Homogenized non-Newtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid

SIAM Journal on Applied Mathematics

Volumn 64, Issue 3, 2004, Pages 1002-1034

  Berlyand, L ^a   Khruslov, E ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

Homogenization; Non Newtonian fluids; Relaxation time; Surface forces; Suspensions; Viscoelasticity. interaction

Indexed keywords

INTERACTING PARTICLES; RELAXATION TIME; SURFACE FORCES;

MATHEMATICAL MODELS; NEWTONIAN FLOW; RHEOLOGY; SUSPENSIONS (FLUIDS); TENSORS; VISCOELASTICITY; VISCOUS FLOW;

NON NEWTONIAN FLOW;

EID: 3142711769     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902403913     Document Type: Article

References (19)

1. L. V. BERLYAND AND E. YA. KHRUSLOV Non-Newtonian Homogenized Model of a Newtonian Fluid with Interacting Particles, available online at http://www.math.psu.edu/beryland.
2. R. BURRIDGE AND J. B. KELLER, Poroelasticity equations derived from microstructure, J. Acoust. Soc. Amer., 70 (1981), pp. 1140-1146.
3. R. P. GILBERT AND A. MIKELIC, Homogenization of acoustic properties of a seabed, Nonlinear Anal., 40 (2000), pp. 185-212.
4. A. I. LEONOV, On rheology of filled polymers, J. Rheol., 34 (1990), pp. 1039-1068.
5. R. G. LARSON, The Structure and Rheology of Complex Fluids. Oxford University Press, New York, Oxford, 1999.
6. H. GOLDSTEIN, Classical Mechanics, 3rd ed., Addison-Wesley Press, Cambridge, MA, 2002.
7. G. MASK, Theory and Problems of Continuum Mechanics, McGraw-Hill, New York, 1970.
8. R. CHRISTENSEN, Mechanics of Composite Materials, John Wiley & Sons, New York, 1982.
9. N. D. KOPACHEVSKIY, S. G. KREIN, AND N. Z. KA, Operator Methods in Linear Hydrodymamics, Nauka, Moscow, 1989.
10. O. A. LADYZHENSKAIA, The Mathematical Theory of Viscous Incompressible Flow, Translated from Russian by Richard A. Silverman, Gordon and Breach, New York, 1963.
11. A. I. MARKUSHEVICH, Theory of Analytic Functions, Nauka, Moscow, 1968 (in Russian).
12. V. V. JIKOV, S. M. KOZLOV, AND O. A. OLEYNIK, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994.
13. O. A. OLEYNIK, A. S. SHAMAEV, AND G. A. YOSIFIAN, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992.
14. J. N. PERNIN AND E. JACQUET, Elasticity and viscoelasticity in highly heterogeneous composite medium: Threshold phenomenon and homogenization, Internat. J. Engrg. Sci., 39 (2001), pp. 1655-1689.
15. J. SANCHEZ-HUBERT, Asymptotic study of the macroscopic behavior of solid-liquid mixture, Math. Methods Appl. Sci., 2 (1980), pp. 1-11.
16. E. SANOHEZ-PALENCIA, Non-homogeneous Media and Vibration Theory, Springer-Verlag, New York, 1980.
17. W. B. RUSSEL, D. A. SAVILLE, AND W. R. SCHOWALTER, Colloidal Dispersions, Cambridge University Press, Cambridge, UK, 1989.
18. R. TEMAM, Navier-Stokes Equations, North-Holland, Amsterdam, New York, Oxford, 1979
19. M. J. WANG, Effect of polymer-filler and filler-filler interactions on dynamic properties of filled vulcanizates, Rubb. Chem. Technol., 71 (1998), pp. 520-589.