Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 281 - 319
DOI https://doi.org/10.1051/mmnp/20116511
Published online 10 August 2011
  1. C. G. Caro, T. J. Pedley, R. C. Schroter, W. A. Seed. The mechanics of the circulation (russian edition). Mir, Moscow, 1981. [Google Scholar]
  2. A. M. Chernukh, P. N. Aleksandrov, O. V. Alekseev. Microcirculation. Medicina, Moscow, 1984. [Google Scholar]
  3. H. L. Goldsmith, R. Skalak. Hemodynamics. Annual Review of Fluid Mechanics, 7 (1975), 213-247. [CrossRef] [Google Scholar]
  4. H. L. Goldsmith, V. T. Turitto. Rheological aspects of thrombosis and haemostasis: basic principles and applications. ICTH-Report–Subcommittee on Rheology of the International Committee on Thrombosis and Haemostasis. Thromb. Haemost., 55 (1986), No. 3, 415-435. [PubMed] [Google Scholar]
  5. H. L. Goldsmith. The Microcirculatory Society Eugene M. Landis Award lecture. The microrheology of human blood. Microvasc. Res., 31 (1986), No. 2, 121-142. [CrossRef] [PubMed] [Google Scholar]
  6. A. S. Popel, P. C. Johnson. Microcirculation and hemorheology. Annu. Rev. Fluid Mech., 37 (2005), 43-69. [CrossRef] [PubMed] [Google Scholar]
  7. H. H. Lipowsky. Microvascular rheology and hemodynamics. Microcirculation, 12 (2005), 5-15. [CrossRef] [PubMed] [Google Scholar]
  8. G. R. Cokelet. Viscometric, in vitro and in vivo blood viscosity relationships: how are they related? (Poiseuille Award Lecture). Biorheology, 36 (1999), 343-358. [PubMed] [Google Scholar]
  9. A. M. Quarteroni, M. Tuveri, A. Veneziani. Computational vascular fluid dynamics: problems, models and methods. Computing and Visualization in Science, 2 (2000), 163-197. [CrossRef] [Google Scholar]
  10. S. Kim, P. K. Ong, O. Yalcin, M. Intaglietta, P. C. Johnson. The cell-free layer in microvascular blood flow. Biorheology, 46 (2009), 181-189. [PubMed] [Google Scholar]
  11. M. Manjunatha, M. Singh. Digital blood flow analysis from microscopic images of mesenteric microvessel with multiple branching. Clin. Hemorheol. Microcirc., 27 (2002), 91-106. [PubMed] [Google Scholar]
  12. M. Manjunatha, S. S. Singh, M. Singh. Blood flow analysis in mesenteric microvascular network by image velocimetry and axial tomography. Microvascular Research, 65 (2003), 49-55. [CrossRef] [PubMed] [Google Scholar]
  13. A. A. Palmer, W. H. Betts. The axial drift of fresh and acetaldehyde-hardened erythrocytes in 25 mum capillary slits of various lengths. Biorheology, 12 (1975), No. 5, 283-293. [PubMed] [Google Scholar]
  14. M. L. Ellsworth, R. N. Pittman. Evaluation of photometric methods for quantifying convective mass transport in microvessels. Am. J. Physiol., 251 (1986), H869-H879. [PubMed] [Google Scholar]
  15. A. R. Pries, K. Ley, M. Claassen, P. Gaehtgens. Red Cell Distribution at Microvascular Bifurcations. Microvasc. Res., 38 (1989), 81-101. [CrossRef] [PubMed] [Google Scholar]
  16. R. H. Phibbs. Distribution of leukocytes in blood flowing through arteries. Am. J. Physiol., 210 (1966), No. 5, 919-925. [PubMed] [Google Scholar]
  17. G. J. Tangelder, H. C. Teirlinck, D. W. Slaaf, R. S. Reneman. Distribution of blood platelets flowing in arterioles. Am. J. Physiol., 248 (1985), H318-H323. [PubMed] [Google Scholar]
  18. B. Woldhuis, G. J. Tangelder, D. W. Slaaf, R. S. Reneman. Concentration profile of blood platelets differs in arterioles and venules. Am. J. Physiol., 262 (1992), H1217-H1223. [PubMed] [Google Scholar]
  19. P. A. Aarts, S. A. van den Broek, G. W. Prins, G. D. Kuiken, J. J. Sixma, R. M. Heethaar. Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arteriosclerosis, 8 (1988), No. 6, 819-824. [CrossRef] [PubMed] [Google Scholar]
  20. H. L. Goldsmith. Red cell motions and wall interactions in tube flow. Fed. Proc., 30 (1971), No. 5, 1578-1590. [PubMed] [Google Scholar]
  21. G. Segré, A. Silberberg. Radial particle displacements in poiseuille flow of suspensions. Nature, 189 (1961), 209-210. [CrossRef] [Google Scholar]
