On a nonlocal dispersive equation modeling particle suspensions

Quarterly of Applied Mathematics

Volumn 57, Issue 3, 1999, Pages 573-600

  Zumbrun, Kevin ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; HYDRODYNAMICS; MATHEMATICAL MODELS; PARTICLES (PARTICULATE MATTER);

HOPF EQUATION;

SUSPENSIONS (FLUIDS);

EID: 0032631786     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1704419     Document Type: Article

References (23)

1. G. K. Batchelor, Sedimentation in a dilute suspension of spheres, J. Fluid Mech. 52, 245 (1972)
2. C. Beenakker and P. Mazur, Phys. Fluids 28, 3203 (1985)
3. R. Caflisch and G. C. Papanicolaou, Dynamic theory of suspensions with Brownian effects, SIAM J. Appl. Math. 43, No. 4, 885-906 (1983)
4. S. Childress, Viscous flow past a random array of spheres, J. Chem. Phys. 56, 2527-2539 (1972)
5. J. Goodman and P. Lax, On dispersive difference schemes. I, Comm. Pure Appl. Math. 41 591-613 (1988)
6. T. Hou and P. Lax, Dispersive approximations in fluid dynamics. Comm. Pure Appl. Math. 44, No. 1, 1-40 (1991)
7. H. Hasimoto, On the periodic fundamental solutions of the Stokes' equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5, 317-328 (1959)
8. J. Happel and H. Brenner, Slow viscous flow past a sphere in a cylindrical tube, J. Fluid Mech. 4, 195-213 (1958)
9. E. J. Hinch, J. Fluid Mech. 83, 695 (1977)
10. M. Khodja, Thesis, University of Michigan.
11. M. Khodja and K. Zumbrun, Stability of an oscillatory shock arising in fluid suspensions, to appear.
12. P. Lax, Hyperbolic Systems of Conservation Laws, SIAM Reg. Conf. Ser. 77, 1973
13. S. R. Merchant and E. A. Rosauer, Clays Clay Miner 17, 289 (1969)
14. R. W. O'Brien, A method for the calculation of the effective transport properties of suspensions of interacting particles, J. Fluid Mech. 91, 17-39 (1979)
15. J. Rubinstein, Evolution equations for stratified dilute suspensions, Phys. Fluids A, vol. 2, No. 1, 3-6 (1990)
16. J. Rubinstein and J. B. Keller, Sedimentation of a dilute suspension, Phys. Fluids A 1, 637-643 (1989)
17. J. Rubinstein and J. B. Keller, Particle distribution functions in suspensions, Phys. Fluids A 1, 1632-1641 (1989)
18. A. S. Sangani and A. Acrivos, J. Multiphase Flow 8, 193 (1982)
19. D. B. Siano, Layered sedimentation in suspensions of monodispersive spherical colloidal particles, J. Colloid. Interface Sci. 68. 111 (1979)
20. G. Strang, Accurate partial difference methods, II. Nonlinear problems, Numer. Math. 6, 37-46 (1964)
21. T. J. Tobias and A. P. Ruotsala, Clays Clay Miner 13, 395 (1966)
22. A. I. Volpert, The spaces BV and quasilinear equations, Math. USSR Sb. 2, 257-267 (1967)
23. A. A. Zick and G. M. Homsy, J. Fluid Mech. 115, 13 (1982)