Slow viscous motion of a solid particle in a spherical cavity

CMES - Computer Modeling in Engineering and Sciences

Volumn 25, Issue 3, 2008, Pages 165-179

  Sellier, A ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Boundary integral equations; Green tensor; Sedimentation; Spherical cavity; Stokes flow; Wall particle interactions

Indexed keywords

BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; NEWTONIAN LIQUIDS; SEDIMENTATION; VISCOSITY;

GREEN TENSORS; SOLID PARTICLES; SPHERICAL CAVITY; STOKES FLOW; WALL PARTICLE INTERACTIONS;

ELEMENTARY PARTICLES;

EID: 44649129091     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. Beskos, D. E. (1998): Introduction to Boundary Element Methods. Elsevier Science Publishers.
2. Bonnet, M. (1999): Boundary Integral Equation Methods for Solids and Fluids. John Wiley & Sons Ltd.
3. Brenner, H. (1961) : The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci., vol. 16, pp. 242-251.
4. A. Brebbia, J. C. T.; Wrobel, L. C. (1984): Boundary Element Techniques. Springer-Verlag, Theory and Applications in Engineering, Berlin Heidelberg New York Tokyo.
5. Chaoui, M.; Feuillebois, F. (2003): Creeping flow around a sphere in shear flow close to a wall. Q. J. Mech. Appl. Math., vol. 56, pp. 381-410.
6. Cichocki, B.; Jones, R. B. (1998): Image representation of a spherical particle near a hard wall. Physica A, vol. 258, pp. 273-302.
7. Cichocki, B.; Jones, R. B.; Kutteh, R.; Wajnryb, E. (2000): Friction and mobility for colloidal spheres in Stokes flow near a boundary. J. Chem. Phys., vol. 112, no. 5, pp. 2548-2561.
8. Cunningham, E. (1910): On the velocity of steady fall os spherical particles through fluid medium. Proc. Roy. Soc, vol. A, pp. 357-365.
9. Dean, W. R.; O'Neill, M. E. (1963): A slow motion of viscous liquid caused by the rotation of a solid sphere. Mathematika, vol. 10, pp. 13-24.
10. F. Duddeck (2006): An Alternative Approach to Boundary Element Methods via the Fourier Transform. CMES: Computer Modeling in Engineering and Science, vol. 15, no. 1, pp. 1-14.
11. Ganatos, P.; Peffer, R.; Weibaum, S. (1980a): A strong interaction therory for the creeping motion of a sphere between plane parallel boundaries. 1. Perpendicular motion. J. Fluid Mech, vol. 9, pp. 739-753.
12. Ganatos, P.; Peffer, R.; Weibaum, S. (1980b): A strong interaction therory for the creeping motion of a sphere between plane parallel boundaries. 1. Parallel motion. J. Fluid Mech, vol. 9, pp.755-783.
13. Gardano, P.; Dabnichki, P. (2006): Application of Boundary Element Method to Modelling of Added Mass and Its Effect on Hydrodynamic Forces. CMES: Computer Modeling in Engineering and Science, vol. 15, no. 2, pp. 87-98.
14. Goldman, A. J.; Cox, R. G.; Brenner, H. (1967a): Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid. Chem. Engng Sci., vol. 22, pp. 637-651.
15. Goldman, A. J.; Cox, R. G.; Brenner, H. (1967b): Slow viscous motion of a sphere parallel to a plane wall. II. Couette flow. Chem. Engng Sci., vol. 12, pp. 653-660.
16. Happel, J.; Brenner, H. (1973): Low Reynolds number hydrodynamics. Martinus Nijhoff.
17. Hsu, R.; Ganatos, P. (1989): The motion of a rigid body in viscous fluid bounded by a plane wall. J. Fluid Mech, vol. 207, pp. 29-72.
18. Hsu, R.; Ganatos, P. (1994): Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number. J. Fluid Mech, vol. 268, pp. 267-292.
19. Jeffery, G. B. (1915) : On the steady rotation of a solid of revolution in a viscous fluid. Proc. Lond. Math. Soc. (Series 2), vol. 14, pp. 327-338.