  22. G. Segré, A. Silberberg. Behaviour of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. Journal of Fluid Mechanics, 14 (1962), 115-135. [CrossRef] [Google Scholar]
  23. G. Segré, A. Silberberg. Behaviour of macroscopic rigid spheres in Poiseuille flow Part 2. Experimental results and interpretation. Journal of Fluid Mechanics, 14 (1962), 136-157. [CrossRef] [Google Scholar]
  24. D. R. Oliver. Influence of particle rotation on radial migration in the Poiseuille flow of suspensions. Nature, 194 (1962), 1269-1271. [CrossRef] [Google Scholar]
  25. M. Takano, H. L. Goldsmith, S. G. Mason. The flow of suspensions through tubes VIII. Radial Migration of Particles in Pulsatile Flow. Journal of Colloid and lnterface Science, 27 (1968), No. 2, 253-267. [CrossRef] [Google Scholar]
  26. L. G. Leal. Particle motions in a viscous fluid. Annu. Rev. Fluid Mech., 12 (1980), 435-476. [CrossRef] [MathSciNet] [Google Scholar]
  27. S. K. Wang, N. H. C. Hwang. On transport of suspended particulates in tube flow. Biorheology, 29 (1992), 353-377. [PubMed] [Google Scholar]
  28. H. Brenner, P. M. Bungay. Rigid-particle and liquid-droplet models of red cell motion in capillary tubes. Fed. Proc., 30 (1971), No. 5, 1565-1577. [PubMed] [Google Scholar]
  29. H. L. Goldsmith, S. G. Mason. The flow of suspensions through tubes I. Single spheres, rods and discs. Journal of Colloid Science, 17 (1962), 448-476. [CrossRef] [Google Scholar]
  30. C. K. W. Tam, W. A. Hyman. Transverse motion of an elastic sphere in a shear field. Journal of Fluid Mechanics, 59 (1973), No. part 1, 177-185. [CrossRef] [Google Scholar]
  31. C. Crowe, M. Sommerfield, Y. Tsuji. Multiphase flows with drops and particles. CRC Press, 1998. [Google Scholar]
  32. P. Cherukat, J. B. McLaughlin, D. S. Dandy. A computational study of the inertial lift on a sphere in a linear shear fow field. International Journal of Multiphase Flow, 25 (1999), 15-33. [CrossRef] [Google Scholar]
  33. J.-P. Matas, J. F. Morris, E. Guazzelli. Inertial migration of rigid spherical particles in Poiseuille flow. Journal of Fluid Mechanics, 515 (2004), 171-195. [CrossRef] [Google Scholar]
  34. L. L. Munn, M. M. Dupin. Blood cell interactions and segregation in flow. Ann. Biomed. Eng, 36 (2008), No. 4, 534-544. [CrossRef] [PubMed] [Google Scholar]
  35. E. E. Michaelides. Hydrodynamic Force and Heat-Mass Transfer From Particles. Journal of Fluids Engineering, 125 (2003), 209-238. [CrossRef] [Google Scholar]
  36. S. I. Rubinow, J. B. Keller. The transverse force on a spinning sphere moving in a viscous fluid. Journal of Fluid Mechanics, 11 (1961), 447-459. [CrossRef] [MathSciNet] [Google Scholar]
  37. R. G. Cox, H. Brenner. The lateral migration of solid particles in Poiseuille flow - I theory. Chemical Engineering Science, 23 (1968), 147-173. [CrossRef] [Google Scholar]
  38. P. G. Saffman. The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics, 22 (1965), No. part 2, 385-400. [CrossRef] [Google Scholar]
  39. J. B. McLaughlin. Inertial migration of a small sphere in linear shear flows. Journal of Fluid Mechanics, 224 (1991), 261-274. [CrossRef] [Google Scholar]
  40. P. Cherukat, J. B. McLaughlin, A. L. Graham. The inertial lift on a rigid sphere translating in a linear shear flow field. International Journal of Multiphase Flow, 20 (1994), No. 2, 339-353. [CrossRef] [Google Scholar]
  41. P. V. Vasseur, R. G. Cox. The lateral migration of a spherical particle in two-dimensional shear flows. Journal of Fluid Mechanics, 78 (1976), 385-413. [CrossRef] [Google Scholar]
  42. R. G. Cox, S. K. Hsu. The lateral migration of solid particles in a laminar flow near a plane. International Journal of Multiphase Flow, 3 (1977), 201-222. [CrossRef] [Google Scholar]
  43. P. Cherukat, D. R. Oliver. The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. Journal of Fluid Mechanics, 263 (1994), 1-18. [CrossRef] [Google Scholar]
