On modeling the response of the synovial fluid: Unsteady flow of a shear-thinning, chemically-reacting fluid mixture

Computers and Mathematics with Applications

Volumn 60, Issue 8, 2010, Pages 2333-2349

  Bridges, Craig ^a   Karra, Satish ^a   Rajagopal, K R ^a  

^a Texas AandM University   (United States)

Author keywords

Constrained mixture; Power law fluid; Shear thinning; Synovial fluid; Unsteady oscillations

Indexed keywords

CONSTRAINED MIXTURE; POWER LAW FLUID; SHEAR-THINNING; SYNOVIAL FLUID; UNSTEADY OSCILLATIONS;

BODY FLUIDS; COMPUTATIONAL GEOMETRY; INVERSE PROBLEMS; MIXTURES;

FLUIDS;

EID: 77957366602     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.08.027     Document Type: Article

References (20)

1. A.G. Ogston, and J.E. Stanier The physiological function of hyaluronic acid in synovial fluid; viscous, elastic and lubricant properties J. Physiol. 119 23 1953 244 252
2. D.A. Gibbs, E.W. Merrill, K.A. Smith, and E.A. Balazs Rheology of hyaluronic acid Pept. Sci. 6 1968 777 791
3. S.P. Rwei, S.W. Chen, C.F. Mao, and H.W. Fang Viscoelasticity and wearability of hyaluronate solutions Biochem. Eng. J. 40 2 2008 211 217
4. G.B. Thurston, and H. Greiling Viscoelastic properties of pathological synovial fluids for a wide range of oscillatory shear rates and frequencies Rheol. Acta 17 4 1978 433 445
5. J.E. Gomez, and G.B. Thurston Comparisons of the oscillatory shear viscoelasticity and composition of pathological synovial fluids Biorheology 30 56 1993 409 427
6. J. Hron, J. Mlek, P. Pustjovsk, and K.R. Rajagopal On the modeling of the synovial fluid Adv. in Tribol. 2010 2010 12 pages 10.1155/2010/104957 Article ID 104957
7. D. Voet, and J.G. Voet Biochemistry 2004 Wiley New Jersey
8. C. Bridges, and K.R. Rajagopal Pulsatile flow of a chemically-reacting nonlinear fluid Comput. Math. Appl. 52 67 2006 1131 1144
9. R.S. Rivlin, and J.L. Ericksen Stress-deformation relations for isotropic materials J. Ration. Mech. Anal. 4 3 1955 323 425
10. C. Truesdell, W. Noll, and S.S. Antman The Non-Linear Field Theories of Mechanics 2004 Springer Verlag Berlin
11. J.E. Dunn, and K.R. Rajagopal Fluids of differential type: critical review and thermodynamic analysis Internat. J. Engrg. Sci. 33 5 1995 689 729
12. P.J. Carreau, D.C.R. De Kee, and R.P. Chhabra Rheology of Polymeric Systems: Principles and Applications 1997 Hanser Publishers Ohio
13. J. Mlek, J. Neas, M. Rokyta, and M. Rika Weak and Measure-Valued Solutions to Evolutionary PDEs Applied Mathematical and Mathematical Computations vol. 13 1996 Chapman and Hall London
14. J. Mlek, K.R. Rajagopal, and M. Rika Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity Math. Models Methods Appl. Sci. 5 6 1995 789 812
15. K.R. Rajagopal, and A.R. Srinivasa A thermodynamic frame work for rate type fluid models J. Non-Newton. Fluid Mech. 88 3 2000 207 227
16. W.M. Lai, S.C. Kuei, and V.C. Mow Rheological equations for synovial fluids J. Biomech. Eng. 100 1978 169 186
17. T.C. Laurent, U.B. Laurent, and J.R. Fraser Functions of hyaluronan Ann. Rheum. Dis. 54 5 1995 429 432
18. R. Bandelli, and K.R. Rajagopal Start-up flows of second grade fluids in domains with one finite dimension Internat. J. Non-Linear Mech. 30 6 1995 817 839
19. K.R. Rajagopal On some unresolved issues in non-linear fluid dynamics Russian Math. Surveys 58 2 2003 319 330
20. R.D. Skeel, and M. Berzins A method for the spatial discretization of parabolic equations in one space variable SIAM J. Sci. Stat. Comput. 11 1 1990 1 32