A second kind integral equation formulation for the low Reynolds number interaction between a solid particle and a viscous drop

Journal of Engineering Mathematics

Volumn 30, Issue 1-2, 1996, Pages 225-237

  Power, H ^a,b  

^a UNIVERSITY OF PORTSMOUTH   (United Kingdom)

^b UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

DROPS; PARTICLES; REYNOLDS NUMBER; SOLID; VISCOUS;

DROP BREAKUP; INTEGRAL EQUATIONS; PARTICLES (PARTICULATE MATTER); REYNOLDS NUMBER; VISCOSITY OF LIQUIDS; VISCOUS FLOW;

NEUTRALLY BUOYANT DROP; SECOND KIND FREDHOLM INTEGRAL EQUATIONS;

FLOW INTERACTIONS;

EID: 0030088244     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00118832     Document Type: Article

References (19)

1. R. Clift, J.R Grace and M.E. Weber, Bubbles, Drops, and Particles. New York: Academic Press (1978) 380 pp.
2. G.K. Batchelor, An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press (1967) 615 pp.
3. J.M. Rallison and A. Acrivos, A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89 (1978) 191-200.
4. H.A. Lorentz, Eene algemeene stelling omtrent de beweging eener vloeistof met wrijving en eenige daaruit afgeleide gevolgen. Zittingsverslag Koninkl. Akad. van Wetensch. Amsterdam 5 (1896) 168-174.
5. F.K.G. Odqvist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten. Math. Zeitsch. 32 (1930) 329-375.
6. O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach (1963) 184 pp.
7. H. Power, On the Rallison and Acrivos solution for the deformation and burst of viscous drops in an extensional flow. J. Fluid Mech. 185 (1987) 547-550.
8. G.K. Youngren and A. Acrivos, Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69 (1975) 377-403.
9. H. Power and L.C. Wrobel, Boundary Integral Methods in Fluid Mechanics. Southampton: Computational Mechanics Publications (1995) 330 pp.
10. H. Power and G. Miranda, Second kind integral equation formulation of Stokes flows past a particle of arbitrary shape. SIAM J. Appl. Math. 47 (1987) 689-698.
11. H. Power, Second kind integral equation solution of Stokes flows past n bodies of arbitrary shape. In: BEM IX, Computational Mechanics Publications, Southampton, and Springer-Verlag, Berlin (1987).
12. S.J. Karrila, Y.O. Fuentes and S. Kim, Parallel computational strategies for hydrodynamic interactions between rigid particles of arbitrary shape in a viscous fluid. J. Rheology 33 (1989) 913-947.
13. H. Power and G. Miranda, Integral equation formulation for the creeping flow of an incompressible viscous fluid between two arbitrary closed surfaces, and a possible mathematical model for the brain fluid dynamics. J. Math. Anal. Appl. 137 (1989) 1-16.
14. S.J. Karrila and S. Kim, Integral equations of the second kind for Stokes flow: direct solution for physical variables and removal of inherent accuracy limitations. Chem. Eng. Commun. 82 (1989) 123-161.
15. S. Kim and S.J. Karrila, Microhydrodynamics: Principles and Selected Applications. London: Butterworth-Heinemann (1991) 507 pp.
16. S.G. Mikhlin, Integral Equations and their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology. London: Pergamon Press (1957) 341 pp.
17. M. Manga and H.A. Stone, Buoyancy-driven interactions between two deformable viscous drops. J. Fluid Mech. 256 (1993) 647-683.
18. M. Manga and H.A. Stone, Low Reynolds number motion of bubbles, drops and rigid sphere through fluid-fluid interface. J. Fluid Mech. 287 (1995) 279-298.
19. H. Power, Low Reynolds number deformation of compound drops in shear flow. Math. Meth. Appl. Sci. 16 (1993) 61-74.