  44. P. W. Longest, C. Kleinstreuer. Comparison of blood particle deposition models for non-parallel fow domains. Journal of Biomechanics, 36 (2003), 421-430. [CrossRef] [PubMed] [Google Scholar]
  45. P. W. Longest, C. Kleinstreuer. Numerical Simulation of Wall Shear Stress Conditions and Platelet Localization in Realistic End-to-Side Arterial Anastomoses. Journal of Biomechanical Engineering, 125 (2003), 671-681. [CrossRef] [PubMed] [Google Scholar]
  46. P. W. Longest, C. Kleinstreuer, J. R. Buchanan. Efficient computation of micro-particle dynamics including wall effects. Computers & Fluids, 33 (2004), 577-601. [CrossRef] [Google Scholar]
  47. H. L. Goldsmith, S. G. Mason. Axial migration of particles in Poiseuille Flow. Nature, 190 (1961), 1095-1096. [CrossRef] [Google Scholar]
  48. M. Abkarian, A. Viallat. Vesicles and red blood cells in shear flow. Soft Matter, 4 (2008), 653-657. [CrossRef] [Google Scholar]
  49. C. Coulliette, C. Pozrikidis. Motion of an array of drops through a cylindrical tube. Journal of Fluid Mechanics, 358 (1998), 1-28. [CrossRef] [MathSciNet] [Google Scholar]
  50. S. Mortazavi, G. Tryggvason. A numerical study of the motion of drops in Poiseuille flow. Part 1.Lateral migration of one drop. Journal of Fluid Mechanics, 411 (2000), 325-350. [CrossRef] [Google Scholar]
  51. C. Pozrikidis. Numerical Simulation of Cell Motion in Tube Flow. Ann. Biomed. Eng, 33 (2005), No. 2, 165-178. [CrossRef] [PubMed] [Google Scholar]
  52. B. Kaoui, G. Biros, C. Masbah. Why Do Red Blood Cells Have Asymmetric Shapes Even in a Symmetric Flow? Physical Review Letters, 103 (2009), No. 18, 188101(1)-188101(4). [Google Scholar]
  53. C. E. Chaffey, H. Brenner, S. G. Mason. Particle motions in sheared suspensions XVIII. Wall Migration (Theoretical). Rheologica Acta, 4 (1965), No. 1, 64-72. [CrossRef] [Google Scholar]
  54. C. E. Chaffey, H. Brenner, S. G. Mason. Correction of the paper Particle motions in sheared suspensions XVIII. Wall Migration (Theoretical). Rheologica Acta, 6 (1967), No. 1, 100. [CrossRef] [Google Scholar]
  55. P. R. Wohl, S. I. Rubinow. The transverse force on a drop in an unbounded parabolic flow. Journal of Fluid Mechanics, 62 (1974), No. part 1, 185-207. [CrossRef] [Google Scholar]
  56. P. C. H. Chan, L. G. Leal. The motion of a deformable drop in a second-order fluid. Journal of Fluid Mechanics, 92 (1979), No. part 1, 131-170. [CrossRef] [Google Scholar]
  57. W. S. J. Uijttewaal, E.-J. Nijhof, R. M. Heethaar. Droplet migration, deformation, and orientation in the presence of a plane wall: A numerical study compared with analytical theories. Phys. Fluids A, 5 (1993), No. 4, 819-825. [CrossRef] [Google Scholar]
  58. S. D. Hudson. Wall migration and shear-induced diffusion of fluid droplets in emulsions. Physics of Fluids, 15 (2003), No. 5, 1106-1113. [CrossRef] [Google Scholar]
  59. M. R. King, D. T. Leighton, Jr. Measurement of shear-induced dispersion in a dilute emulsion. Physics of Fluids, 13 (2001), No. 2, 397-406. [CrossRef] [Google Scholar]
  60. M. Scott. 2005. The modeling of Blood Rheology in small vessels. University of Waterloo, Waterloo, Ontario, Canada. [Google Scholar]
  61. P. Olla. The lift on a tank-treading ellipsoidal cell in a shear flow. Journal de Physique II, 7 (1997), No. 10, 1533-1540. [CrossRef] [EDP Sciences] [Google Scholar]
  62. M. Faivre, M. Abkarian, K. Bickraj, H. A. Stone. Geometrical focusing of cells in a microfluidic device: An approach to separate blood plasma. Biorheology, 43 (2006), 147-159. [PubMed] [Google Scholar]
  63. P. L. Blackshear, Jr., R. J. Forstrom, F. D. Dorman, G. O. Voss. Effect of flow on cells near walls. Fed. Proc., 30 (1971), No. 5, 1600-1609. [PubMed] [Google Scholar]
  64. C. D. Eggleton, A. S. Popel. Large deformation of red blood cell ghosts in a simple shear flow. Physics of Fluids, 10 (1998), No. 8, 1834-1845. [CrossRef] [Google Scholar]