20. Jones, R. B. (2004): Spherical particle in Poiseuille flow between planar walls. Journal of Chemical Physics, vol. 121, pp. 483-500.
21. Jones, R. B. (2008): Dynamics of a colloid in a spherical cavity. To appear in Methods of creeping flows. Editors: F.Feuillebois and & A. Sellier.
22. Kim, S.; Karrila, S. J. (1991): Microhydrodynamics: Principles and Selected Applications. Butterworth.
23. O'Neill, M. E. (1964): A slow motion of viscous liquid caused by a slowly moving solid sphere. Mathematika, vol. 11, pp. 67-74.
24. O'Neill, M. E. (1967) : A slow motion of viscous liquid caused by a slowly moving solid sphere: an addendum. Mathematika, vol. 14, pp. 170-172.
25. O'Neill, M. E.; Majumdar, S. R. (1970): Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part I: the determination of exact solutions for any values of the ratio of radii and separation parameters. J. Appl. Math. Phys., vol. 21, pp. 164-179.
26. O'Neill, M. E.; Majumdar, S. R. (1970): Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part II: asymptotic forms of the solutions when the minimum clearance between the spheres apporaches zero. J. Appl. Math. Phys., vol. 21, pp. 180-187.
27. O'Neill, M. E.; Stewartson, K. (1967): On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech., vol. 27, pp. 705-724.
28. Oseen, C. W. (1927): Neure Methoden und Ergebnisse in der Hydrodynamik. Akademische Verlagsgesellschat M. B. H.
29. P. B. Wang and Z. H. Yao (2005): A New Fast Multipole boundary Element Method for large sacie analysis of mechanical properties in 3D particle-reinforced composites. CMES: Computer Modeling in Engineering and Science, vol. 7, no. 1, pp. 85-96.
30. P. B. Wang and Z. H. Yao and T. Lei (2006): Analysis of solid with numerous microcracks using the Fast Multipole DBEM. CMC: Computers, Materials, & Continua, vol. 3, no. 2, pp. 65-76.
31. Pasol, L.; Chaoui, M.; Yahiaoui, S.; Feuillebois, F. (2005): Analytical solutions for a spherical particle near a wall in axisymmetrical polynomial creeping flows. Phys. Fluids 17, vol. 17, pp. 073602.1-073602.13.
32. Pasol, L.; Sellier, A. (2006): Gravitational motion of a two-particle cluster between two parallel plane walls. Comptes Rendus Mécanique, vol. 334, pp. 105-110.
33. Pasol, L.; Sellier, A.; Feuillebois, F. (2006): A sphere in a second degree polynomial creeping flow parallel to a wall. Q. J. Mech. Appl. Math, vol. 59, pp. 587-614.
34. Pozrikidis, C. (1992): Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press.
35. Sanz, J.; Solis, M.; Dominguez, J. (2007): Hypersingular BEM for Piezoelectric Solids: Formulation and Applications for Fracture Mechanics. CMES: Computer Modeling in Engineering and Science, vol. 17, no. 3, pp. 215-230.
36. Sellier, A. (2007): Slow viscous migration of a conducting solid particle under the action of uniform ambient electric and magnetic fields. CMES: Computer Modeling in Engineering and Science, vol. 21, no. 2, pp. 105-132.
37. Sellier, A.; Pasol, L. (2006): Sedimentation of a Solid Particle Immersed in a Fluid Film. CMES: Computer Modeling in Engineering and Science, vol. 16, no. 3, pp. 187-196.
38. Staben, M. E.; Zinchenko, A. Z.; Davis, R. H. (2003) : Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Physics of Fluids, vol. 15, pp. 1711-1733.
39. Stimson, M.; Jeffery, G. B. (1926): The motion of two spheres in a viscous Fluid. Proc. Roy. Soc., vol. A 111, pp. 110-121.
40. Williams, E. (1915): On the motion of a sphere in a viscous fluid. Phil. Mag. 6th Serie, vol. 29, pp. 526-555.