메뉴 건너뛰기




Volumn 19, Issue 9, 2007, Pages

Solution of the adjoint problem for instabilities with a deformable surface: Rosensweig and Marangoni instability

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; PROBLEM SOLVING; SURFACE TENSION;

EID: 34848883620     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2757709     Document Type: Article
Times cited : (12)

References (32)
  • 1
    • 84959616825 scopus 로고
    • "The interfacial stability of a ferromagnetic fluid"
    • JFLSA70022-112010.1017/S0022112067001697
    • M. D. Cowley and R. E. Rosensweig, "The interfacial stability of a ferromagnetic fluid," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112067001697 30, 671 (1967).
    • (1967) J. Fluid Mech. , vol.30 , pp. 671
    • Cowley, M.D.1    Rosensweig, R.E.2
  • 2
    • 0004120840 scopus 로고
    • (Cambridge University Press, Cambridge, UK)
    • R. E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, UK, 1985).
    • (1985) Ferrohydrodynamics
    • Rosensweig, R.E.1
  • 3
    • 32544437986 scopus 로고    scopus 로고
    • "Surface waves and Rosensweig instability in isotropic ferrogels"
    • ZPCFAX0942-935210.1524/zpch.2006.220.1.97
    • S. Bohlius, H. R. Brand, and H. Pleiner, "Surface waves and Rosensweig instability in isotropic ferrogels," Z. Phys. Chem. ZPCFAX0942-935210.1524/zpch.2006.220.1.97 200, 97 (2006).
    • (2006) Z. Phys. Chem. , vol.200 , pp. 97
    • Bohlius, S.1    Brand, H.R.2    Pleiner, H.3
  • 4
    • 33749507526 scopus 로고    scopus 로고
    • "Via hexagons to squares: Experiments on hysteretic surface transformations under variation of the normal magnetic field"
    • JCOMEL0953-898410.1088/0953-8984/18/38/S08
    • C. Gollwitzer, I. Rehberg, and R. Richter, "Via hexagons to squares: Experiments on hysteretic surface transformations under variation of the normal magnetic field," J. Phys.: Condens. Matter JCOMEL0953-898410.1088/0953-8984/18/38/S08 18, S2643 (2006).
    • (2006) J. Phys.: Condens. Matter , vol.18
    • Gollwitzer, C.1    Rehberg, I.2    Richter, R.3
  • 5
    • 84869709358 scopus 로고
    • "On the stability of steady finite amplitude convection"
    • JFLSA70022-112010.1017/S0022112065001271
    • A. Schlüter, D. Lortz, and F. Busse, "On the stability of steady finite amplitude convection," J. Fluid Mech. JFLSA70022-112010.1017/S0022112065001271 23, 129 (1965).
    • (1965) J. Fluid Mech. , vol.23 , pp. 129
    • Schlüter, A.1    Lortz, D.2    Busse, F.3
  • 6
    • 0001510852 scopus 로고
    • "Existence of a hexagonal relief on the surface of a dielectric fluid in an external electrical field"
    • SPHJAR0038-5646
    • E. A. Kuznetsov and M. D. Spektor, "Existence of a hexagonal relief on the surface of a dielectric fluid in an external electrical field," Sov. Phys. JETP SPHJAR0038-5646 44, 136 (1976).
    • (1976) Sov. Phys. JETP , vol.44 , pp. 136
    • Kuznetsov, E.A.1    Spektor, M.D.2
  • 7
    • 0000271503 scopus 로고
    • "Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field"
    • JFLSA70022-112010.1017/S0022112077000731
    • A. Gailitis, "Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field," J. Fluid Mech. JFLSA70022-112010.1017/S0022112077000731 82, 401 (1977).
    • (1977) J. Fluid Mech. , vol.82 , pp. 401
    • Gailitis, A.1
  • 8
    • 4043074453 scopus 로고    scopus 로고
    • "Pattern and wave number selection in magnetic fluids"
    • PLEEE81063-651X10.1103/PhysRevE.64.021406
    • R. Friedrichs and A. Engel, "Pattern and wave number selection in magnetic fluids," Phys. Rev. E PLEEE81063-651X10.1103/ PhysRevE.64.021406 64, 021406 (2001).