  65. N. Korin, A. Bransky, U. Dinnar. Theoretical model and experimental study of red blood cell (RBC) deformation in microchannels. Journal of Biomechanics, 40 (2007), 2088-2095. [CrossRef] [PubMed] [Google Scholar]
  66. P. R. Nott, J. F. Brady. Pressure-driven flow of suspensions: simulation and theory. Journal of Fluid Mechanics, 275 (1994), 157-199. [CrossRef] [Google Scholar]
  67. J. F. Morris, J. F. Brady. Pressure-driven flow in a suspension: buoyancy effects. International Journal of Multiphase Flow, 24 (1998), No. 1, 105-130. [CrossRef] [Google Scholar]
  68. K. Tsubota, S. Wada, H. Kamada, Y. Kitagawa, R. Lima, T. Yamaguchi. A Particle Method for Blood Flow Simulation -Application to Flowing Red Blood Cells and Platelets. Journal of the Earth Simulator, 5 (2006), 2-7. [Google Scholar]
  69. S. Chen, G. D. Doolen. Lattice Boltzmann Method for Fluid Flows. Annu. Rev. Fluid Mech., 30 (1998), 329-364. [CrossRef] [Google Scholar]
  70. M. M. Dupin, I. Halliday, C. M. Care, L. Alboul, L. L. Munn. Modeling the flow of dense suspensions of deformable particles in three dimensions. Physical Review E., 066707 (2007), 1-17. [Google Scholar]
  71. L. M. Crowl, A. L. Fogelson. Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Commun. Numer. Meth. Engng, (2009). [Google Scholar]
  72. C. Sun, C. Migliorini, L. L. Munn. Red Blood Cells Initiate Leukocyte Rolling in Postcapillary Expansions: A Lattice Boltzmann Analysis. Biophysical Journal, 85 (2003), 208-222. [CrossRef] [PubMed] [Google Scholar]
  73. P. Bagchi. Mesoscale Simulation of Blood Flow in Small Vessels. Biophysical Journal, 92 (2007), 1858-1877. [CrossRef] [PubMed] [Google Scholar]
  74. P. Bagchi, P. C. Johnson, A. S. Popel. Computational Fluid Dynamic Simulation of Aggregation of Deformable Cells in a Shear Flow. Transactions of the ASME, 127 (2005), 1070-1080. [Google Scholar]
  75. J. Zhang, P. C. Johnson, A. S. Popel. Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. Journal of Biomechanics, 41 (2008), 47-55. [CrossRef] [PubMed] [Google Scholar]
  76. J. Zhang, P. C. Johnson, A. S. Popel. Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc. Res., 77 (2009), 265-272. [CrossRef] [PubMed] [Google Scholar]
  77. S. Svetina, P. Ziherl. Morphology of small aggregates of red blood cells. Bioelectrochemistry, 73 (2008), No. 2, 84-91. [CrossRef] [PubMed] [Google Scholar]
  78. A. L. Fogelson. A Mathematical Model and Numerical Method for Studying Platelet Adhesion and Aggregation during Blood Clotting. Journal of Computational Physics, 56 (1984), 111-134. [CrossRef] [MathSciNet] [Google Scholar]
  79. I. V. Pivkin, P. D. Richardson, G. Karniadakis. Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi. PNAS, 103 (2006), No. 46, 17164-17169. [CrossRef] [Google Scholar]
  80. H. Miyazaki, T. Yamaguchi. Formation and destruction of primary thrombi under the influence of blood flow and von Willebrand factor analyzed by a discrete element method. Biorheology, 40 (2003), 265-272. [PubMed] [Google Scholar]
  81. K. Yano, K. Tsubota, S. Wada, T. Yamaguchi. 2003. Computational mechanical simulation of the aggregation and adhesion of platelets in the blood flow. In Summer Bioengineering Conference. Sonesta Beach Resort in Key Biscayne, Florida. 0613-0614. [Google Scholar]
  82. N. Filipovic, D. Ravnic, M. Kojic, S. J. Mentzer, S. Haber, A. Tsuda. Interactions of blood cell constituents: Experimental investigation and computational modeling by discrete particle dynamics algorithm. Microvasc. Res., 75 (2008), 279-284. [CrossRef] [PubMed] [Google Scholar]
  83. D. Mori, K. Yano, K. Tsubota, T. Ishikawa, S. Wada, T. Yamaguchi. Simulation of platelet adhesion and aggregation regulated by fibrinogen and von Willebrand factor. Thromb. Haemost., 99 (2008), No. 1, 108-115. [PubMed] [Google Scholar]
