A new boundary integral formulation to describe three-dimensional motions of interfaces between magnetic fluids

Applied Mathematics and Computation

Volumn 199, Issue 1, 2008, Pages 70-83

  Cunha, F R ^a   Couto, H L G ^a  

^a UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

Boundary integral; Ferrofluid; Magnetic interfaces; Reciprocal theorem

Indexed keywords

MAGNETIC FLUIDS; REYNOLDS NUMBER; THEOREM PROVING; VISCOUS FLOW;

BOUNDARY INTEGRAL FORMULATION; LORENTZ RECIPROCAL THEOREM;

BOUNDARY INTEGRAL EQUATIONS;

EID: 41949124290     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.09.035     Document Type: Article

References (33)

1. Alvarenga R.C., and Cunha F.R. Boundary integral simulations of three dimensional inviscid flows. Lat. Am. J. Sol. Struct. 3 (2006) 161
2. Arkhipenko V.I., Barkov Y.D., and Bashtovoi V.G. Shape of a drop of a magnetized fluid in a homogeneous magnetic field. Magnetohydrodyn 14 (1978) 373
3. Bacri J.C., and Salin D. Instability of ferrofluid magnetic drops under magnetic field. J. Phys. Lett. 43 (1982) L649
4. Bacri J.C., Salin R., and Massart D. Shape of the deformation of ferrofluid droplets in a magnetic fluid. J. Phys. Lett. 43 (1982) L179
5. Bacri J.C., Cēbers A., Lācis S., and Perzynski R. Shapes of 2D magnetic fluid droplets in a rotating magnetic field. Magnetohydrodyn 31 (1996) 48
6. Bacri J.C., Cēbers A., Lācis S., and Perzynski R. Numerical simulation of the transient stages of a 2D magnetic fluid droplet in high-frequency rotating magnetic fields. Magnetohydrodyn 32 (1996) 22
7. Bacri J.C., and Salin D. Dynamic of the shape transition of a magnetic ferrofluid. J. Phys. Lett. 44 (1983) L415
8. Cristini V., Blawzdziewicz J., and Loewenberg M. Drop breakup in three-dimensional viscous flows. Phys. Fluids 10 (1998) 1781
9. Cristini V., Blawzdziewicz J., and Loewenberg M. An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comput. Phys. 168 (2001) 445
10. Cunha F.R., Souza A.J., and Morais P.C. The dynamic behaviour of a collapsing bubble in a magnetic field. Journal of Magnetism and Magnetic Materials 252 (2002) 271
11. Cunha F.R., Almeida M.H., and Loewenberg M. Direct numerical simulation of emulsion flows. J. Braz. Soc. Mech. Sci. Eng. 25 (2003) 30
12. Cunha F.R., Souza A.J., and Loewenberg M. A mathematical formulation of the boundary integral equations for compressible Stokes flow. Comp. App. Math. 22 (2003) 53
13. Drozdova V.I., Skrobotova T.V., and Chekanov V.V. Experimental study of the hydrostatics characterizing the interphase boundary in a ferrofluid. Magnetohydrodyn 15 (1979) 12
14. Grant I.S., and Philips W.R. Electromagnetism (1990), Wiley, West Sussex, UK
15. Guido S., and Simeone M. Binary collision of drops in simple shear flow by computer-assisted video optical microscopy. J. Fluid Mech. 357 (1998) 1
16. Happel J., and Brenner H. Low Reynolds Number Hydrodynamics (1965), Prentice Hall
17. Jaswon M.A., and Symm G.T. Integral Equation Methods in Potential Theory and Elastostatics (1977), Academic Press, New York, USA
18. Kellogg O.D. Foundations of Potential Theory (1954), Dover, New York, USA
19. Kim S., and Karrila S.J. Microhydrodynamics: Principles and Selected Applications (1991), Butterworth-Heinemann, Stoneham, USA
20. Kraynik A.M., Reinelt D.A., and Princen H.M. The nonlinear elastic behavior of polydisperse hexagonal foams and concentrated emulsions. J. Rheol. 35 (1991) 1235
21. Ladyzhenskaya O.A. The Mathematical Theory of Viscous Incompressible Flow (1969), Gordon & Breach, New York
22. Loewenberg M., and Hinch E.J. Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321 (1996) 395
23. Loewenberg M., and Hinch E.J. Collision of two deformable drops in shear flow. J. Fluid Mech. 338 (1997) 299
24. T.F. Oliveira, Microhydrodynamics and Emulsion Rheology. PhD Thesis, PUC-RJ, 2007, pp. 189 (in Portuguese).
25. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow (1992), Cambridge University Press, Cambridge, UK
26. Rallison J.M. A numerical study of deformation and burst of a viscous drop in extensional flow. J. Fluid Mech. 89 (1978) 191
27. Rallison J.M. A numerical study of deformation and burst of a viscous drop in general shear flow. J. Fluid Mech. 109 (1981) 465
28. Rallison J.M. The deformation of small viscous drops and bubbles in shear flows. J. Fluid Mech. 16 (1984) 45
29. Rosensweig R.E. Ferrohydrodynamics (1997), Dover, New York, US
30. Sherwood J.D. Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188 (1988) 133
31. Stone H.A. Dynamics of drop deformation and breakup in viscous fluids. J. Fluid Mech. 26 (1994) 65
32. Youngreen G.K., and Acrivos A. Stokes flow past a particle of a arbitrary shape: a numerical method of solution. J. Fluid Mech 69 (1975) 377 Corrigenda: J. Fluid Mech. 69 (1975) 813
33. Zinchenko A., and Davis R. Shear flow of highly concentrated emulsions of deformable drops by numerical simulations. J. Fluid Mech. 69 (2002) 377 Corrigenda, J. Fluid Mech. 455 (1975) 21