Network approximation for effective viscosity of concentrated suspensions with complex geometry

SIAM Journal on Mathematical Analysis

Volumn 36, Issue 5, 2005, Pages 1580-1628

  Berlyand, Leonid ^a   Borcea, Liliana ^b   Panchenko, Alexander ^a,c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b Rice University   (United States)

^c WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Concentrated suspension; Discrete network; Effective viscosity; Variational bounds

Indexed keywords

CONCENTRATED SUSPENSIONS; DISCRETE NETWORKS; EFFECTIVE VISCOSITY; VARIATIONAL BOUNDS;

BOUNDARY CONDITIONS; ESTIMATION; GRAPH THEORY; INCOMPRESSIBLE FLOW; INTERFACES (MATERIALS); MATRIX ALGEBRA; REYNOLDS NUMBER; SUSPENSIONS (FLUIDS); VISCOSITY; VISCOUS FLOW;

APPROXIMATION THEORY;

EID: 25144496926     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141003424708     Document Type: Article

References (33)

1. G. ALLAIRE, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes, Arch. Ration. Mech. Anal., 113 (1990), pp. 209-259.
2. G. ALLAIRE, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II. Noncritical sizes of the holes for a volume distribution and a surface distribution of holes, Arch. Ration. Mech. Anal., 113 (1990), pp. 261-298.
3. 2, J. Fluid Mech., 56 (1972), pp. 401-427.
4. L. BERLYAND AND E. KHRUSLOV, Homogenized non-Newtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid, SIAM J. Appl. Math., 64 (2004), pp.1002-1034.
5. L. BERLYAND AND A. KOLPAKOV, Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite, Arch. Ration. Mech. Anal., 159 (2001), pp. 179-227.
6. L. BERLYAND AND A. NOVIKOV, Error of the network approximation for densely packed composites with irregular geometry, SIAM J. Math. Anal., 34 (2002), pp. 385-408.
7. L. BERLYAND AND A. PANCHENKO, Geometric Instability in the Asymptotics of the Effective Viscosity for Highly Packed Suspensions of Rigid Particles, preprint.
8. L. BORCEA, Asymptotic analysis of quasi-static transport in high contrast conductive media, SIAM J. Appl. Math., 59 (1998), pp. 597-635.
9. L. BORCEA, J. G. BERRYMAN, AND G. PAPANICOLAOU, Matching pursuit for imaging high contrast conductivity, Inverse Problems, 15 (1999), pp. 811-849.
10. L. BORCEA AND G. PAPANICOLAOU, Network approximation for transport properties of high contrast materials, SIAM J. Appl. Math., 58 (1998), pp. 501-539.
11. L. BORCEA AND G. PAPANICOLAOU, Low frequency electromagnetic fields in high contrast media, in Surveys on Solution Methods for Inverse Problems, D. Colton, H. W. Engl, A. Louis, J. R. McLaughlin, and W. Rundell, eds., Springer, New York, 2000, pp. 195-233.
12. J. F. BRADY, The rheological behavior of concentrated colloidal suspensions, J. Chem. Phys., 99 (1993), pp. 567-581.
13. R. COURANT AND D. HILBERT, Methods of Mathematical Physics, Vol. I, John Wiley, New York, 1953.
14. A. EINSTEIN, Eine neue Bestimmung der Moleküldimensionen, Ann. Phys., 19 (1906), p. 289,
15. A. EINSTEIN, Ann. Phys., 34 (1906), p. 591.
16. N. A. FRANKEL AND A. AKRIVOS, On the viscosity of a concentrated suspension of solid spheres, Chem. Engrg. Sci., 22 (1967), pp. 847-853.
17. A. L. GRAHAM, On the viscosity of suspension of solid spheres, Appl. Sci. Res., 37 (1981), pp. 275-286.
18. B. I. HALPERIN, Remarks on percolation and transport in networks with a wide range of bond strengths, Phys. D, 38 (1989), pp. 179-183.
19. L. HÖRMANDER, Analysis of Linear Partial Differential Operators, Vol. 1, Springer, New York, 1983.
20. D. J. JEFFREY AND A. ACRIVOS, The rheological properties of suspensions of rigid particles, American Institute of Chemical Engineering, 22 (1976), pp. 417-432.
21. J. B. KELLER, Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders, J. Appl. Phys., 43 (1963), pp. 991-993.
22. J. KOPLIK, Creeping flow in two-dimensional networks, J. Fluid Mech., 119 (1982), pp. 219-247.
23. S. M. KOZLOV, Geometric aspects of averaging, Russian Math. Surveys, 44 (1989), pp. 91-144.
24. L. D. LANDAU AND E. M. LIFSHITZ, Fluid Mechanics, Pergamon Press, New York, 1987.
25. R. LARSEN, The Structure and Rheology of Complex Fluids, Oxford University Press, New York, 1999.
26. T. LEVY AND E. SANCHEZ-PALENCIA, Suspension of solid particles in a Newtonian fluid, J. Non-Newtonian Fluid Mech., 13 (1983), pp. 63-78.
27. E. E. MOISE, Geometric Topology in Dimensions 2 and 3, Springer, New York, 1977.
28. K. C. NUNAN AND J. B. KELLER, Effective viscosity of a periodic suspension, J. Fluid Mech., 142 (1984), pp. 269-287.
29. L. M. SCHWARTZ, J. R. BANAVAR, AND B. I. HALPERIN, Biased-diffusion calculations of effective transport in inhomogeneous continuum systems, Phys. Rev. B, 3 (1989), pp. 9155-9161.
30. C. B. SHAH AND Y. C. YORTSOS, The permeability of strongly disordered systems, Phys. Fluids, 8 (1996), pp. 280-282.
31. C. A. SHOOK AND M. C. ROCKO, Slurry Flow. Principles and Practice, Butterworth-Heinemann, New York, 1991.
32. A. SIEROU AND J. F. BRADY, Accelerated Stokesian dynamic simulations, J. Fluid Mech., 448 (2001), pp. 115-146.
33. B. VEYTSMAN, J. MORRISON, AND A. SCARONI, The packing viscosity of concentrated poly disperse coal/water slurries, Energy Fuels, 12 (1998), pp. 1031-1039.