  84. T. Almomani, H. S. Udaykumar, J. S. Marshall, K. B. Chandran. Micro-scale dynamic simulation of erythrocyte-platelet interaction in blood flow. Ann. Biomed. Eng, 36 (2008), No. 6, 905-920. [CrossRef] [PubMed] [Google Scholar]
  85. R. M. Miller, J. F. Morris. Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions. Journal of Non-Newtonian Fluid Mechanics, 135 (2006), 149-165. [CrossRef] [Google Scholar]
  86. L. G. Loitzanskii. Mechanics of Fluid and Gas. Nauka, Moscow, 1978. [Google Scholar]
  87. A. Sequeira, J. Janela. An overview of some mathematical models of blood rheology. In A Portrait of State-of-the-Art Research at the Technical University of Lisbon. M. S. Pereira, editor. Springer, 2007. pp. 65-87. [Google Scholar]
  88. A. M. Robertson, A. Sequeira, M. V. Kameneva. Hemorheology. In Hemodynamical Flows: Modeling, Analysis and Simulation (Oberwolfach Seminars). Birkhauser Basel, 2008. pp. 63-120. [Google Scholar]
  89. G. R. Cokelet. The Rheology and Tube Flow of Blood. In Handbook of Bioengineering. R. Skalak, S. Chen, editors. McGraw-Hill, New York, 1987. [Google Scholar]
  90. B. J. B. M. Wolters, M. C. M. Rutten, G. W. H. Schurink, U. Kose, J. d. Hart, F. N. v. d. Vosse. A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. Medical Engineering & Physics, 27 (2005), 871-883. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  91. J. Jung, A. Hassenein, R. W. Lyczkowski. Hemodynamic Computation Using Multiphase Flow Dynamics in a Right Coronary Artery. Ann. Biomed. Eng, 34 (2006), No. 3, 393-407. [CrossRef] [PubMed] [Google Scholar]
  92. J. Jung, R. W. Lyczkowski, C. B. Panchal, A. Hassenein. Multiphase hemodynamic simulation of pulsatile flow in a coronary artery. Journal of Biomechanics, 39 (2006), 2064-2073. [CrossRef] [PubMed] [Google Scholar]
  93. J. Jung, A. Hassenein. Three-phase CFD analytical modeling of blood flow. Medical Engineering & Physics, 30 (2008), 91-103. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  94. D. Quemada, C. Berli. Energy of interaction in colloids and its implications in rheological modeling. Advances in Colloid and Interface Science, 98 (2002), 51-85. [CrossRef] [PubMed] [Google Scholar]
  95. A. Marcinkowska-Gapinska, J. Gapinski, W. Elikowski, F. Jaroszyk, L. Kubisz. Comparison of three rheological models of shear flow behavior studied on blood samples from post-infarction patients. Medical and Biological Engineering and Computing, 45 (2007), No. 9, 837-844. [CrossRef] [Google Scholar]
  96. B. Das, P. C. Johnson, A. S. Popel. Effect of nonaxisimmetric hematoctit distribution on non-newtonian blood flow in small tubes. Biorheology, 35 (1998), No. 1, 69-87. [CrossRef] [PubMed] [Google Scholar]
  97. J. R. Buchanan, Jr., C. Kleinstreuer, J. K. Comer. Rheological effects on pulsatile hemodynamics in a stenosed tube. Computers & Fluids, 29 (2000), 695-724. [CrossRef] [Google Scholar]
  98. B. Das, G. Enden, A. S. Popel. Stratified multiphase model for blood flow in a venular bifurcation. Annals of Biomedical Engineering, 25 (1997), 135-153. [CrossRef] [PubMed] [Google Scholar]
  99. A. S. Popel, G. Enden. An analytical solution for steady flow of a Quemada fluid in a circular tube. Rheologica Acta, 32 (1993), 422-426. [CrossRef] [Google Scholar]
  100. C. L. Berli, D. Quemada. Aggregation behavior of red blood cells in shear flow. A theoretical interpretation of simultaneous rheo-optical and viscometric measurements. Biorheology, 38 (2001), No. 1, 27-38. [PubMed] [Google Scholar]
  101. D. Quemada. Rheological modelling of complex fluids. I. The concept of effective volume fraction revisited. The European Physical J. AP, 1 (1998), 119-127. [CrossRef] [EDP Sciences] [Google Scholar]
  102. D. Quemada, C. Berli. Energy of interaction in colloids and its implications in rheological modeling. Adv. Colloid Interface Sci., 98 (2002), No. 1, 51-85. [CrossRef] [PubMed] [Google Scholar]
  103. P. Neofytou. Comparison of blood rheological models for physiological flow simulation. Biorheology, 41 (2004), No. 6, 693-714. [PubMed] [Google Scholar]
