Skip to main content
SpringerLink
Log in

Surface Instabilities of Ferrofluids

  • Chapter
  • First Online:
Colloidal Magnetic Fluids

Part of the book series: Lecture Notes in Physics ((LNP,volume 763))

Abstract

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer are taken into account.

In the nonlinear regime the fully developed peak pattern can be predicted by a minimization of the free energy and by numerics employing the finite element method. For a comparison with the results of both methods, the three-dimensional surface profile is recorded by a radioscopic measurement technique. In the bistable regime of the flat and patterned state we generate localized states (ferrosolitons) which are recovered in analytical and numerical model descriptions. For higher fields an inverse hysteretic transition from hexagonal to square planforms is measured. % Via a horizontal field component the symmetry can be broken in the experiment, resulting in liquid ridges and distorted hexagons, as predicted by theory. Replacing ferrofluid by ferrogel also an elastic energy contribution has to be taken into account for a proper model description, yielding a linear shift of the threshold and an increased bistability range.

Parametric excitation in combination with magnetic fields is widening the horizon of pattern formation even further. For the mono-spike oscillator harmonic and subharmonic response as well as deterministic chaos is observed and modeled. In a ring of spikes the formation of domains of different wavelengths and spatio-temporal intermittency is quantitatively studied. For an extended layer of ferrofluid we predict that a stabilizing horizontal field counteracted by vertical vibrations will result in oblique rolls with preselected orientation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Castellvecchi, D.: Physical Review Focus, http://focus.aps.org/story/v15/st18, (2005)

  2. Rosensweig, R.E.: Ferrohydrodynamics. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  3. Cowley, M.D., Rosensweig, R.E.: J. Fluid Mech. 30, 671 (1967).

    Article  ADS  Google Scholar 

  4. Papell, S.S.: Low viscosity magnetic fluid obtained by the colloidal suspension of magnetic particles, US Patent No. 3,215,572, (1965)

    Google Scholar 

  5. Cross M.C., Hohenberg, P.C.: Rev. Mod. Phys. 65, 851 (1993)

    Article  ADS  Google Scholar 

  6. Peinke, J., Parisi, J., Rössler, O.E., Stoop, R.: Encounter, with Chaos: Self-Organized Hierarchical Complexity in Semiconductor Experiments. (Springer, Berlin, Heidelberg, New York) (1992)

    Book  Google Scholar 

  7. Prigogine, I.: Vom Sein zum, Werden. Zeit und Komplexität in den Naturwissenschaften, 1sted. Piper, München, Zürich (1988)

