On uniqueness for the slow flow of a dilute suspension of solid particles in a fluid
Author:
K. A. Pericak-Spector
Journal:
Quart. Appl. Math. 49 (1991), 609-625
MSC:
Primary 76T05; Secondary 35Q35, 76D99
DOI:
https://doi.org/10.1090/qam/1134743
MathSciNet review:
MR1134743
Full-text PDF Free Access
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Additional Information
D. F. McTigue, R. C. Givler, and J. W. Nunziato, Rheological effects of non-uniform particle distributions in dilute suspensions, J. Rheol. 5, 1053–1076 (1986)
A. Einstein, Eine neue Bestimmung der Moleküldimensionen, Ann. Physik 19, 289–306 (1906).
G. K. Batchelor, Sedimentation in a dilute dispersion of spheres, J. Fluid Mech. 52, 245–268 (1972)
G. K. Batchelor and J. T. Green, The determination of the bulk stress in a suspension of spherical particles to order $c^{2}$, J. Fluid Mech. 56, 401–427 (1972)
D. Bedeaux, The effective viscosity for a suspension of spheres, J. Col. Interface Sci. 118, 80–86 (1987)
N. A. Frankel and A. Acrivos, On the viscosity of a concentrated suspension of solid spheres, Chem. Engrg. Sci. 22, 847–853 (1967)
F. Parsi and F. Gadala-Maria, Fore-and-aft asymmetry in a concentrated suspension of solid spheres, J. Rheol. 8, 725–732 (1987)
C. Segre and A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams J. Fluid Mech. 14, 115–135 (1962)
A Karnis, H. L. Goldsmith, and S. G. Mason, The flow of suspensions through tubes V. Inertial effects, Canad. J. Chem. Engrg. 44, 181–193 (1966)
H. Aoki, Y. Kurosaki, and H. Anzai, Study on the tubular pinch effect in a pipe flow I. Lateral migration of a single particle in laminar Poiseuille flow, Bull. JSME 22, 206–212 (1979)
- W. O. Williams, On the theory of mixtures, Arch. Rational Mech. Anal. 51 (1973), 239–260. MR 342045, DOI https://doi.org/10.1007/BF00250532
- Dario Graffi, Il teorema di unicità nella dinamica dei fluidi compressibili, J. Rational Mech. Anal. 2 (1953), 99–106 (Italian). MR 52270, DOI https://doi.org/10.1512/iumj.1953.2.52004
M. E. Gurtin, The Linear Theory of Elasticity, Handbuch der Physik VI a/2 (C. Truesdell, ed.), Springer-Verlag, Berlin, 1972
D. F. McTigue, R. C. Givler, and J. W. Nunziato, Rheological effects of non-uniform particle distributions in dilute suspensions, J. Rheol. 5, 1053–1076 (1986)
A. Einstein, Eine neue Bestimmung der Moleküldimensionen, Ann. Physik 19, 289–306 (1906).
G. K. Batchelor, Sedimentation in a dilute dispersion of spheres, J. Fluid Mech. 52, 245–268 (1972)
G. K. Batchelor and J. T. Green, The determination of the bulk stress in a suspension of spherical particles to order $c^{2}$, J. Fluid Mech. 56, 401–427 (1972)
D. Bedeaux, The effective viscosity for a suspension of spheres, J. Col. Interface Sci. 118, 80–86 (1987)
N. A. Frankel and A. Acrivos, On the viscosity of a concentrated suspension of solid spheres, Chem. Engrg. Sci. 22, 847–853 (1967)
F. Parsi and F. Gadala-Maria, Fore-and-aft asymmetry in a concentrated suspension of solid spheres, J. Rheol. 8, 725–732 (1987)
C. Segre and A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams J. Fluid Mech. 14, 115–135 (1962)
A Karnis, H. L. Goldsmith, and S. G. Mason, The flow of suspensions through tubes V. Inertial effects, Canad. J. Chem. Engrg. 44, 181–193 (1966)
H. Aoki, Y. Kurosaki, and H. Anzai, Study on the tubular pinch effect in a pipe flow I. Lateral migration of a single particle in laminar Poiseuille flow, Bull. JSME 22, 206–212 (1979)
W. O. Williams On the theory of mixtures, Arch. Rational Mech. Anal. 51, 239–260 (1973)
D. Graffi, Il teorema di unicità nella dinamica dei fluidi compressible, JRMA 2, 99–106 (1973)
M. E. Gurtin, The Linear Theory of Elasticity, Handbuch der Physik VI a/2 (C. Truesdell, ed.), Springer-Verlag, Berlin, 1972
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Article copyright:
© Copyright 1991
American Mathematical Society
