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

Journal of Fluid Mechanics

Volumn 617, Issue , 2008, Pages 327-354

  Moyers Gonzalez, Miguel ^a   Owens, Robert G ^a   Fang, Jiannong ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD VESSELS; CONSTITUTIVE MODELS; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; RHEOLOGY; TUBES (COMPONENTS);

APPARENT VISCOSITY; AXISYMMETRIC FLOW; HEALTHY HUMANS; MODEL DERIVATIONS; MODELING FEATURES; NON-HOMOGENEOUS; NON-NEWTONIAN FLUIDS; NUMERICAL RESULTS;

BLOOD;

BLOOD; CONSTITUTIVE EQUATION; HEMATOLOGY; NUMERICAL MODEL; PREDICTION; STEADY FLOW;

EID: 57149111089     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200800428X     Document Type: Article

References (39)

1. AZELVANDRE, F. & OIKNINE, C. 1976 Effet Fahraeus et effet Fahraeus-Lindqvist: Résultats expérimentaux et modèles théoriques. Biorheology 13, 325-335.
2. BAGCHI, P. 2007 Mesoscale simulation of blood flow in small vessels. Biophys. J. 92, 1858-1877.
3. 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.
4. BASKURT, O. K. & MEISELMAN, H, J. 2003 Blood rheology and hemodynamics. Semin. Thromb. Hemost. 29, 435-450.
5. 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.
6. BHAVE, A. V., ARMSTRONG, R. C. & BROWN, R. A. 1991 Kinetic theory and Theology of dilute, non-homogeneous polymer solutions. J. Chem. Phys. 95, 2988-3000.
7. BLAIR, G. W. S. 1958 The importance of the sigma phenomenon in the study of the flow of blood. Rheol. Acta 1, 123-126.
8. BUGLIARELLO, G. & SEVILLA, J. 1970 Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tube. Biorheology 7, 85-107.
9. BUREAU, M., HEALY, J. C., BOURGOIN, D. & JOLY, M. 1980 Rheological hysteresis of blood at low shear rate. Biorheology 17, 191-203.
10. CARO, C. G., PEDLEY, T. J., SCHROTER, R. C. & SEED, W. A. 1978 The Mechanics of the Circulation. Oxford University Press.
11. CHIEN, S. & JAN. K.-M. 1973 Ultrastructural basis of the mechanism of rouleaux formation. Microvascular Res. 5, 155-166.
12. 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.
13. CROSS, M. M. 1965 Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems. J. Colloid Sci. 20, 417-437.
14. FÅHRAEUS, R. 1929 The suspension stability of the blood. Physiol. Rev. 9, 241-274.
15. FÅHRAEUS, R. & LINDQVIST, T. 1931 The viscosity of the blood in narrow capillary tubes. Am. J. Physiol. 96, 562-568.
16. FANG, J. & OWENS, R. G. 2006 Numerical simulations of pulsatile blood flow using a new constitutive model. Biorheology 43, 637-660.
17. 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.
18. GOLDSMITH, H. L., COKELET, G. R. & GAEHTGENS, P. 1989 Robin Fåhraeus: Evolution of his concepts in cardiovascular physiology. Am. J. Physiol. 257, H1005-H1015.
19. 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.
20. KRAMERS, H. A. 1944 Het gedrag van macromoleculen in een stroomende vloeistof. Physica 11, 1-19
21. LIU, Y. & LIU, W. K. 2006 Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220, 139-154.
22. MAYER, G. 1965 Anomalous viscosity of human blood. Am. J. Physiol. 208, 1267-1269.
23. MCKAY, C. B. & MEISELMAN, H. J. 1988 Osmolality-mediated Fahraeus and Fahraeus-Lindqvist effects for human RBC suspensions. Am. J. Physiol. 254, H238-H249.
24. 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.
25. 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.
26. MURATA, T. & SECOMB, T. W. 1988 Effects of shear rate on rouleau formation in simple shear flow. Biorheology 25, 113-122.
27. ONUKI, A. 2002 Phase Transition Dynamics. Cambridge University Press.
28. OWENS, R. G. 2006 A new microstructure-based constitutive model for human blood. J. Non-Newtonian Fluid Mech. 140, 57-70.
29. PRIES, A. R., NEUHAUS, D. & GAEHTGENS, P. 1992 Blood viscosity in tube flow: Dependence on diameter and haematocrit. Am. J. Physiol. 263, H1770-H1778.
30. 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.
31. 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.
32. 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.
33. 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. C. Pozrikidis), pp. 163-196. Chapman and Hall.
34. 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.
35. 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.
36. SUN, C. & MUNN, L. L. 2005 Particulate nature of blood determines macroscopic rheology: A 2D lattice Boltzmann analysis. Biophys. J. 88, 1635-1645.
37. 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.
38. THURSTON, G. B. 1975 Elastic effects in pulsatile blood flow. Microvasc. Res. 9, 145-157.
39. 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.