    Google Scholar 

  8. Swan, J.W.: Proc. R. Soc. (London) 62, 38 (1897)

    Google Scholar 

  9. Taylor, G.I.: Z. Angew. Math. Mech. 13, 147 (1933)

    Article  Google Scholar 

  10. Lange C.G., Newell, A.C.: SIAM J. Appl. Math. 605 (1971)

    Google Scholar 

  11. Shipman P.D., Newell, A.C.: Phys. Rev. Lett. 92, 168102 (2004)

    Article  ADS  Google Scholar 

  12. Taylor G.I. McEwan, A.D.: J. Fluid Mech. 22, 1 (1965)

    Article  ADS  Google Scholar 

  13. Grimes, C.C.: Surface Sci. 73, 379 (1978)

    Article  ADS  Google Scholar 

  14. Faraday, M.: Philos. Trans. R. Soc. London 52, 319 (1831)

    Google Scholar 

  15. Mahr T., Rehberg, I.: Phys. Rev. Lett. 81, 89 (1998)

    Article  ADS  Google Scholar 

  16. Pétrélis, F., Falcon, é., Fauve, S.: Eur. Phys. J. B 15, 3 (2000)

    Article  ADS  Google Scholar 

  17. Hyun-Jae Pi, J.L., Park So-ycon, Lee, K.J.: Phys. Rev. Lett. 84, 5316 (2000)

    Google Scholar 

  18. Barkov Y.D., Bashtovoi, V.G.: Magnetohydrodynamics (N.Y.) 13, 497 (1977)

    Google Scholar 

  19. Odenbach, S.: Magnetoviscous Effects in Ferrofluids. Springer, Berlin, Heidelberg, New York (2002)

    MATH  Google Scholar 

  20. Uhlmann, E., Bajat, N.: Production Eng. 10, 125 (2003)

    Google Scholar 

  21. Frenkel’, Y.I., Eksp, Zh.: Teor. Fiz. 3, 347 (1936)

    Google Scholar 

  22. Landau, L.D., Lifshitz, E.: Fluid Mechanics. Pergamon Press, Oxford (1987)

    Google Scholar 

  23. Mahr, T., Groisman, A., Rehberg, I.: J. Magn. Magn. Mater. 159, L45 (1996)

    Article  ADS  Google Scholar 

  24. Browaeys, J., Bacri, J.-C., Flament, C., Neveu, S., Perzynski, R.: Eur. Phys. J. B. 9, 335 (1999)

    Article  ADS  Google Scholar 

  25. Wanner M., Leiderer, P.: Phys, Rev. Lett. 42, 315 (1979)

    Article  ADS  Google Scholar 

  26. Leiderer, P.: Phy. Rev. B 20, 4511 (1979)

    Article  ADS  Google Scholar 

  27. Landau L.D., Lifschitz, E.M.: Electrodynamics of Continuous Media, 3rd edn. (Pergamon, Oxford, 1960), Vol.8.

    Google Scholar 

  28. Gailitis, A., Magnetohydrodynamics 5, 44 (1969)

    Google Scholar 

  29. Gailitis, A.: J. Fluid Mech. 82, 401 (1977)

    Article  ADS  Google Scholar 

  30. Kuznetsov E.A., Spektor, M.D.: Zh. Eksp. Teor. Fiz. 71, 262 (1976)

    Google Scholar 

  31. Friedrichs R., Engel, A.: Phys. Rev. E 64, 021406 (2001)

    Article  ADS  Google Scholar 

  32. Richter, R., Reimann, B., Lange, A., Rupp, P., Rothert, A.: Adv. Solid State Phys. 43, 789 (2003)

    Article  Google Scholar 

  33. Friedrichs, R.: Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, 2003.

    Google Scholar 

  34. Bacri, J.-C., Salin, D., J. Phys. (France) 45, L559 (1984)

    Article  Google Scholar 

  35. Boudouvis, A., Puchalla, J., Scriven, L., Rosensweig, R.: J. Magn. Magn. Mater. 65, 307 (1987)

    Article  ADS  Google Scholar 

  36. Lange, A., Reimann, B., Richter, R.: Magnetohydrodynamics 37, 261 (2001)

    Article  ADS  Google Scholar 

  37. Salin, D., Europhys. Lett. 21, 667 (1993)

    Article  ADS  Google Scholar 

  38. Lange, A., Reimann, B., Richter, R.: Phys. Rev. E 61, 5528 (2000)

    Article  ADS  Google Scholar 

  39. Reimann, B., Richter, R., Rehberg, I., Lange, A.: Phys. Rev. E 68, 036220 (2003)

    Article  ADS  Google Scholar 

  40. Weilepp J., Brand, H.R.: J. Phys. II France 6, 419 (1996)

    Article  Google Scholar 

  41. Abou, B., Néron de Surgy, G., J.E. Wesfreid, J. Phys. II France 7, 1159 (1997)

    Article  Google Scholar 

  42. Müller, H.W.: Phys. Rev. E 55, 6199 (1998)

    Article  ADS  Google Scholar 

  43. Mahr, T., Ph.D. thesis, Otto-von-Guericke Universität Magdeburg (1998)

    Google Scholar 

  44. Schäffer, E., Thurn-Albrecht, T., Russell, T.P. Steiner, U.: Europhys. Lett. 15, 518-?524 (2001)

    Article  ADS  Google Scholar 

  45. Gollwitzer, C., Matthis, G., Richter, R., Rehberg, I., Tobiska, L.: J. Fluid Mech. 571, 455 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  46. Leach, K.A., Lin, Z., Russel, T.P.: Macromolecules 38, 4868 (2005)

    Article  ADS  Google Scholar 

  47. Lange, A., Europhys. Lett. 55, 327 (2001)

    Article  ADS  Google Scholar 

  48. Knieling, H., Richter, R., Matthis, G., Rehberg, I., Lange, A.: The growth of surface undulations at the Rosensweig instability, to Phys. Rev. E 76 066301 (2007)

    Google Scholar 

  49. Richter R., Bläsing, J.: Rev. Sci. Instrum. 72, 1729 (2001)

    Article  ADS  Google Scholar 

  50. Busse, F.H.: J. Fluid Mech. 30, 625 (1962)

    Article  ADS  Google Scholar 

  51. Allais D., Wesfreid, J.-E.: Bull. Soc. Fr. Phys. Suppl. 57, 20 (1985)

    Google Scholar 

  52. Newell A., Whitehead, J.A.: J. Fluid Mech. 38, 279 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  53. Zaitsev V.M., Shliomis, M.I.: DAN S.S.S.R. 188, 12611 (1969)

