On the modelling of particle-body interactions in stokes flows involving a sphere and circular disc or a torus and circular cylinder using point singularities

Chemical Engineering Communications

Volumn 148-50, Issue , 1996, Pages 161-182

  O'Neill, M E ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Particle body interactions; Point singularity; Stokes flows

Indexed keywords

CYLINDERS (SHAPES); DISKS (STRUCTURAL COMPONENTS); DRAG; HYDRODYNAMICS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; NUMERICAL METHODS; SPHERES; THREE DIMENSIONAL;

BRENNER FIRST ORDER INTERACTION FORMULAE; BRENNER FIRST ORDER WALL CORRECTION THEORY; PARTICLE BODY INTERACTIONS; POINT SINGULARITY; STOKES EQUATIONS; STOKES FLOW; THREE DIMENSIONAL ROTLET; THREE DIMENSIONAL STOKESLET;

FLOW INTERACTIONS;

BODIES-CYLINDERS(CIRCULAR); PARTICLE INTERACTION; STOKES FLOW;

EID: 0030461250     PISSN: 00986445     EISSN: None     Source Type: Journal    
DOI: 10.1080/00986449608936514     Document Type: Article

References (28)

1. Amarakoon, A. M. D., Hussey, R. G., Good, B. J., and Grimsal, E. G., Drag measurements for axisymmetric motion of a torus at low Reynolds number, Phys. of Fluids, 25(9), 1495 (1982).
2. Brenner, H., The slow motion of a sphere through a viscous fluid towards a plane surface, Chem. Engng. Sci., 16, 242 (1961).
3. Brenner, H., Effect of finite boundaries on the Stokes resistance of an arbitrary particle, J. Fluid Mech., 12, 35 (1962).
4. Brenner, H., Effect of finite boundaries on the Stokes resistance of an arbitrary particle. Part II: Asymmetric orientations, J. Fluid Mech., 18, 144 (1964).
5. Brenner, H., Slow viscous rotation of an axisymmetric body within a circular cylinder of finite length, Appl. Sci. Res., 13, 81 (1964).
6. Brenner, H., Hydrodynamic resistance of particles at small Reynolds numbers, Advances in Chemical Engineering, 6, 287 (1966).
7. Brenner, H., and Sonshine, R. M., Slow rotation of a sphere in a circular cylinder, Q. J. Mech. Appl. Math., 17, 55 (1964).
8. Bungay, P. M. and Brenner, H., The motion of a closely fitting sphere in a fluid-filled tube, Int. J. Multiphase Flow, 1, 24 (1973).
9. Davis, A. M. J., O'Neill, M. E., and Brenner, H., Axisymmetric Stokes flows due to a rotlet or stokeslet near a hole in a plane wall: filtration flows, J. Fluid Mech., 103, 183 (1981).
10. Dagan, Z., Pfeffer, R. and Weinbaum, S., Axisymmetric stagnation flow of a spherical particle near a finite planar surface at zero Reynolds number, J. Fluid Mech., 122, 273 (1982).
11. Dorrepaal, J. M., O'Neill, M. E., and Ranger, K. B., Axisymmetrical Stokes flow past a spherical cap, J. Fluid Mech., 75, 273 (1976).
12. Dorrepaal, J. M., Majumdar, S. R., O'Niell, M. E., and Ranger, K. B., A closed torus in Stokes flow, Q. J. Mech. Appl. Math., 29, 381 (1976).
13. Goren, S. L., and O'Neill, M. E., On the hydrodynamic resistance to a particle of a dilute suspension when in the neighbourhood of a large obstacle, Chem. Engng. Sci., 26, 325 (1971).
14. Goren, S. L. and O'Neill, M. E., Asymmetric creeping motion of an open torus, J. Fluid Mech., 101(1), 97 (1980).
15. Gradshteyn, I. S., and Ryzhik, I. M., Tables of Integrals, Series and Products, Academic Press, London (1980).
16. Happel, J., and Brenner, H., Low Reynolds Number Hydrodynamics, Noordhoff International, Leyden (1973).
17. Jeffery, G. B., On the steady rotation of a solid of revolution in a viscous fluid, Proc. Lond. Math. Soc., 2(4), 327 (1915).
18. Kim, S., and Karrila, S. J., Microhydrodynamics, Butterworth-Heinemann, New York (1991).
19. Majumdar, S. R., and O'Neill, M. E., On asymmetrical Stokes flow past a torus, J. Appl. Maths. Phys., 28, 541 (1977).
20. O'Neill, M. E., Small particles in viscous media, Science Progress, Oxf., 67, 149 (1981).
21. O'Neill, M. E., On the settling of a torus in a circular tube, Jour. Math. Phys. Sci., 18, 541 (1984).
22. Ranger, K. B., The Stokes drag for asymmetric flow past a spherical cap, J. Appl. Maths. Phys., 24, 801 (1973).
23. Robin, L., Fonctions Spheriques de Legendre et Fonctions Spheroidales, III Gauther-Villars, Paris (1959).
24. Schneider, J. C., O'Neill, M. E., and Brenner, H., On the slow viscous rotation of a body straddling the interface between two immiscible semi-infinite fluids, Mathematika, 20, 175 (1973).
25. Snow, C., U.S. Nat. Bureau of Standards J. of Research, 43, 377 (1949).
26. Sonshine, R. M., Cox, R. G., and Brenner, H., The Stokes translation of a particle of arbitrary shape along the axis of a circular cylinder, Appl. Sci. Res., 16, 273 (1966).
27. Weinbaum, S., Ganatos, P., and Yan, Z.-Y., Numerical multipole and boundary integral equation techniques in Stokes flow, Annual Rev. Fluid Mech., 22, 275 (1990).
28. Williams, W. E., Boundary effects in Stokes flow, J. Fluid Mech., 24, 285 (1966).