    • (2001) Phys. Rev. E , vol.64 , pp. 021406
    • Friedrichs, R.1    Engel, A.2
  • 9
    • 33749521662 scopus 로고    scopus 로고
    • "Pattern formation in ferrogels: Analysis of the Rosensweig instability using the energy method"
    • JCOMEL0953-898410.1088/0953-8984/18/38/S10
    • S. Bohlius, H. Pleiner, and H. R. Brand, "Pattern formation in ferrogels: Analysis of the Rosensweig instability using the energy method," J. Phys.: Condens. Matter JCOMEL0953-898410.1088/0953-8984/ 18/38/S10 18, S2671 (2006).
    • (2006) J. Phys.: Condens. Matter , vol.18
    • Bohlius, S.1    Pleiner, H.2    Brand, H.R.3
  • 10
    • 0009532098 scopus 로고
    • "Bifurcation instabilities of the free surface of a ferrofluid"
    • SJMAAH0036-141010.1137/0514056
    • E. E. Twombly and J. W. Thomas, "Bifurcation instabilities of the free surface of a ferrofluid," SIAM J. Math. Anal. SJMAAH0036-141010.1137/0514056 14, 736 (1983).
    • (1983) SIAM Math. Anal. , vol.14 , pp. 736
    • Twombly, E.E.1    Thomas, J.W.2
  • 11
    • 0001895770 scopus 로고
    • "Pattern selection in ferrofluids"
    • PDNPDT0167-278910.1016/0167-2789(88)90099-1
    • M. Silber and E. Knobloch, "Pattern selection in ferrofluids," Physica D PDNPDT0167-278910.1016/0167-2789(88)90099-1 30, 83 (1988).
    • (1988) Physica D , vol.30 , pp. 83
    • Silber, M.1    Knobloch, E.2
  • 12
    • 0001530578 scopus 로고
    • "Stability of fronts separating domains with different symmetries in hydrodynamical instabilities"
    • CHAOEH1054-150010.1063/1.166052
    • H. Herrero, C. Pérez-García, and M. Bestehorn, "Stability of fronts separating domains with different symmetries in hydrodynamical instabilities," Chaos CHAOEH1054-150010.1063/ 1.166052 4, 15 (1994).
    • (1994) Chaos , vol.4 , pp. 15
    • Herrero, H.1    Pérez-García, C.2    Bestehorn, M.3
  • 13
    • 0000991771 scopus 로고    scopus 로고
    • "Fronts between hexagons and squares in a generalized Swift-Hohenberg equation"
    • PLEEE81063-651X10.1103/PhysRevE.54.1560
    • C. Kubstrup, H. Herrero, and C. Pérez-García, "Fronts between hexagons and squares in a generalized Swift-Hohenberg equation," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.54.1560 54, 1560 (1996).
    • (1996) Phys. Rev. E , vol.54 , pp. 1560
    • Kubstrup, C.1    Herrero, H.2    Pérez-García, C.3
  • 14
    • 0021513152 scopus 로고
    • "Nonlinear dispersive instabilities in magnetic fluids"
    • QAMAAY0033-569X
    • S. K. Malik and M. Singh, "Nonlinear dispersive instabilities in magnetic fluids," Q. Appl. Math. QAMAAY0033-569X 42, 359 (1984).
    • (1984) Q. Appl. Math. , vol.42 , pp. 359
    • Malik, S.K.1    Singh, M.2
  • 15
    • 0023145520 scopus 로고
    • "Nonlinear focussing in magnetic fluids"
    • QAMAAY0033-569X
    • S. K. Malik and M. Singh, "Nonlinear focussing in magnetic fluids," Q. Appl. Math. QAMAAY0033-569X 44, 629 (1987).
    • (1987) Q. Appl. Math. , vol.44 , pp. 629
    • Malik, S.K.1    Singh, M.2
  • 16
    • 0037197156 scopus 로고    scopus 로고
    • "The adjoint problem in the presence of a deformed surface: The example of the Rosensweig instability on magnetic fluids"
    • IJPBEV0217-979210.1142/S0217979202010105
    • A. Lange, "The adjoint problem in the presence of a deformed surface: The example of the Rosensweig instability on magnetic fluids," Int. J. Mod. Phys. B IJPBEV0217-979210.1142/ S0217979202010105 16, 1155 (2002).