    Google Scholar 

  54. Kuznetsov E.A., Spektor, M.D.: Sov. Phys. JETP 44, 136 (1976)

    ADS  Google Scholar 

  55. Ciliberto, S., Coullet, P., Lega, J., Pamploni, E., Perez-Garcia, C., Phys. Rev. Lett. 65, 2370 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  56. Twombley E.E., Thomas, J.W.: SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 14, 736 (1983)

    Google Scholar 

  57. Silber M., Knobloch, E.: Physica D 30, 83 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  58. Herrero, H., Perez-Garzia, C., Bestehorn, M.: Chaos 4, 15 (1994)

    Article  ADS  Google Scholar 

  59. Kubstrup, C., Herrero, H., Perez-Garcia, C.: Phys. Rev. E 54, 1560 (1996)

    Article  ADS  Google Scholar 

  60. Matthies G., Tobiska, L.: J. Magn. Magn. Mater. 289, 346 (2005)

    Article  ADS  Google Scholar 

  61. Vislovich, A.N.: Magnetohydrodynamics 26, 178 (1990)

    Google Scholar 

  62. Bashtovoi, V.G., Lavrova, O.A., Polevikov, V.K., Tobiska, L.: J. Magn. Magn. Mater. 252, 299?301 (2002)

    Article  ADS  Google Scholar 

  63. Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V., Tobiska, L.: Lect. Notes Comput. Sci. Eng. 35, 160 (2003)

    Article  Google Scholar 

  64. Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V., Tobiska, L.: J. Phys. Condens. Matter 18, 2657 (2006)

    Article  ADS  Google Scholar 

  65. Perlin, M., Lin, H., Ting, C.: J. Fluid Mech. 255, 597 (2000)

    Article  ADS  Google Scholar 

  66. Wernet, A., Wagner, C., Papathanassiou, D., Müller, H.W., Knorr, K.: Phys. Rev. E 63, 036305 (2001)

    Article  ADS  Google Scholar 

  67. Megalios, E., Kapsalis, N., Paschalidis, J., Papathanasiou, A., Boudouvis, A.: J. Coll. Int. Sci. 288, 505 (2005)

    Article  ADS  Google Scholar 

  68. Mahr T., Rehberg, I.: Phys. Rev. Let. 81, 89 (1998)

    Article  ADS  Google Scholar 

  69. Abou, B., Wesfreid, J.-E., Roux, S.: J. Fluid Mech. 416, 217 (2001)

    Article  ADS  Google Scholar 

  70. Wright, W.B., Budakian, R., Putterman, S.J.: Phys. Rev. Lett. 76, 4528 (1996)

    Article  ADS  Google Scholar 

  71. Kityk, A., Embs, J., Mekhonoshin, V.V., Wagner, C.: Phys. Rev. E 72, 036209 (2005)

    Article  ADS  Google Scholar 

  72. Petit, P., de Albuquerque, M., Cabuil, V., Molho, P.: J. Magn. Magn. Mater. 122, 271 (1993)

    Article  ADS  Google Scholar 

  73. Reimann, B., Experimente zur Normal- und Schrägfeldinstabilität magnetischer Flüssigkeiten. Shaker Verlag, Aachen, (2003)

    Google Scholar 

  74. Reimann, B., Richter, R., Knieling, H., Friedrichs, R., I.: Rehberg, Phys. Rev. E 71, 055202(R) (2005)

    Article  ADS  Google Scholar 

  75. Rehberg, I., Bodenschatz, E., Winkler, B., Busse, F.H.: Phys. Rev. Lett. 59, 282 (1987)

    Article  ADS  Google Scholar 

  76. Umbanhowar, P.B., Melo, F., Swinney, H.L.: Nature (London) 382, 793 (1996)

    Article  ADS  Google Scholar 

  77. Russell, J.S., Rep. 14th Meet. British. assoc. Adv. Sci. 311 (1844)

    Google Scholar 

  78. Scott, A.C., Chu, F.Y.F., McLaughlin, D.W.: Proceedings of the IEEE 61, 1443 (1973)

    Google Scholar 

  79. Remoissenet, M., Waves called Solitons. Concepts and Experiments, 3rd rev. and enlarged ed. ed. Springer, Berlin Heidelberg (1996)

    MATH  Google Scholar 

  80. Mollenauer, L.F., Stolen, R.H., Gordon, J.P.: Phys. Rev. Lett. 45, 1095 (1980)

    Article  ADS  Google Scholar 

  81. Christov C.I., Velarde, M.G.: Physica D 86, 323 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  82. Fauve S., Thual, O.: Phys. Rev. Lett. 64, 282 (1990)