  104. G. R. Cokelet, H. L. Goldsmith. Decreased hydrodynamic resistance in the two-phase flow of blood through small vertical tubes at low flow rates. Circ. Res., 68 (1991), No. 1, 1-17. [PubMed] [Google Scholar]
  105. J. R. Buchanan, Jr., C. Kleinstreuer. Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenoses. J. Biomech. Eng, 120 (1998), No. 4, 446-454. [CrossRef] [PubMed] [Google Scholar]
  106. S. A. Regirer. Lections on Biological Mechanics [in russian]. Izdatelstvo MGU, Moscow, 1980. [Google Scholar]
  107. M. Sharan, A. S. Popel. A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology, 38 (2001), 415-428. [PubMed] [Google Scholar]
  108. J. H. Ware, F. Y. Sorrell, R. M. Felder. A model of steady blood flow. Biorheology, 11 (1974), 97-109. [PubMed] [Google Scholar]
  109. B. Das, P. C. Johnson, A. S. Popel. Computational fluid dynamic studies of leukocyte adhesion effects. Biorheology, 37 (2000), 239-258. [PubMed] [Google Scholar]
  110. J. Perkkio, R. Keskinen. On the effect of the concentration profile of red cells on blood flow in the artery with stenosis. Bull. Math. Biol., 45 (1983), No. 2, 259-267. [MathSciNet] [PubMed] [Google Scholar]
  111. D. Lerche. Modelling hemodynamics in small tubes (hollow fibers) considering . In Biomechanical Transport Processes. F. e. al. Mosora, editor. Plenum, New York, 1990. pp. 243-250. [Google Scholar]
  112. R. T. Carr, M. Lacoin. Nonlinear Dynamics of Microvascular Blood Flow. Annals of Biomedical Engineering, 28 (2000), 641-652. [CrossRef] [PubMed] [Google Scholar]
  113. P. Brunn. The general solution to the equations of creeping motion of a micropolar fluid and its application. International Journal of Engineering Science, 20 (1982), 575-585. [CrossRef] [MathSciNet] [Google Scholar]
  114. V. K. Stokes. Couple stress in fluids. The Physics of Fluids, 9 (1966), No. 9, 1709-1715. [CrossRef] [Google Scholar]
  115. A. C. Eringen. Theory of Micropolar Fluids. Journal of Mathematics and Mechanics, 16 (1966), No. 1, 1-18. [Google Scholar]
  116. A. Askar, A. S. Cakmak. A structural model of a micropolar continuum. International Journal of Engineering Science, 6 (1968), 583-589. [CrossRef] [Google Scholar]
  117. T. Ariman. Microcontinuum fluid mechanics - a review. International Journal of Engineering Science, 11 (1973), 905-930. [CrossRef] [Google Scholar]
  118. T. Ariman, M. A. Turk, N. D. Sylvester. Application of microcontinuum fluid mechanics. International Journal of Engineering Science, 12 (1974), 273-293. [CrossRef] [Google Scholar]
  119. K. A. Kline. Predictions from Polar Fluid Theory Which Are Independent of Spin Boundary Condition. Transactions of the society of rheology, 19 (1975), No. 1, 139-145. [CrossRef] [Google Scholar]
  120. S. C. Cowin. A Note on the Predictions from Polar Fluid Theory Which Are Independent of the Spin Boundary Condition. Transactions of the society of rheology, 20 (1976), No. 2, 195-202. [CrossRef] [Google Scholar]
  121. H. A. Hogan, M. Henriksen. An evaluation of a micropolar model for blood flow through an idealized stenosis. Journal of Biomechanics, 22 (1989), No. 3, 211-218. [CrossRef] [PubMed] [Google Scholar]
  122. R. N. Pralhad, D. H. Schultz. Modeling of arterial stenosis and its applications to blood diseases. Mathematical Biosciences, 190 (2004), 203-220. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  123. G. Akay, A. Kaye. Numerical solution of time dependent stratified two-phase flow of micropolar fluids and its application to flow of blood through fine capillaries. International Journal of Engineering Science, 23 (1985), No. 3, 265-276. [CrossRef] [Google Scholar]
  124. Md. A. Ikbal, S. Chakravarty, P. K. Mandal. Two-layered micropolar fluid flow through stenosed artery: Effect of peripheral layer thickness. Computers and Mathematics with Applications, 58 (2009), 1328-1339. [CrossRef] [MathSciNet] [Google Scholar]
