, T. 2008 Shear-induced fluid-tracer diffusion in a semi-dilute suspension of spheres. Phys. Rev. E 77, 041402.Google Scholar
Lac, E., Morel, A. & Barthès-Biesel, D. 2007 Hydrodynamic interaction between two identical capsules in simple shear flow. J. Fluid Mech. 573, 149–169.Google Scholar
Lima, R., Ishikawa, T., Imai, Y., Takeda, M., Wada, S. & Yamaguchi, T. 2008 Radial dispersion of red blood cells in blood flowing through glass capillaries: the role of hematocrit and geometry. J. Biomech. 41, 2188–2196.Google Scholar
Loewenberg, M. & Hinch, E. J. 1997 Collision of two deformable drops in shear flow. J. Fluid Mech. 338, 299–315.Google Scholar
Omori, T., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2012a Reorientation of a non-spherical capsule in creeping shear flow. Phys. Rev. Lett. 108, 138102.Google Scholar
Omori, T., Ishikawa, T., Barthés-Biesel, D., Salsac, A.-V., Imai, Y. & Yamaguchi, T. 2012b Tension of red blood cell membrane in simple shear flow. Phys. Rev. E 86, 056321.Google Scholar
Omori, T., Ishikawa, T., Barthès-Biesel, D., Salsac, A.-V., Walter, J., Imai, Y. & Yamaguchi, T. 2011 Comparison between spring network models and continuum constitutive laws: application to the large deformation of a capsule in shear flow. Phys. Rev. E 83, 041918.Google Scholar
Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.CrossRefGoogle Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.Google Scholar
Puig-de-Morales-Marinkovic, M., Turner, K. T., Butler, J. P., Fredberg, J. J. & Suresh, S. 2007 Viscoelasticity of the human red blood cell. Am. J. Physiol. Cell Physiol. 293, 597–605.Google Scholar
Ramanujan, S. & Pozrikidis, C. 1998 Deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 361, 117–143.CrossRefGoogle Scholar
Ross, R. & Harker, L. 1976 Hyperlipidemia and atherosclerosis. Science 193, 1094–1100.Google Scholar
Ruggeri, Z. M. 2003 Von Willebrand factor, platelets and endothelial cell interactions. J. Thrombosis Haemostasis 1, 1335–1342.Google Scholar
Saadatmand, M., Ishikawa, T., Matsuki, N., Abdekhodaie, M. J., Imai, Y., Ueno, H. & Yamaguchi, T. 2011 Fluid particle diffusion through high-hematocrit blood flow within a capillary tube. J. Biomech. 44, 170–175.Google Scholar
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264.CrossRefGoogle ScholarPubMed
Tarbell, J. M. 2003 Mass transport in arteries and the localization of atherosclerosis. Annu. Rev. Biomed. Engng 5, 79–118.Google Scholar
Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shape. J. Fluid Mech. 676, 318–347.Google Scholar
Walter, J., Salsac, A.-V., Barthès-Biesel, D. & Tallec, P. L. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Intl J. Numer. Meth. Engng 83, 829–850.Google Scholar