    Article  ADS  Google Scholar 

  83. Lioubashevski, O., Arbell, H., Fineberg, J.: Phys. Rev. Lett. 76, 3959 (1996)

    Article  ADS  Google Scholar 

  84. Lioubashevski, O., Hamiel, Y., Agnon, A., Reches, Z., Fineberg, J.: Phys. Rev. Lett. 83, 3190 (1999)

    Article  ADS  Google Scholar 

  85. Arbell H., Fineberg, J.: Phys. Rev. Lett. 85, 756 (2000)

    Article  ADS  Google Scholar 

  86. Astruc D., Fauve, S.: Fluid Mechanics and Its Applications. Vol. 62, pp. 39–46 2001 Kluwer, Dordrecht(2001)

    Article  Google Scholar 

  87. Astrov Y.A., Logvin, Y.A.: Phys. Rev. Lett. 79, 2983 (1997)

    Article  ADS  Google Scholar 

  88. Müller, I., Ammelt, E., Purwins, H.-G.: Phys. Rev. Lett. 82, 3428 (1999)

    Article  ADS  Google Scholar 

  89. Koga S., Kuramoto, Y.: Prog. Theor. Phys. 63, 106 (1980)

    Article  ADS  Google Scholar 

  90. Lee, K.L., Cormick, W.D., Ouyang, Q., Swinney, H.: Science 261, 189 (1993)

    Article  ADS  Google Scholar 

  91. Haim, D., Li, G., Ouyang, Q., McCormick, W., Swinney, H., Hagberg, A., Meron, E.: Phys. Rev. Lett. 77, 190 (1996)

    Article  ADS  Google Scholar 

  92. Vanag V., Epstein, I.: Phys. Rev. Lett. 92, 128301 (2004)

    Article  ADS  Google Scholar 

  93. Spina, A., Tompre, J., Knobloch, E.: Phys. Rev. E 57, 524 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  94. Banchflower, S.: Phys. Lett. A 261, 74 (2002)

    Article  ADS  Google Scholar 

  95. Batiste O., Knobloch, E.: Phys. Rev. Lett. 95, 244501 (2005)

    Article  ADS  Google Scholar 

  96. Taranenko, V.B., Staliunas, K., Weiss, C.O.: Phys. Rev. A 56, 1582 (1997)

    Article  ADS  Google Scholar 

  97. Schäpers, B., Feldmann, M., Ackemann, T., Lange, W.: Phys. Rev. Lett. 85, 748 (2000)

    Article  ADS  Google Scholar 

  98. Barland, S., Tredicce, J.R., Brambilla, M., Lugiato, L.A., Balle, S., Giudici, M., Maggipinto, T., Spinelli, L., Tissoni, G., Knoedl, T., Miller, M., Jaeger, R.: Nature 419, 699 (2002)

    Article  ADS  Google Scholar 

  99. Riecke, H.: in Pattern Formation in Continuous and Coupled Systems: A Survey Volume. Golubitsky, M., Luss, D., Strogatz S.H.: Springer, New York, Vol.115. (1999)

