Numerical simulations of interfacial instabilities on a rotating miscible magnetic droplet with effects of Korteweg stresses

Physics of Fluids

Volumn 17, Issue 4, 2005, Pages

  Chen, Ching Yao ^a   Wu, H J ^b  

^a NATIONAL YUNLIN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^b DA YEH UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; INTERFACES (MATERIALS); STABILITY; STRESSES; SURFACE TENSION; TRAJECTORIES;

FINGERING PATTERNS; KORTEWEG STRESSES; LINEAR PATTERNS; MAGNETIC DROPLETS;

MAGNETIC MATERIALS;

DROPLET; MISCIBLE DISPLACEMENT;

EID: 17444421567     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1870017     Document Type: Article

References (34)

1. L. Schwart, "Instabilities and fingering in a rotating Hele-Shaw cell or porous medium," Phys. Fluids APFADEB 0899-8213 10.1063/ 1.857543 1, 167 (1989).
2. L. Carrillo, F. Magaleno, J. Casademunt, and J. Ortin, "Experiments in a rotating Hele-Shaw cell," Phys. Rev. EPLEEE8 1063-651X 10.1103/ PhysRevE.54.6260 54, 6260 (1996).
3. L. Carrillo, J. Soriano, and J. Ortin, "Radial displacement of a fluid annulus in a rotating Hele-Shaw cell," Phys. Fluids PHFLE6 1070-6631 10.1063/1.869950 11, 778 (1999).
4. L. Carrillo, J. Soriano, and J. Ortin, "Interfacial instability of a fluid annulus in a rotating Hele-Shaw cell," Phys. Fluids PHFLE6 1070-6631 10.1063/1.870419 12, 1685 (2000).
5. C.-Y. Chen and S. Wang, "Interfacial instabilities of miscible fluids in a rotating Hele-Shaw cell," Fluid Dyn. Res. FDRSEH 0169-5983 10.1016/S0169-5983(02)00059-X 30, 315 (2002).
6. C.-Y. Chen and S. Wang, "Stabilities of miscible interfaces in a rotating Hele-Shaw cell," Transact. Aeronaut. Astronaut. Soc. ROC 34, 239 (2002).
7. E. Alvarez-Lacalle, J. Ortin, and J. Casademunt, "Low viscosity contrast fingering in a Hele-Shaw cell," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1644149 16, 908 (2004).
8. D. Korteweg, "Sur la forme que prennent les équations du movement des fluides si l'on tient compte des forces capillaires causées par des variations de densité," Arch. Neel. Sci. Ex. Nat. II, 6 (1901).
9. D. Joseph and Y. Renardy, Fundamentals of Two-Fluid Dynamics, Part II (Springer, Berlin, 1992).
10. C.-Y. Chen, L. Wang, and E. Meiburg, "Miscible droplets in a porous medium and the effect of Korteweg stresses," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1387468 13, 2447 (2001).
11. H. Davis, "A theory of tension at a miscible displacement front. Numerical simulation in oil recovery," IMA Volumes in Mathematics and its Applications (Springer, Berlin, 1988), Vol. 11.
12. G. Galdi, D. Joseph, L. Prezisi, and S. Rionero, "Mathematical problems for miscible, incompressible fluids with Korteweg stresses," Eur. J. Mech. B/Fluids EJBFEV 0997-7546 10, 253 (1991).
13. H. Hu and D. Joseph, "Miscible displacement in a Hele-Shaw cell," ZAMP ZAMPDB 0044-2275 10.1007/BF00946254 43, 626 (1992).
14. P. Petitjeans and P. Kurowski, "Fluides nonmiscibles: Fluides miscibles: Des similitudes interessantes," C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. CMCAEK 1251-8069 10.1016/ S1251-8069(97)88173-0 325, 587 (1997).
15. C.-Y. Chen and E. Meiburg, "Miscible displacements in capillary tubes: Influences of Korteweg stresses and divergence effects," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1481507 14, 2052 (2002).
