Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 1 - 24
DOI https://doi.org/10.1051/mmnp/20116501
Published online 10 August 2011
  1. M. Anand, K.R. Rajagopal. A shear-thinning viscoelastic fluid model for describing the flow of blood. Int. J. of Cardiovascular Medicine and Science, 4, 2 (2004), 59–68. [Google Scholar]
  2. M. Anand, K.R. Rajagopal. A mathematical model to describe the change in the constitutive character of blood due to platelet activation. C. R. Méchanique, 330 (2002), 557–562. [CrossRef] [Google Scholar]
  3. 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. J. of Theoretical Medicine, 5, 3–4 (2003), 183–218. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Anand, K. Rajagopal, K.R. Rajagopal. A model for the formation and lysis of blood clots. Pathophysiology Haemostasis Thrombosis, 34 (2005), 109-120. [CrossRef] [PubMed] [Google Scholar]
  5. M. Anand, K. Rajagopal, K.R. Rajagopal. A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J. of Theoretical Biology, 253 (2008), 725–738. [CrossRef] [PubMed] [Google Scholar]
  6. N. Arada, M. Pires, A. Sequeira. Viscosity effects on flows of generalized Newtonian fluids through curved pipes. Computers and Mathematics with Applications, 53 (2007), pp. 625-646. [Google Scholar]
  7. N. Arada, M. Pires, A. Sequeira. Numerical simulations of shear-thinning Oldroyd-B fluids in curved pipes. IASME Transactions, Issue 6, 2 (2005), pp. 948-959. [Google Scholar]
  8. P.D. Bailyk, D.A. Steinman, C.R. Ethier. Simulation of non-Newtonian blood flow in an end-to-side anastomosis. Biorheology, 31 (5) (1994) 565-586. [PubMed] [Google Scholar]
  9. A.A. Berger, L. Talbot, L.-S. Yao. Flow in curved pipes. Annu. Rev. Fluid Mech., 15 (1983) 461512. [Google Scholar]
  10. T. Bodnár, A. Sequeira. Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel. In: Advances in Mathematical Fluid Mechanics (edited by R. Rannacher & A. Sequeira), pp. 83–104. Springer Verlag (2010). [Google Scholar]
  11. T. Bodnár, J. Příhoda. Numerical simulation of turbulent free-surface flow in curved channel. Journal of Flow, Turbulence and Combustion, 76 (4) (2006) 429–442. [Google Scholar]
  12. T. Bodnár, A. Sequeira. Numerical simulation of the coagulation dynamics of blood. Computational and Mathematical Methods in Medicine, 9 (2) (2008) 83–104. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Bodnár, A. Sequeira, L. Pirkl. Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd - B Model In: Numerical Analysis and Applied Mathematics, Vols 1 and 2. Melville, New York: American Institute of Physics, (2009), vol. 2, pp. 645–648. [Google Scholar]
  14. T. Bodnár, A. Sequeira, M. Prosi. On the Shear-Thinning and Viscoelastic Effects of Blood Flow under Various Flow Rates. Applied Mathematics and Computation, 217 (2011), 5055–5067. [CrossRef] [MathSciNet] [Google Scholar]
  15. S.E. Charm, G.S. Kurland. Viscometry of human blood for shear rates of 0-100,000 sec-1. Nature, 206 (1965), 617–618. [CrossRef] [PubMed] [Google Scholar]
  16. S. Chien, S. Usami, H.M. Taylor, J.L. Lundberg, M.I. Gregersen. Effect of hematocrit and plasma proteins on human blood rheology at low shear rates. Journal of Applied Physiology, 21, 1 (1966), 81–87. [PubMed] [Google Scholar]
  17. S. Chien, S. Usami, R.J. Dellenback, M.I. Gregersen.Blood viscosity: Influence of erythrocyte aggregation. Science, 157, 3790 (1967), 829–831. [CrossRef] [PubMed] [Google Scholar]
  18. S. Chien, S. Usami, R.J. Dellenback, M.I. Gregersen. Blood viscosity: Influence of erythrocyte deformation. Science, 157, 3790 (1967), 827–829. [CrossRef] [PubMed] [Google Scholar]
  19. S. Chien, S. Usami, R. J. Dellenback, M.I. Gregersen. Shear-dependent deformation of erythrocytes in rheology of human blood. American Journal of Physiology, 219 (1970), 136–142. [Google Scholar]
  20. S. Chien, K.L.P. Sung, R. Skalak, S. Usami, A.L. Tozeren. Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophysical Journal, 24, 2 (1978), 463–487. [CrossRef] [PubMed] [Google Scholar]
  21. E.A. Evans, R.M. Hochmuth. Membrane viscoelasticity. Biophysical Journal, 16, 1 (1976), 1–11. [CrossRef] [PubMed] [Google Scholar]
  22. Y. Fan, R.I. Tanner, N. Phan-Thien. Fully developed viscous and viscoelastic flows in curved pipes. J. Fluid Mech., 440 (2001), 327-357. [Google Scholar]
  23. F. Gijsen, F. van de Vosse, J. Janssen. The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. Journal of Biomechanics, 32 (1999), 601-608. [CrossRef] [PubMed] [Google Scholar]
  24. J. Hron, J. Málek, S. Turek. A numerical investigation of flows of shear-thinning fluids with applications to blood rheology. Int. J. Numer. Meth. Fluids, 32 (2000), 863-879. [CrossRef] [Google Scholar]
  25. A. Jameson, W.Schmidt, E. Turkel. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping scheme. In: AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto (1981), AIAA paper 81-1259. [Google Scholar]
  26. A. Leuprecht, K. Perktold. Computer simulation of non-Newtonian effects of blood flow in large arteries. Comp. Methods in Biomech. and Biomech. Eng., 4 (2001), 149–163. [CrossRef] [Google Scholar]
  27. D. Quemada. Rheology of concentrated disperse systems III. General features of the proposed non-Newtonian model. Comparison with experimental data. Rheol. Acta, 17 (1978), 643–653. [CrossRef] [Google Scholar]
  28. K.R. Rajagopal, A.R. Srinivasa. A thermodynamic frame work for rate type fluid models. Journal of Non-Newtonian Fluid Mechanics, 80 (2000), 207–227. [CrossRef] [Google Scholar]
  29. K.R. Rajagopal, A.R. Srinivasa. A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials. Proc. R. Soc. A, 467 (2011), 39–58. [CrossRef] [Google Scholar]
  30. G.B. Thurston. Viscoelasticity of human blood. Biophysical Journal, 12 (1972), 1205–1217. [CrossRef] [PubMed] [Google Scholar]
  31. G.B. Thurston. Frequency and shear rate dependence of viscoelasticity of blood. Biorheology, 10, 3 (1973), 375–381. [PubMed] [Google Scholar]
  32. G.B. Thurston. Non-Newtonian viscosity of human blood: Flow induced changes in microstructure. Biorheology, 31(2), (1994), 179–192. [PubMed] [Google Scholar]
  33. J. Vierendeels, K. Riemslagh, E. Dick. A multi-grid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids. J. Comput. Phys., 154 (1999), 310–344. [CrossRef] [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.