    Google Scholar 

  100. Müller, H.-W.: J., Magn. Magn. Mater. 201, 350 (1999)

    Article  ADS  Google Scholar 

  101. Pomeau, Y.: Lect. Notes Phys. 210, 207 (1984)

    Article  ADS  Google Scholar 

  102. Pomeau, Y.: Physica D 23, 3 (1986)

    Article  ADS  Google Scholar 

  103. Sakaguchi H., Brand, H.R.: Physica D 97, 274 (1996)

    Article  ADS  Google Scholar 

  104. Pismen, L.M.: Patterns and Interfaces, M1.sted. Springer, Berlin, Heidelberg, New York (2006)

    MATH  Google Scholar 

  105. Bacri J.-C., Salin, D.: J. Phys. (France) Lett. 45, L767 (1984)

    Article  Google Scholar 

  106. Richter R., Barashenkov, I.V.: Phys. Rev. Lett. 94, 184503 (2005)

    Article  ADS  Google Scholar 

  107. Sakaguchi H., Brand, H.R.: Europhys. Lett. 38, 341 (1997)

    Article  ADS  Google Scholar 

  108. Lavrova, O., poleuikov, V., Tobiska, L.: PAMM Proc. Appl. Math. Mech 5, 837 (2005)

    Article  Google Scholar 

  109. Bödeker, H.U., Liehr, A.W., Frank, T.D., Friedrich, R., Purwins, H.-G.: New J. Phys. 6, 62 (2004)

    Article  ADS  Google Scholar 

  110. Crawford C., Riecke, H.: Physica D 129, 83 (1999)

    Article  ADS  Google Scholar 

  111. Stroebel G.J., Warner, W.H.: J. Elast. 3, 185 (1973)

    Article  Google Scholar 

  112. Leiderer, P., Ebner, W., Shinkin, V.B.: Surface Sci. 113, 405 (1982)

    Article  ADS  Google Scholar 

  113. Coullet, P., Riera, C., Tresser, C.: Phys. Rev. Lett. 84, 3069 (2000)

    Article  ADS  Google Scholar 

  114. Gollwitzer, C., Rehberg, I., Richter, R.: J. Phys. Condens. Matter 18, 2643 (2006)

    Article  ADS  Google Scholar 

  115. Nitschke, K.: Phys. Rev. E 52, R5772 (1995)

    Article  ADS  Google Scholar 

  116. Thiele U., Eckert, K.: Phys. Rev. E 58, 3458 (1998)

    Article  ADS  Google Scholar 

  117. Schatz, M., Vanhook, S.J., McCormick, W.D., Swift, J.B., Swinney, H.L.: Phys. Fluids 11, 2577 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  118. Aumann, A., Ackemann, T., Westhoff, E., Lange, W.: Int. J. Bif. Chaos (2001)

    Google Scholar 

  119. Melo, F., Umbanhowar, P.B., Swinney, H.L.: Phys. Rev. Lett. 75, 3838 (1995)

    Article  ADS  Google Scholar 

  120. Malomed, B.A., Nepomnyashchy, A.A., Tribelsky, M.I.: Phys. Rev. A 42, 7244 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  121. Bestehorn, M., Phys. Rev. Lett. 76, 46 (1996)

    Article  ADS  Google Scholar 

  122. Bragard J., Velarde, M.G.: J. Fluid Mech. 368, 165 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  123. Stoner, E.C.: Rev. Mod. Phys. 52, 2 (1953)

    Article  ADS  Google Scholar 

  124. D.C. Jiles and D.L. Atherton, J. Appl. Phys. 55, 2115 (1984)

    Article  ADS  Google Scholar 

  125. Girard P., Boissel, J.-P.: J. Pharmacokinetics and Pharmacodynamics 17, 401 (1989)

    Article  Google Scholar 

  126. Millán M.S., Escofet, J. Applied Optics 35, 6253 (1996)

    Article  ADS  Google Scholar 

  127. Fortune, S.J.: in: Vol.1 of Du, D.-Z., Hwangeds: F. World Scientific, Singapore, (1995)

    Google Scholar 

  128. Steinhardt, P.J., Nelson, D.R., Ronchetti, M.: Phys. Rev. B 28, 784 (1983)

    Article  ADS  Google Scholar 

  129. Pismen, L.M.: private communication (2006)

    Google Scholar 

  130. Benard H., Avsec, D.: Le journal de physique et Le radium 486 (1938)

    Google Scholar 

  131. Ackemann, T., Giese, B., Schäpers, B., Lange, W.: J. Opt. B: Quantum Semiclassical Opt. 1, 70 (1999)

    Article  ADS  Google Scholar 

  132. Zelazo R.E., Melcher, J.R.: J. Fluid Mech. 39, 1 (1969)

    Article  ADS  Google Scholar 

  133. Bajaj R., Malik, S.K.: J. Magn. Magn. Mater. 149, 158 (1995)

    Article  ADS  Google Scholar 

  134. Friedrichs, R.: Phys. Rev. E 66, 066215 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  135. Aitta, A., Ahlers, G., Cannel, D.S.: Phys. Rev. Lett. 54, 673 (1985)

    Article  ADS  Google Scholar 

  136. Pfister G., Rehberg, I.: Phy. Lett. 83A, 19 (1981)

    Article  ADS  Google Scholar 

  137. Embs, J., Müller, H.W., Krill, C.E., Meyer, F., Natter, H., Müller, B., Wiegand, S., Lücke, M., Hempelmann, R., Knorr, K.: Magnetohydrodynamics 37, 222 (2001)