16. C.-Y. Chen, "Numerical simulations of fingering instabilities in miscible magnetic fluids in a Hele-Shaw cell and the effects of Korteweg stresses," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1558317 15, 1086 (2003).
17. R. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985).
18. A. Dickstein, S. Erramilli, R. Goldstein, D. Jackson, and S. Langer, "Labyrinthine pattern formation in magnetic fluids," Science SCIEAS 0036-8075 261, 1012 (1993).
19. A. Cebers, "Stabilities of diffusion fronts of magnetic particles in porous media (Hele-Shaw cell) under the action of external magnetic field," Magnetohydrodynamics (N.Y.) MGHDAG 0024-998X 33, 67 (1997).
20. C. Flament, G. Pacitto, J. Bacri, I. Drikis, and A. Cebers, "Viscous fingering in a magnetic fluid. I. Radial Hele-Shaw flow," Phys. Fluids PHFLE6 1070-6631 10.1063/1.869765 10, 2464 (1998).
21. I. Drikis and A. Cebers, "Viscous fingering in magnetic fluids: Numerical simulation of radial Hele-Shaw flow," J. Magn. Magn. Mater. JMMMDC 0304-8853 10.1016/S0304-8853(99)00052-9 201, 339 (1999).
22. G. Pacitto, C. Flament, and J. Bacri, "Viscous fingering in a magnetic fluid. II. Linear Hele-Shaw flow," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1398041 13, 3196 (2001).
23. A. Igonin and A. Cebers, "Labyrinthine instability of miscible magnetic fluids," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1568949 15, 1734 (2003).
24. C.-Y. Chen, H.-J. Wu, and L. Hsu, "Numerical simulations of labyrinthine instabilities on a miscible elliptical magnetic droplet," J. Magn. Magn. Mater. JMMMDC 0304-8853 289, 365 (2005).
25. J. Miranda, "Rotating Hele-Shaw cells with ferrofluids," Phys. Rev. EPLEEE8 1063-651X 10.1103/PhysRevE.62.2985 62, 2985 (2000).
26. D. Jackson and J. Miranda, "Controlling fingering instabilities in rotating ferrofluids," Phys. Rev. EPLEEE8 1063-651X 10.1103/ PhysRevE.67.017301 67, 017301 (2003).
27. C.-Y. Chen and H.-J. Wu, "Fingering instabilities of a miscible magnetic droplet on a rotating Hele-Shaw cell," J. Magn. Magn. Mater.JMMMDC0304-8853 289, 339 (2005).
28. J. Fernandez, P. Kurowski, L. Limat, and P. Petitjeans, "Wavelength selection of fingering instability inside Hele-Shaw cells," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1410120 13, 3120 (2001).
29. J. Fernandez, P. Kurowski, P. Petitjeans, and E. Meiburg, "Density-driven unstable flows of miscible fluids in a Hele-Shaw cell," J. Fluid Mech. JFLSA7 0022-1120 451, 239 (2002).
30. F. Graf, E. Meiburg, and C. Hartel, "Density-driven instabilities of miscible fluids in a Hele-Shaw cell: Linear stability analysis of the three-dimensional Stokes equations," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S002211200200109X 451, 261 (2002).
31. D. Jackson, R. Goldstein, and A. Cebers, "Hydrodynamics of fingering instabilities in dipolar fluids," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.50.298 50, 298 (1994).
32. M. Ruith and E. Meiburg, "Miscible rectilinear displacements with gravity override. Part 1: Homogeneous porous medium," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112000001543 420, 225 (2000).
33. E. Meiburg and C.-Y. Chen, "High-accuracy implicit finite difference simulations of homogeneous and heterogeneous miscible porous media flows," SPEJ SPJRFW 1086-055X 5, 2 (2000).
34. I. Drikis and A. Cebers, "Labyrinthine pattern formation in magnetic liuids," Free Boundary Problems: Theory and Applications (Chapman & Hall/CRC, Boca Raton, FL, 1999).