    • (2002) Int. J. Mod. Phys. B , vol.16 , pp. 1155
    • Lange, A.1
  • 17
    • 0000610727 scopus 로고    scopus 로고
    • "Nonlinear analysis of coupled gravitational and capillary thermoconvection in thin fluid layers"
    • PLEEE81063-651X10.1103/PhysRevE.54.411
    • P. M. Parmentier, V. C. Regnier, and G. Lebon, "Nonlinear analysis of coupled gravitational and capillary thermoconvection in thin fluid layers," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.54.411 54, 411 (1996).
    • (1996) Phys. Rev. E , vol.54 , pp. 411
    • Parmentier, P.M.1    Regnier, V.C.2    Lebon, G.3
  • 18
    • 84947690949 scopus 로고
    • "On convection cells induced by surface tension"
    • JFLSA70022-112010.1017/S0022112058000616
    • J. R. A. Pearson, "On convection cells induced by surface tension," J. Fluid Mech. JFLSA70022-112010.1017/S0022112058000616 4, 489 (1958).
    • (1958) Fluid Mech. , vol.4 , pp. 89
    • Pearson, J.R.A.1
  • 19
    • 84913346476 scopus 로고
    • "Surface tension and buoyancy effects in cellular convection"
    • JFLSA70022-112010.1017/S0022112064000763
    • D. A. Nield, "Surface tension and buoyancy effects in cellular convection," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112064000763 19, 341 (1964).
    • (1964) J. Fluid Mech. , vol.19 , pp. 341
    • Nield, D.A.1
  • 20
    • 33645843688 scopus 로고
    • "On cellular convection driven by surface-tension gradients: Effects of mean surface tension and surface viscosity"
    • JFLSA70022-112010.1017/S0022112064000751
    • L. E. Scriven and C. V. Sternling, "On cellular convection driven by surface-tension gradients: Effects of mean surface tension and surface viscosity," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112064000751 19, 321 (1964).
    • (1964) J. Fluid Mech. , vol.19 , pp. 321
    • Scriven, L.E.1    Sternling, C.V.2
  • 21
    • 0000562744 scopus 로고
    • "On convective instability induced by surface-tension gradients"
    • JFLSA70022-112010.1017/S0022112066000727
    • K. A. Smith, "On convective instability induced by surface-tension gradients," J. Fluid Mech. JFLSA70022-112010.1017/S0022112066000727 24, 401 (1966).
    • (1966) J. Fluid Mech. , vol.24 , pp. 401
    • Smith, K.A.1
  • 22
    • 0019601741 scopus 로고
    • "Surface tension driven instability in a horizontal liquid layer with a deformable free surface. I. Stationary convection"
    • JUPSAU0031-901510.1143/JPSJ.50.2745
    • M. Takashima, "Surface tension driven instability in a horizontal liquid layer with a deformable free surface. I. Stationary convection," J. Phys. Soc. Jpn. JUPSAU0031-901510.1143/JPSJ.50.2745 50, 2745 (1981).
    • (1981) J. Phys. Soc. Jpn. , vol.50 , pp. 2745
    • Takashima, M.1
  • 23
    • 0019600336 scopus 로고
    • "Surface tension driven instability in a horizontal liquid layer with a deformable free surface. II. Overstability"
    • JUPSAU0031-901510.1143/JPSJ.50.2751
    • M. Takashima, "Surface tension driven instability in a horizontal liquid layer with a deformable free surface. II. Overstability," J. Phys. Soc. Jpn. JUPSAU0031-901510.1143/JPSJ.50.2751 50, 2751 (1981).
    • (1981) J. Phys. Soc. Jpn. , vol.50 , pp. 2751
    • Takashima, M.1
  • 24
    • 36449003767 scopus 로고
    • "Linear stability analysis of Bènard-Marangoni convection in fluids with a deformable surface"
    • PFADEB0899-821310.1063/1.858137
    • C. Pérez-García and G. Carneiro, "Linear stability analysis of Bènard-Marangoni convection in fluids with a deformable surface," Phys. Fluids A PFADEB0899-821310.1063/1.858137 3, 292 (1991).