    Article  ADS  Google Scholar 

  138. Daniels, K.E., Plapp, B.B., Bodenschatz, E.: Phys. Rev. Lett. 84, 5320 (2000)

    Article  ADS  Google Scholar 

  139. Busse F.H., Clever, R.M.: Eur. J. Mechanics B 9, 225 (1990)

    ADS  Google Scholar 

  140. Ouyang Q., Swinney, H.: Nature 352, 610 (1991)

    Article  ADS  Google Scholar 

  141. Hernández L.F., Green, P.B.: The Plant Cell 5, 1725 (1993)

    Article  Google Scholar 

  142. Varga, Z., Feher, J., Filipcsei, G., Zrinyi, M.: Macromol. Symp 200, 93 (2003)

    Article  Google Scholar 

  143. Zrinyi, M.: Colloid. Polym. Sci. 278, 98 (2000)

    Article  Google Scholar 

  144. Zrinyi, M., Barsi, L., Büki, A.: J. Chem. Phys. 104, 8750 (1996)

    Article  ADS  Google Scholar 

  145. Collin, D., Auernhammer, G., Gavat, O., Martinoty, P., Brand, H.: Macromol. Rapid Commun. 24, 737 (2003)

    Article  Google Scholar 

  146. Lattermann G., Krekhova, M.: Macromol. Rapid. Commun. 1373

    Google Scholar 

  147. Ballauff, M., Brand, H.E., Lattermann, G., Richter, R.: Oberflächeninstabilitäten in Magnetogelen, Teilantrag zur Forschergruppe ‘‘Nichtlineare Dynamik komplexer Kontinua’’ (2005)

    Google Scholar 

  148. Bohlius, S., Brand, H.R., Pleiner, H.: Z. Chem. Phys. 220, 97 (2006)

    Article  Google Scholar 

  149. Bohlius, S., Pleiner, H., Brand, H.R.: J. Phys. Condens. Matter 18, 2671 (2006)

    Article  ADS  Google Scholar 

  150. Jarkova, E., Pleiner, H., Müller, H.-W.: Euro. Phys. J. E 5, 583 (2001)

    Article  Google Scholar 

  151. Perry M.P., Jones, T.B.: J. Appl. Phys. 46, 759 (1974)

    Google Scholar 

  152. Cebers A., Maiorov, M.M.: Magn. Girodin. 25, 445 (1989)

    Google Scholar 

  153. Bacri, J.-C., d’Ortona, U., Salin, D.: Phys. Rev. Lett. 67, 50 (1991)

    Article  ADS  Google Scholar 

  154. Mahr T., Rehberg, I.: Europhys. Lett. 43, 23 (1998)

    Article  ADS  Google Scholar 

  155. Sudo, S., Ohaba, M., Katagiri, K., Hashimoto, H.: J. Magn. Magn. Mater. 122, 248 (1993)

    Article  ADS  Google Scholar 

  156. Mahr T., Rehberg, I.: Physica D 111, 335 (1997)

    Article  ADS  Google Scholar 

  157. Friedrichs R., Engel, A.: Eur. Phys. J. B 18, 329 (2000)

    Article  ADS  Google Scholar 

  158. Lange, A., Langer, H., Engel, A.: Physica D 140, 294 (2000)

    Article  ADS  Google Scholar 

  159. Raitt D., Riecke, H.: Phys. Rev. E 55, 5448 (1997)

    Article  ADS  Google Scholar 

  160. Reimann, B., Mahr, T., Richter, R., Rehberg, I.: J. Magn. Magn. Mater. 201, 303 (1999)

    Article  ADS  Google Scholar 

  161. Lorenz, E.N.: J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  162. Li T., Yorke, J.: Am Math Monthly 82, 985 (1995)

    Article  Google Scholar 

  163. Rössler, O.E.: Phys. Lett. 57 A, 397 (1996)

    ADS  Google Scholar 

  164. Morris, S.W., Bodenschatz, E., Cannell, D.S., Ahlers, G.: Phys. Rev. Lett. 71, 2026 (1993)

    Article  ADS  Google Scholar 

  165. Bergé, P., Pomeau, Y., Vidal, C.: L’espace Chaotique. Hermmann Editions, Paris (1998)

    MATH  Google Scholar 

  166. Ruelle J., Takens, F.: Commun. Math. Phys. 20, 67 (1971)

    Article  Google Scholar 

  167. Feigenbaum, M.: J. Stat. Phys. 19, 25 (1978)

    Article  ADS  Google Scholar 

  168. Pomeau Y., Manneville, P.: Phys. Lett. A 75, 1 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  169. D.J.: Tritton, Physical Fluid Dynamics, 2ndedn. Oxford University Press, Oxford, (1988)

    MATH  Google Scholar 

  170. Monin A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2, p. 598. MIT Press, Cambridge (1975)

    ADS  Google Scholar 

  171. Chaté, H., Manneville, P.: in: Tabelling Cardosoeds. O. Turbulence: A Tentative Dictionary, p. 111. P., Plenum Press, New York (1995)

    Book  Google Scholar 

  172. Kaneko, K.: Prog. Theor. Phys. 74, 1033 (1985)

    Article  ADS  Google Scholar 

  173. Manneville, P.: Dissipative structures and weak turbulence. Academic Press, Boston (1990)

    MATH  Google Scholar 

  174. Rabinovitch, M.I., Ezersky, A.B., Weidmann, P.D.: The Dynamics, of Pattern. World Scientific Publishing, Singapore, (1998)