  125. D. Biswas. Blood Flow Models: A Comparative Study. Mittal Publications , 2002. [Google Scholar]
  126. C. K. Kang, A. C. Eringen. The effect of microstructure on the rheological properties of blood. Bull. Math. Biol., 38 (1976), 135-159. [PubMed] [Google Scholar]
  127. A. S. Popel, S. A. Regirer. Ob osnovnih uravneniyah hydrodinamiki krovi. Nauchnie trudi instituta mechaniki MGU, 1 (1970), 3-20. [Google Scholar]
  128. A. S. Popel, S. A. Regirer, P. I. Usick. A Continuum Model of Blood Flow. Biorheology, 11 (1974), 427-437. [PubMed] [Google Scholar]
  129. A. S. Popel. O hydrodynamike suspensii. Mechanika zjidkosti i gaza, 4 (1969), 24. [Google Scholar]
  130. A. C. Eringen. Microcontinuum Field Theories II: Fluent media. Springer-Verlag, 2001. [Google Scholar]
  131. V. A. Levtov, S. A. Regirer, N. Kh. Shadrina. Aggregation and diffusion of Erythrocites. Sovremennie problemi biomekhaniki, 9 (1994), 5-41. [Google Scholar]
  132. V. L. Kolpashchikov, N. P. Migun, P. P. Prokhorenko. Experimental determination of material micropolar fluid constants. International Journal of Engineering Science, 21 (1983), No. 4, 405-411. [CrossRef] [Google Scholar]
  133. A. D. J. Kirwan. Boundary conditions for micropolar fluids. International Journal of Engineering Science, 24 (1986), No. 7, 1237-1242. [CrossRef] [Google Scholar]
  134. H. L. Goldsmith, J. C. Marlow. Flow Behavior of Erythrocytes II. Particle Motions in Concentrated Suspensions of Ghost Cells. Journal of Colloid and lnterface Science, 71 (1979), No. 2, 383-407. [CrossRef] [Google Scholar]
  135. V. A. Levtov, S. A. Regirer, N. Kh. Shadrina. Rheology of Blood. Medicina, Moscow, 1982. [Google Scholar]
  136. G. Ahmadi. A continuum theory of blood flow. Scientia Sinica, 24 (1981), No. 10, 1465-1473. [MathSciNet] [PubMed] [Google Scholar]
  137. G. Ahmadi. A Continuum Theory for Two Phase Media. Acta Mechanica, 44 (1982), 299-317. [CrossRef] [Google Scholar]
  138. J. Jung, D. Gidaspow, I. K. Gamwo. Bubble Computation, Granular Temperatures, and Reynolds Stresses. Chem. Eng. Comm., 193 (2006), 946-975. [CrossRef] [Google Scholar]
  139. E. C. Eckstein, D. G. Bailey, A. H. Shapiro. Self-diffusion of particles in shear flow of a suspension. Journal of Fluid Mechanics, 79 (1977), No. part 1, 191-208. [CrossRef] [Google Scholar]
  140. D. Leighton, A. Acrivos. The shear-induced migration of particles in concentrated suspensions. Journal of Fluid Mechanics, 181 (1987), 415-439. [CrossRef] [Google Scholar]
  141. H. Aref, S. W. Jones. Enhanced separation of diffusing particles by chaotic advection. Phys. Fluids A, 1 (1989), No. 3, 470-474. [CrossRef] [MathSciNet] [Google Scholar]
  142. C. J. Koh, P. Hookham, L. G. Leal. An experimental investigation of concentrated suspension flows in a rectangular channel. Journal of Fluid Mechanics, 266 (1994), 1-32. [CrossRef] [Google Scholar]
  143. M. K. Lyon, L. G. Leal. An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. Journal of Fluid Mechanics, 363 (1998), 25-56. [CrossRef] [Google Scholar]
  144. R. J. Phillips, R. C. Armstrong, R. A. Brown. A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A, 4 (1992), No. 1, 30-40. [CrossRef] [Google Scholar]
  145. J. E. Butler, R. T. Bonnecaze. Imaging of particle shear migration with electrical impedance tomography. Physics of Fluids, 11 (1999), No. 8, 1982-1994. [CrossRef] [Google Scholar]
  146. M. Hofer, K. Perctold. Computer simulation of concentrated fluid-perticle suspension flows in axisimmetric geometries. Biorheology, 54 (1997), No. 4/5, 261-279. [CrossRef] [Google Scholar]
  147. M. K. Lyon, L. G. Leal. An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 2. Bidisperse systems. Journal of Fluid Mechanics, 363 (1998), 57-77. [CrossRef] [Google Scholar]
  148. J. F. Morris, F. Boulay. Curvilinear flows of noncolloidal suspensions: The role of normal stresses. Journal of Rheology, 43 (1999), No. 5, 1213-1236. [CrossRef] [Google Scholar]
