Stokes flow caused by the motion of a rigid sphere close to a viscous interface

Chemical Engineering Science

Volumn 53, Issue 19, 1998, Pages 3413-3434

  Danov, K D ^a   Gurkov, T D ^a   Raszillier, H ^b   Durst, F ^b  

^a UNIVERSITY OF SOFIA   (Bulgaria)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

IMMOBILIZATION; LIQUID FLOW; VISCOSITY;

DRAG; INTEGRATION; INTERFACES (MATERIALS); MATHEMATICAL MODELS; PRESSURE DISTRIBUTION; REYNOLDS NUMBER; SHEAR FLOW; SPHERES; STRESSES; SURFACE PROPERTIES; VISCOSITY;

BOUSSINESQ-SCRIVEN MODEL; CAPILLARY NUMBERS; CREEPING FLOW; STOKES FLOW; SURFACE VISCOSITY; VISCOUS INTERFACE;

FLOW OF FLUIDS;

INTERFACE; STOKES FLOW; TWO-PHASE FLOW; VISCOUS FLOW;

EID: 0032476197     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0009-2509(98)00137-7     Document Type: Article

References (28)

1. Arfken, G. (1985) Mathematical Methods for Physicists. Academic Press, Boston.
2. Berdan, C. II and Leal, L. G. (1982) Motion of a sphere in the presence of a deformable interface. I. Perturbation of the interface from flat: the effects on drag and torque. J. Colloid Interface Sci. 87, 62-80.
3. Boussinesq, M. J. (1913) Sur l'éxistance d'une viscosité superficielle, dans la mince couche de transition separant un liquide d'une autre fluide contigue. Ann. Chim. Phys. 29, 349-357.
4. Cooley, M. D. A. and O'Neill, M. E. (1968) On the slow rotation of a sphere about a diameter parallel to a nearby plane wall. J. Inst. Math. Appl. 4, 163-173.
5. Danov, K. D., Aust, R., Durst, F. and Lange, U. (1995) Influence of the surface viscosity on the drag and torque coefficients of a solid particle in a thin liquid layer. Chem. Engng Sci. 50, 263-277.
6. Dean, W. R. and O'Neill, M. E. (1963) A slow motion of viscous liquid caused by a slowly rotating solid sphere. Mathematika 10, 13-24.
7. Edwards, D. A., Brenner, H. and Wasan, D. T. (1991) Interfacial Transport Processes and Rheology. Butterworth-Heinemann, Boston.
8. Faxén, H. (1921) Dissertation. Uppsala University.
9. Goldman, A. J., Cox, R. G. and Brenner, H. (1967) Slow viscous motion of a sphere parallel to a plane wall. Chem. Engng Sci. 22, 637-651.
10. Graham, D. E. and Phillips, M. C. (1980a) Proteins at liquid interfaces. IV. Dilatational properties. J. Colloid Interface Sci. 76, 227-239.
11. Graham, D. E. and Phillips, M. C. (1980b) Proteins at liquid interfaces. V. Shear properties J. Colloid Interface Sci. 76, 240-250.
12. Happel, J. and Brenner, H. (1965) Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media. Prentice-Hall, Englewood Cliffs, NJ.
13. Hunter, R. J. (1987) Foundations of Colloid Science, Vol. 1, pp. 608-611. Clarendon Press, Oxford.
14. Jahnke, E., Emde, F. and Lösch, F. (1960) Tafeln Höherer Funktionen. B. G. Teubner Verlagsgesellschaft, Stuttgart.
15. Kim, S. and Karrila, S. J. (1991) Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann, Boston.
16. Lamb, H. (1945) Hydrodynamics. Dover, New York.
17. Lee, S. H. and Leal, L. G. (1980) Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates. J. Fluid Mech. 98, 193-224.
18. O'Neill, M. E. (1964) A slow motion of viscous liquid caused by a slowly moving solid sphere. Mathematika 11, 67-74.
19. O'Neill, M. E. and Ranger, K. B. (1979) Rotation of a sphere in two phase flow. Int. J. Multiphase Flow 5, 143-148.
20. O'Neill, M. E. and Stewartson, K. (1967) On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech. 27, 705-724.
21. Petkov, J. T., Denkov, N. D., Danov, K. D., Velev, O. D., Aust, R. and Durst, F. (1995) Measurement of the drag coefficient of spherical particles attached to fluid interfaces. J. Colloid Interface Sci. 172, 147-154.
22. Scriven, L. E. (1960) Dynamics of a Fluid Interface. Chem. Engng Sci. 12, 98-108.
23. Shapira, M. and Haber, S. (1988) Low Reynolds number motion of a droplet between two parallel flat plates. Int. J. Multiphase Flow 14, 483-506.
24. Shapira, M. and Haber, S. (1990) Low Reynolds number motion of a droplet in shear flow including wall effects. Int. J. Multiphase Flow 16, 305-321.
25. Slattery, J. C. (1990) Interfacial Transport Phenomena. Springer, New York.
26. Smoluchowski, M. (1911) On the mutual action of spheres which move in a viscous liquid. Bull. Acad. Sci. Cracovie A 1, 28-39.
27. Stokes, G. G. (1851) On the effect of the internal friction of fluids on the motion of a pendulum. Trans. Cambridge Phil. Soc. 1, 104-106.
28. Wakiya, S. (1956) Res. Rep. Fac. Engng Niigata University, Japan 5, 1.