The constitutive relation of suspensions of noncolloidal particles in viscous fluids

Physics of Fluids

Volumn 15, Issue 7, 2003, Pages 1888-1896

  Mauri, Roberto ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; DIFFUSION; FUNCTIONS; PARTICLE SIZE ANALYSIS; SUSPENSIONS (FLUIDS); TENSORS;

NONCOLLOIDAL PARTICLES;

VISCOUS FLOW;

COLLOID; CONVECTION; SUSPENSION; VISCOUS FLUID;

EID: 0042827340     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1580478     Document Type: Article

References (41)

1. A. Acrivos, "Shear-induced particle diffusion in concentrated suspensions of noncolloidal particles," J. Rheol. 39, 813 (1995).
2. V. Breedveld, D. Van den Ende, A. Tripathi, and A. Acrivos, "The measurement of the shear-induced particle and fluid tracer diffusivities in concentrated suspensions by a novel method," J. Fluid Mech. 375, 297 (1998).
3. G. Bossis and J.F. Brady, "Self diffusion of Brownian particles in concentrated suspensions under shear," J. Chem. Phys. 87, 5437 (1987).
4. D. Leighton and A. Acrivos, "The shear-induced migration of particles in concentrated suspensions," J. Fluid Mech. 181, 415 (1987).
5. R.J. Phillips, R.C. Armstrong, R.A. Brown, A.L. Graham, and J.R. Abbott, "A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration," Phys. Fluids A 4, 30 (1992).
6. P.R. Nott and J.F. Brady, "Measurement of shear-induced self diffusion in concentrated suspensions of spheres," J. Fluid Mech. 275, 157 (1994).
7. M. Marchioro and A. Acrivos, "Shear-induced particle diffusivities from numerical simulations," J. Fluid Mech. 443, 101 (2001).
8. D. Leighton and A. Acrivos, "Measurement of shear-induced self diffusion of particles in shear flow of a suspension," J. Fluid Mech. 179, 191 (1987).
9. A. Acrivos, G.K. Batchelor, E.J. Hinch, D.L. Koch, and R. Mauri, "Longitudinal shear-induced diffusion of spheres in a dilute suspensions," J. Fluid Mech. 240, 651 (1992).
10. Y.G. Wang, R. Mauri, and A. Acrivos, "The transverse shear-induced liquid and particle tracer diffusivities of a dilute suspension of spheres undergoing a simple shear flow," J. Fluid Mech. 327, 255 (1996).
11. M. Loewenberg and E.J. Hinch, "Collision of two deformable drops in shear flow," J. Fluid Mech. 338, 299 (1997).
12. F.R. DaCunha and E.J. Hinch, "Shear-induced dispersion in a dilute suspension of rough spheres," J. Fluid Mech. 309, 211 (1996).
13. Y.G. Wang, R. Mauri, and A. Acrivos, "Transverse shear-induced gradient diffusion in a dilute suspension of spheres," J. Fluid Mech. 357, 279 (1998).
14. Y.G. Wang and R. Mauri, "Longitudinal shear-induced gradient diffusion in a dilute suspension of spheres," Int. J. Multiphase Flow 25, 875 (1999).
15. G.I. Taylor, "Diffusion by continuous movement," Proc. London Math. Soc. 20, 196 (1921).
16. G.K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, UK, 1953).
17. P.G. Saffman, "On the effect of the molecular diffusivity in turbulent diffusion," J. Fluid Mech. 8, 273 (1962).
18. R.H. Kraichnan, "Diffusion by a random velocity field." Phys. Fluids 13, 22 (1970).
19. A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (MIT, Cambridge, MA, 1971), Vol. 1, pp. 540-547 and 591-606.
20. S. Whitaker, "The transport equations for multiphase systems," Chem. Eng. Sci. 28, 139 (1973).
21. H. Brenner, "Dispersion resulting from flow through spatially periodic porous media," Philos. Trans. R. Soc. London, Ser. A 297, 81 (1980).
22. H. Brenner and P. Adler, "Dispersion resulting from flow through spatially periodic porous media. II. Surface and intraparticle transport," Philos. Trans. R. Soc. London, Ser. A 307, 149 (1982).
23. D.L. Koch and J.F. Brady, "Dispersion in fixed beds," J. Fluid Mech. 154, 399 (1985).
24. D.L. Koch and J.F. Brady, "A non-local description of advection-diffusion with application to dispersion in porous media," J. Fluid Mech. 180, 387 (1987).
25. D.W. McLaughlin, G.C. Papanicolaou, and O.R. Pironneau, "Convection of microstructures and related problems," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 45, 780 (1985).
26. J. Rubinstein and R. Mauri, "Dispersion and convection in periodic porous media," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 46, 1018 (1986).
27. R. Mauri, "Dispersion, convection and reaction in porous media," Phys. Fluids A 3, 743 (1991).
28. R. Mauri. "Heat and mass transport in random velocity fields with application to dispersion in porous media," J. Eng. Math. 29, 77 (1995).
29. G.I. Taylor. "Dispersion of soluble matter in solvent flowing slowly through a tube," Proc. R. Soc. London, Ser. A 219, 186 (1953).
30. R. Aris, "On the dispersion of a solute in a fluid flowing through a tube." Proc. R. Soc. London. Ser. A 235, 67 (1956).
31. W.N. Gill and R. Sankarasubramanian, "Exact analysis of unsteady convective diffusion," Proc. R. Soc. London, Ser. A 316, 341 (1970).
32. H. Brenner and D.A. Edwards, Macrotransport Processes (Butterworth-Heinemann. Boston, 1993).
33. S. Haber and R. Mauri, "Lagrangian approach to time-dependent laminar dispersion in rectangular conduits." J. Fluid Mech. 190, 201 (1989).
34. R. Mauri and S. Haber, "Time-dependent dispersion of small particles in rectangular conduits," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math, 51, 1538 (1991).
35. R. Zwanzig, in Lectures in Theoretical Physics (Wiley-Interscience, New York, 1961). Vol. 3.
36. S.R. DeGroot and P. Mazur, Non-Equilibrium Thermodynamics (Dover, New York, 1962).
37. A. Bensoussan, J.L. Lions, and G. Papanicolaou. Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam, 1978).
38. E. Sanchez-Palencia, NonHomogeneous Media and Vibration Theory (Springer, Berlin, 1980).
39. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II. Nonequilibrium Statistical Mechanics (Springer, Berlin, 1991), pp. 62-69.
40. H.J. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations (Oxford University Press, Oxford, 1981), pp. 322-340.
41. R. Mauri and D.T. Papageorgiou, "The onset of particle segregation in plane Couette flows of concentrated suspensions," Int. J. Multiphase Flow 28, 127 (2002).