Interception of two spheres with slip surfaces in linear Stokes flow

Journal of Fluid Mechanics

Volumn 581, Issue , 2007, Pages 129-156

  Luo, H ^a   Pozrikidis, C ^b  

^a George Washington University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; FLOW OF FLUIDS; FLOW VELOCITY; SHEAR FLOW; VISCOSITY;

FOURIER COEFFICIENT; LINEAR STOKES FLOW; NAVIER-MAXWELL-BASSET LAW;

FLUID MECHANICS;

BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; FLOW OF FLUIDS; FLOW VELOCITY; FLUID MECHANICS; SHEAR FLOW; VISCOSITY;

BOUNDARY ELEMENT METHOD; FOURIER TRANSFORM; INTERCEPTION; NAVIER-STOKES EQUATIONS; SPHERE; VISCOSITY;

EID: 34548147059     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007005551     Document Type: Article

References (29)

1. BASSET, A. B. 1888 A Treatise on Hydrodynamics. Cambridge University Press (Reprinted by Dover, 1961).
2. BATCHELOR, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545-570.
3. BATCHELOR, G. K. & GREEN, J. T. 1972a The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375-400.
4. BATCHELOR, G. K. & GREEN, J. T. 1972b The determination of the bulk stress in a suspension of spherical particles to order c 2. J. Fluid Mech. 56, 401-427.
5. BEAVERS, G. S. & JOSEPH, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197-207.
6. BLACK, W. B. & GRAHAM, M. D. 2001 Slip, concentration fluctuations and flow instability in sheared polymer solutions. Macromolecules 34, 5731-5733.
7. CERCIGNANI, C. 2000 Rarefied Gas Dynamics. Cambridge University Press.
8. CICHOCKI, B., FELDERHOF, B. U. & SCHMITZ, R. 1988 Hydrodynamic interactions between two spherical particles. Physicochem. Hydrodyn. 10, 383-403.
9. DAVIS, R. H., ZHAO, Y., GALVIN, K. P., & WILSON, H. J. 2003 Solid-solid contacts due to surface roughness and their effects on suspension behaviour. Phil. Trans. R. Soc. Lond. A 361, 871-894.
10. EINSTEIN, A. 1906 Eine neue Bestimmung der Moleküledimensionen. Annalen Phys. 19, 289-306.
11. FELDERHOF, B. U. 1976a Force density on a sphere in linear hydrodynamics. I. Fixed sphere, stick boundary conditions. Physica A 84, 557-568.
12. FELDERHOF, B. U. 1976b Force density on a sphere in linear hydrodynamics. II. Moving sphere, mixed boundary conditions. Physica A 84, 569-576.
13. FELDERHOF, B. U. & JONES, R. B. 1986 Hydrodynamics scattering theory of flow about a sphere. Physica A 136, 77-98.
14. HOCKING, L. M. 1973 The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres. J. Engng. Math. 7 207-221.
15. JONES, R. B. & SCHMITZ, R. 1988 Mobility matrix for arbitrary spherical particles in solution. Physica A 149, 373-394.
16. KIM, S. & KARRILA, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
17. LUO, H. & POZRIKIDIS, C. 2007 Effect of slip on the motion of a spherical particle in infinite flow and near a plane wall. J. Engng Maths (Submitted).
18. MAXWELL, J. C. 1879 On stresses in rarefied gases arising from inequalities of temperature. Phil. Trans. Roy. Soc. Lond. 170 231-256.
19. NAVIER, C. L. M. H. 1823 Mémoire sur les lois du mouvement des fluides. Mémoires de l'Académie Royale des Sciences de l'Institut de France VI, 389-440.
20. POZRIKIDIS, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
21. SCHAAF, S. A. & CHAMBRE, P. L. 1961 Flow of Rarefied Gases. Princeton University Press.
22. SCHMITZ, R. & FELDERHOF, B. U. 1978 Creeping flow about a sphere. Physica A 92, 423-437.
23. SCHMITZ, R. & FELDERHOF, B. U. 1982a Creeping flow about a spherical particle. Physica A 113, 90-102.
24. SCHMITZ, R. & FELDERHOF, B. U. 1982b Friction matrix for two spherical particles with hydrodynamic interaction. Physica A 113, 103-116.
25. SCHMITZ, R. & FELDERHOF, B. U. 1982c Mobility matrix for two spherical particles with hydrodynamic interaction. Physica A 116, 163-177.
26. TAYLOR, G. I. 1932 The viscosity of a fluid containing small drops of another liquid. Proc. R. Soc. Lond. A 138, 41-48.
27. VINOGRADOVA, O. I. 1999 Slippage of water over hydrophobic surfaces. J. Miner. Proc. 56, 31-60.
28. WILSON, H. J. & DAVIS, R. H. 2000 The viscosity of a dilute suspension of rough spheres. J. Fluid Mech. 421, 339-367.
29. WILSON, H. J. & DAVIS, R. H. 2002 Shear stress of a monolayer of rough spheres. J. Fluid Mech. 452, 425-441.