    Google Scholar 

  175. Kaneko K., Tsuda, I.: Complex Systems:, Chaos and Beyond. Springer, Berlin, Heidelberg, New York (2000)

    MATH  Google Scholar 

  176. Frisch, U., She, Z.S., Thual, O.: J. Fluid Mech. 168, 221 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  177. Chaté H., Manneville, P.: Phys. Rev. Lett. 58, 112 (1987)

    Article  ADS  Google Scholar 

  178. Deissler, R.J.: J. Stat. Phys. 40, 371 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  179. Daviaud, F., Lega, J., Berge, P., Coullet, P., Dubois, M.: Physica D 55, 287 (1992)

    Article  ADS  Google Scholar 

  180. van Hecke, M.: Phys. Rev. Lett. 80, 1896 (1998)

    Article  ADS  Google Scholar 

  181. Zimmermann, M.G., Toral, R., Piro, O., SanMiguel, M.: Phys. Rev. Lett. 85, 3612 (2000)

    Article  ADS  Google Scholar 

  182. Chaté H., Manneville, P.: Physica D 32, 409 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  183. Grassberger P., Schreiber, T.: Physica D 50, 177 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  184. Wolfram, S.: Physica D 10, 1 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  185. Chaté H., Manneville, P.: Physica D 37, 33 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  186. Stauffer D., Aharony, A.: Perkolationstheorie, - Eine Einfürung. VCH, Weinheim (1995)

    MATH  Google Scholar 

  187. Hinrichsen, H.: Adv. Phys. 49, 815 (2000)

    Article  ADS  Google Scholar 

  188. Jensen, I.: J. Phys. A 32, 5233 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  189. Grassberger, P.: In: Puried. S., Narosa publishing, New Dehli (1997)

    Google Scholar 

  190. Ciliberto S., Bigazzi, P.: Phys. Rev. Lett. 60, 286 (1988)

    Article  ADS  Google Scholar 

  191. S. Ciliberto, in: Abraham N.B., Meassures of Complexity and Chaos, p. 245. Albanoeds. A.M., Plenum Press, New York (1990)

    Google Scholar 

  192. Ciliberto, S., in: P.193. Coullet P., Huerreeds. P. Plenum Press, New York (1990)

    Google Scholar 

  193. Caponeri M., Ciliberto, S.: Physica D 58, 365 (1992)

    Article  ADS  Google Scholar 

  194. Daviaud, F., Bonetti, M., Dubois, M.: Phys. Rev. A 42, 3388 (1990)

    Article  ADS  Google Scholar 

  195. Michalland, S., Rabaud, M., Couder, Y.: Europhys. Lett. 22, 17 (1993)

    Article  ADS  Google Scholar 

  196. Willaime, H., Cardoso, O., Tabeling, P.: Phys. Rev. E 48, 288 (1993)

    Article  ADS  Google Scholar 

  197. Degen, M.M., Mutabazi, I., Andereck, C.D.: Phys. Rev. E 53, 3495 (1996)

    Article  ADS  Google Scholar 

  198. Colovas P.W., Andereck, C.D.: Phys. Rev. E 55, 2736 (1997)

    Article  ADS  Google Scholar 

  199. Bottin, S., Dauchot, O., Daviaud, F.: Phys. Rev. Lett. 79, 4377 (1997)

    Article  ADS  Google Scholar 

  200. Vallette, D.P., Jacobs, G., Gollub, J.P.: Phys. Rev. E 55, 4274 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  201. Rupp, P., Richter, R., Rehberg, I.: Phys. Rev. E 67, 036209 (2003)

    Article  ADS  Google Scholar 

  202. We are grateful to ‘‘Magdeburger Verkehrsbetriebe’’ which donated the soft iron pole shoe, previously part of a street car criss-crossing the city.

    Google Scholar 

  203. Rupp, P.: Ph.D. thesis, Universität Bayreuth (2003)

    Google Scholar 

  204. Janssen, H.K., Kutbay, U., Oerding, K.: J. Phys. A 32, 1809 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  205. Bohr, T., van Hecke, M., Mikkelsen, R., Ipsen, M.: Phys. Rev. Lett. 86, 5482 (2001)

