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A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

Published online by Cambridge University Press:  25 December 2008

MIGUEL MOYERS-GONZALEZ ,
ROBERT G. OWENS  and
JIANNONG FANG
MIGUEL MOYERS-GONZALEZ
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal QC H3C 3J7, Canada
ROBERT G. OWENS*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal QC H3C 3J7, Canada
JIANNONG FANG
Affiliation:
GEOLEP-ICARE-ENAC, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*
‡Email address for correspondence: owens@dms.umontreal.ca
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Abstract

The earlier constitutive model of Fang & Owens (Biorheology, vol. 43, 2006, p. 637) and Owens (J. Non-Newtonian Fluid Mech. vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus–Lindqvist effect whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in sufficiently small vessels. That this is due to the development of a slippage layer of cell-depleted fluid near the vessel walls and a decrease in the tube haematocrit is demonstrated from the numerical results. Although clearly influential, the reduction in tube haematocrit observed in small-vessel blood flow (the so-called Fåhraeus effect) does not therefore entirely explain the Fåhraeus–Lindqvist effect.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 617 , 25 December 2008 , pp. 327 - 354
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Azelvandre, F. & Oiknine, C. 1976 Effet Fahraeus et effet Fahraeus-Lindqvist: résultats expérimentaux et modèles théoriques. Biorheology 13, 325–335.CrossRefGoogle Scholar
Bagchi, P. 2007 Mesoscale simulation of blood flow in small vessels. Biophys. J. 92, 1858–1877.CrossRefGoogle ScholarPubMed
Barbee, J. H. & Cokelet, G. R. 1971 Predictions of blood flow in tubes with diameters as small as 29 μm. Microvasc. Res. 3, 17–21.CrossRefGoogle Scholar
Baskurt, O. K. & Meiselman, H. J. 2003 Blood rheology and hemodynamics. Semin. Thromb. Hemost. 29, 435–450.Google ScholarPubMed
Beris, A. N. & Mavrantzas, V. G. 1994 On the compatibility between various macroscopic formalisms for the concentration and flow of dilute polymer solutions. J. Rheol. 38, 1235–1250.CrossRefGoogle Scholar
Bhave, A. V., Armstrong, R. C. & Brown, R. A. 1991 Kinetic theory and rheology of dilute, non-homogeneous polymer solutions. J. Chem. Phys. 95, 2988–3000.CrossRefGoogle Scholar
Blair, G. W. S. 1958 The importance of the sigma phenomenon in the study of the flow of blood. Rheol. Acta 1, 123–126.CrossRefGoogle Scholar
Bugliarello, G. & Sevilla, J. 1970 Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes. Biorheology 7, 85–107.CrossRefGoogle ScholarPubMed
Bureau, M., Healy, J. C., Bourgoin, D. & Joly, M. 1980 Rheological hysteresis of blood at low shear rate. Biorheology 17, 191–203.CrossRefGoogle ScholarPubMed
Caro, C. G., Pedley, T. J., Schroter, R. C. & Seed, W. A. 1978 The Mechanics of the Circulation. Oxford University Press.Google Scholar
Chien, S. & Jan, K.-M. 1973 Ultrastructural basis of the mechanism of rouleaux formation. Microvascular Res. 5, 155–166.CrossRefGoogle ScholarPubMed
Cook, L. P. & Rossi, L. F. 2004 Slippage and migration in models of dilute wormlike micellar solutions and polymeric fluids. J. Non-Newtonian Fluid Mech. 116, 347–369.CrossRefGoogle Scholar
Cross, M. M. 1965 Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J. Colloid Sci. 20, 417–437.CrossRefGoogle Scholar
Fåhraeus, R. 1929 The suspension stability of the blood. Physiol. Rev. 9, 241–274.CrossRefGoogle Scholar
Fåhraeus, R. & Lindqvist, T. 1931 The viscosity of the blood in narrow capillary tubes. Am. J. Physiol. 96, 562–568.CrossRefGoogle Scholar
Fang, J. & Owens, R. G. 2006 Numerical simulations of pulsatile blood flow using a new constitutive model. Biorheology 43, 637–660.Google ScholarPubMed