    • (1991) Phys. Fluids A , vol.3 , pp. 292
    • Pérez-García, C.1    Carneiro, G.2
  • 25
    • 0020151092 scopus 로고
    • "Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers"
    • JFLSA70022-112010.1017/S0022112082002687
    • S. Rosenblat, S. H. Davis, and G. M. Homsy, "Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112082002687 120, 91 (1982).
    • (1982) J. Fluid Mech. , vol.120 , pp. 91
    • Rosenblat, S.1    Davis, S.H.2    Homsy, G.M.3
  • 26
    • 0020153533 scopus 로고
    • "Nonlinear Marangoni convection in bounded layers. Part 2. Rectangular cylindrical containers"
    • JFLSA70022-112010.1017/S0022112082002699
    • S. Rosenblat, G. M. Homsy, and S. H. Davis, "Nonlinear Marangoni convection in bounded layers. Part 2. Rectangular cylindrical containers," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112082002699 120, 123 (1982).
    • (1982) J. Fluid Mech. , vol.120 , pp. 123
    • Rosenblat, S.1    Homsy, G.M.2    Davis, S.H.3
  • 27
    • 0027698626 scopus 로고
    • "Hexagonal Marangoni convection in a rectangular box with slippery walls"
    • QJMMAV0033-561410.1093/qjmam/46.4.683
    • P. C. Dauby, G. Lebon, P. Colinet, and J. C. Legros, "Hexagonal Marangoni convection in a rectangular box with slippery walls," Q. J. Mech. Appl. Math. QJMMAV0033-561410.1093/qjmam/46.4.683 46, 683 (1993).
    • (1993) Q. Mech. Appl. Math. , vol.46 , pp. 683
    • Dauby, P.C.1    Lebon, G.2    Colinet, P.3    Legros, J.C.4
  • 28
    • 0020013617 scopus 로고
    • "Buoyancy and surface-tension driven instabilities in presence of negative Rayleigh and Marangoni numbers"
    • AMHCAP0001-597010.1007/BF01176278
    • G. Lebon and A. Cloot, "Buoyancy and surface-tension driven instabilities in presence of negative Rayleigh and Marangoni numbers," Acta Mech. AMHCAP0001-597010.1007/BF01176278 43, 141 (1982).
    • (1982) Acta Mech. , vol.43 , pp. 141
    • Lebon, G.1    Cloot, A.2
  • 29
    • 0034315418 scopus 로고    scopus 로고
    • "Planform selection in two-layer Bénard-Marangoni convection"
    • PLEEE81063-651X10.1103/PhysRevE.62.6540
    • A. Engel and J. B. Swift, "Planform selection in two-layer Bénard-Marangoni convection," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.62.6540 62, 6540 (2000).
    • (2000) Phys. Rev. E , vol.62 , pp. 6540
    • Engel, A.1    Swift, J.B.2
  • 30
    • 4644356071 scopus 로고    scopus 로고
    • "Hydrodynamics of isotropic ferrogels"
    • PLEEE81063-651X10.1103/PhysRevE.68.041706
    • E. Jarkova, H. Pleiner, H.-W. Müller, and H. R. Brand, "Hydrodynamics of isotropic ferrogels," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.68.041706 68, 041706 (2003).
    • (2003) Phys. Rev. E , vol.68 , pp. 041706
    • Jarkova, E.1    Pleiner, H.2    Müller, H.-W.3    Brand, H.R.4
  • 32
    • 0030109998 scopus 로고    scopus 로고
    • "Competition between the Bénard-Marangoni and the Rosensweig instability in magnetic fluids"
    • JPAHER1155-431210.1051/jp2:1996189
    • J. Weilepp and H. R. Brand, "Competition between the Bénard-Marangoni and the Rosensweig instability in magnetic fluids," J. Phys. II JPAHER1155-431210.1051/jp2:1996189 6, 419 (1996).
    • (1996) Phys. II , vol.6 , pp. 419
    • Weilepp, J.1    Brand, H.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.