  149. E. F. Grabowski, Friedman L.I., E. F. Leonard. Effects of Shear Rate on the Diffusion and Adhesion of Blood Platelets to a Foreign Surface. Ind. Eng. Chem. Fundamen., 11 (1972), No. 2, 224-232. [CrossRef] [Google Scholar]
  150. A. B. Strong, G. D. Stubley, G. Chang, D. R. Absolom. Theoretical and experimental analysis of cellular adhesion to polymer surfaces. J. Biomed. Mater. Res., 21 (1987), No. 8, 1039-1055. [CrossRef] [PubMed] [Google Scholar]
  151. G. D. Stubley, A. B. Strong, W. E. Hale, D. R. Absolom. A review of mathematical models for the prediction of blood cell adhesion. PCH PhysicoChem. Hydrodynics, 8 (1987), No. 2, 221-235. [Google Scholar]
  152. D. M. Wootton, C. P. Markou, S. R. Hanson, D. N. Ku. A mechanistic model of acute platelet accumulation in thrombogenic stenoses. Ann. Biomed. Eng, 29 (2001), No. 4, 321-329. [CrossRef] [PubMed] [Google Scholar]
  153. E. N. Sorensen, G. W. Burgreen, W. R. Wagner, J. F. Antaki. Computational simulation of platelet deposition and activation: II. Results for Poiseuille flow over collagen. Ann. Biomed. Eng, 27 (1999), No. 4, 449-458. [CrossRef] [PubMed] [Google Scholar]
  154. E. N. Sorensen, G. W. Burgreen, W. R. Wagner, J. F. Antaki. Computational simulation of platelet deposition and activation: I. Model development and properties. Ann. Biomed. Eng, 27 (1999), No. 4, 436-448. [CrossRef] [PubMed] [Google Scholar]
  155. T. David, P. G. Walker. Activation and extinction models for platelet adhesion. Biorheology, 39 (2002), 293-298. [PubMed] [Google Scholar]
  156. M. Anand, K. Rajagopal, K. R. Rajagopal. A Model Incorporating some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood. Computational and Mathematical Methods in Medicine, 5 (2003), No. 3&4, 183-218. [Google Scholar]
  157. A. L. Fogelson, R. D. Guy. Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution. Math. Med. Biol., 21 (2004), No. 4, 293-334. [CrossRef] [PubMed] [Google Scholar]
  158. N.-T. Wang, A. L. Fogelson. Computational methods for continuum models of platelet aggregation. Journal of Computational Physics, 151 (1999), 649-675. [CrossRef] [MathSciNet] [Google Scholar]
  159. A. L. Fogelson. Continuum models of platelet aggregation: formulation and mechanical properties. SIAM J. Appl. Math., 52 (1992), No. 4, 1089-1110. [CrossRef] [MathSciNet] [Google Scholar]
  160. A. Jordan, T. David, S. Homer-Vanniasinkam, A. Graham, P. Walker. The effects of margination and red cell augmented platelet diffusivity on platelet adhesion in complex flow. Biorheology, 41 (2004), 641-653. [PubMed] [Google Scholar]
  161. E. C. Eckstein, D. L. Bilsker, C. M. Waters, J. S. Kippenhan, A. W. Tilles. Transport of platelets in flowing blood. Ann. N. Y. Acad. Sci., 516 (1987), 442-452. [CrossRef] [PubMed] [Google Scholar]
  162. E. C. Eckstein, F. Belgacem. Model of platelet transport in flowing blood with drift and diffusion terms. Biophys. J., 60 (1991), No. 1, 53-69. [CrossRef] [PubMed] [Google Scholar]
  163. C. Yeh, A. C. Calvez, E. C. Eckstein. An estimated shape function for drift in a platelet-transport model. Biophys. J., 67 (1994), No. 3, 1252-1259. [CrossRef] [PubMed] [Google Scholar]
  164. A. L. Zydney, C. K. Colton. Augmented solute transport in the shear flow of a concentrated suspension. PCH PhysicoChem. Hydrodynamics, 10 (1988), No. 1, 77-96. [Google Scholar]
  165. S. N. Antontsev, A. V. Kazhikhov, V. N. Monakov. Boundary Value Problems in the Mechanics of Heterogeneous Fluids, Novosibirsk, Nauka, 1983. [Google Scholar]
  166. J. Málek, J. Nečas, M. Pokyta, M. Ruzička. Weak and Measure-valued Solutions to Evolutionary DPEs. Chapman and Hall, London, 1996. [Google Scholar]
  167. G. P. Galdi, R. Rannacher, A. H. Robertson, S. Turek. Hemodynamical Flows Modeling: Analysis and Simulation. Oberwolfach Seminar, Birkhauser, Basel, Boston, Berlin, 2008. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.