Gaehtgens, P., Albrecht, K. H. & Kreutz, F. 1978 Fahraeus effect and cell screening during tube flow of human blood. I. Effect of variation of flow rate. Biorheology 15, 147–154.CrossRefGoogle Scholar
Goldsmith, H. L., Cokelet, G. R. & Gaehtgens, P. 1989 Robin Fåhraeus: evolution of his concepts in cardiovascular physiology. Am. J. Physiol. 257, H1005–H1015.Google Scholar
Goldsmith, H. L. & Marlow, J. C. 1979 Flow behavior of erythrocytes. II. Particle motions in concentrated suspensions of ghost cells. J. Colloid Interface Sci. 71, 383–407.CrossRefGoogle Scholar
Kramers, H. A. 1944 Het gedrag van macromoleculen in een stroomende vloeistof. Physica 11, 1–19.CrossRefGoogle Scholar
Liu, Y. & Liu, W. K. 2006 Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220, 139–154.CrossRefGoogle Scholar
Mayer, G. 1965 Anomalous viscosity of human blood. Am. J. Physiol. 208, 1267–1269.CrossRefGoogle ScholarPubMed
McKay, C. B. & Meiselman, H. J. 1988 Osmolality-mediated Fahraeus and Fahraeus-Lindqvist effects for human RBC suspensions. Am. J. Physiol. 254, H238–H249.Google ScholarPubMed
Moyers-Gonzalez, M. & Owens, R. G. 2008 A non-homogeneous constitutive model for human blood. Part II: Asymptotic solution for large Péclet numbers. J. Non-Newtonian Fluid Mech. in press.CrossRefGoogle Scholar
Moyers-Gonzalez, M., Owens, R. G. & Fang, J. 2008 A non-homogeneous constitutive model for human blood. Part III: Oscillatory flow. J. Non-Newtonian Fluid Mech. in press.CrossRefGoogle Scholar
Murata, T. & Secomb, T. W. 1988 Effects of shear rate on rouleau formation in simple shear flow. Biorheology 25, 113–122.CrossRefGoogle ScholarPubMed
Onuki, A. 2002 Phase Transition Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Owens, R. G. 2006 A new microstructure-based constitutive model for human blood. J. Non-Newtonian Fluid Mech. 140, 57–70.CrossRefGoogle Scholar
Pries, A. R., Neuhaus, D. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and haematocrit. Am. J. Physiol. 263, H1770–H1778.Google Scholar
Pries, A. R. & Secomb, T. W. 2005 Microvascular blood viscosity in vivo and the endothelial surface layer. Am. J. Physiol. Heart Circ. Physiol. 289, H2657–H2664.CrossRefGoogle ScholarPubMed
Pries, A. R., Secomb, T. W., Gaehtgens, P. & Gross, J. F. 1990 Blood flow in microvascular networks. Experiments and simulation. Circ. Res. 67, 826–834.CrossRefGoogle ScholarPubMed
Rossi, L. F., McKinley, G. & Cook, L. P. 2006 Slippage and migration in Taylor-Couette flow of a model for dilute wormlike micellar solutions. J. Non-Newtonian Fluid Mech. 136, 79–92.CrossRefGoogle Scholar
Secomb, T. W. 2003 Mechanics of red blood cells and blood flow in narrow tubes. In Modeling and Simulation of Capsules and Biological cells (ed. Pozrikidis, C.), pp. 163–196. Chapman and Hall.Google Scholar
Sharan, M. & Popel, A. S. 2001 A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 38, 415–428.Google Scholar
Shiga, T., Imaizumi, K., Harada, N. & Sekiya, M. 1983 Kinetics of rouleaux formation using TV image analyzer. I. Human erythrocytes. Am. J. Physiol. 245, H252–H258.Google ScholarPubMed
Sun, C. & Munn, L. L. 2005 Particulate nature of blood determines macroscopic rheology: a 2D lattice Boltzmann analysis. Biophys. J. 88, 1635–1645.CrossRefGoogle ScholarPubMed
Sutera, S. P., Seshadri, V., Croce, P. A. & Hochmuth, R. M. 1970 Capillary blood flow : II. Deformable model cells in tube flow. Microvasc. Res. 2, 420–433.CrossRefGoogle ScholarPubMed
Thurston, G. B. 1975 Elastic effects in pulsatile blood flow. Microvasc. Res. 9, 145–157.CrossRefGoogle ScholarPubMed
Yen, R. T. & Fung, Y. C. 1977 Inversion of Fahraeus effect and effect of mainstream flow on capillary haematocrit. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 42, 578–586.CrossRefGoogle Scholar