    Article  ADS  Google Scholar 

  206. Brunet P., Limat, L.: Phys. Rev. E 70, 046207 (2004)

    Article  ADS  Google Scholar 

  207. Vojta, T.: Phys. Rev. E 70, 0426108 (2004)

    Article  ADS  Google Scholar 

  208. Pirat, C., Naso, A., Meunier, J.-L., Maïssa, P., Mathis, C.: Phys. Rev. Lett. 94, 134502 (2005)

    Article  ADS  Google Scholar 

  209. Müller, H.W., Wittmer, H., Wagner, C., Albers, J., Knorr, K.: Phys. Rev. Lett. 78, 2357 (1997)

    Article  ADS  Google Scholar 

  210. Edwards W.S., Fauve, S.: J. Fluid Mech. 278, 123 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  211. Kudrolli, A., Pier, B., Gollub, J.P.: Physica D 123, 99 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  212. Müller, H.W.: Phys. Rev. Lett. 71, 3287 (1993)

    Article  ADS  Google Scholar 

  213. Arbell H., Fineberg, J.: Phys. Rev. Lett. 81, 4384 (1998)

    Article  ADS  Google Scholar 

  214. Arbell H., Fineberg, J.: Phys. Rev. Lett. 84, 654 (2000)

    Article  ADS  Google Scholar 

  215. Edwards W.S., Fauve, S.: J. Fluid Mech. 278, 123 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  216. Bashtovoi V.G., Rosensweig, R.E.: J. Magn. Magn. Mater. 122, 234 (1993)

    Article  ADS  Google Scholar 

  217. Ko, H., Lee, J., Lee, K.J.: Phys. Rev. E 65, 056222 (2002)

    Article  ADS  Google Scholar 

  218. Ko, H., Lee, J., Lee, K.J.: Phys. Rev. E 67, 026218 (2003)

    Article  ADS  Google Scholar 

  219. Blums, E., Cebers, A., Maiorov, M.M.: Magnetic, Fluids. Walter de Gruyter & Co., Berlin, New York (1997)

    Google Scholar 

  220. Bacri, J.C., Cebers, A., Dabadie, J.-C., Neveu, S., Perzynski, R.: Europhys. Lett. 27, 437 (1994)

    Article  ADS  Google Scholar 

  221. Bacri, J.C., Cebers, A., Dabadie, J.-C., Perzynski, R.: Phys. Rev. E 50, 2712 (1994)

    Article  ADS  Google Scholar 

  222. Elias, F., Flament, C., Bacri, J.-C.: Phys. Rev. Lett. 77, 643 (1996)

    Article  ADS  Google Scholar 

  223. Kumar K., Tuckerman, L.: J. Fluid Mech. 279, 49 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  224. Chen P., Viñals,J.: Phys. Rev. Lett. 79, 2670 (1997)

    Article  ADS  Google Scholar 

  225. Chen P., Viñals, J.: Phys. Rev. E 60, 559 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  226. Mekhonoshin V.V., Lange, A.: Phys. Rev. E 65, 061509 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  227. Saldivar-Guerrero, R., Richter, R., Rehberg, I., Aksel, N., Heymann, L., Rodriguez-Fernandez, O.S.: Magnetohydrodynamics 41, 385 (2005)

    Article  ADS  Google Scholar 

  228. Saldivar-Guerrero, R., Richter, R., Rehberg, I., Aksel, N.,Heymann, L., Rodriguez-Fernandez, O.S.: J. Chem. Phys. 125, 084907 (2006)

    Article  ADS  Google Scholar 

  229. Gollwitzer, C., Saldivar-Guerrero, R., Fernandez, O.R., Rehberg, I., Richter, R.: Experiments on Hysteretic Surface Transformations in an Inverse Magnetic Fluid, in preparation (2008)

    Google Scholar 

  230. Bacri J.-C., Salin, D.: Phys. Lett. 43, 649 (1982)

    Article  Google Scholar 

  231. Bönnemann, H., Brijoux, W., Brinkmann, R., Matoussevitch, N., Waldöfner, N., Palina, N., Modrow, H.: Inorganica Chimica Acta 350, 617 (2003)

    Article  Google Scholar 

  232. Bönnemann, H., Brijoux, W., Brinkmann, R., Matoussevitch, N., Waldöfner, N.: German patent DE 10227779.6., (2003)

    Google Scholar 

  233. Rannacher D., Engel, A.: New J. Phys. 8, 108 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Bayreuth, Experimentalphysik 5, D-95440 Bayreuth, Germany

    R. Richter

  2. Fraunhofer Institute for Material and Beam Technology, Winterbergstraβe 28, D-01277 Dresden, Germany

    A. Lange

Authors
  1. R. Richter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Lange
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Richter .

Editor information

Editors and Affiliations

  1. Institut für Strömungsmechanik, TU Dresden, Dresden, 01062, Germany

    Stefan Odenbach

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Richter, R., Lange, A. (2009). Surface Instabilities of Ferrofluids. In: Odenbach, S. (eds) Colloidal Magnetic Fluids. Lecture Notes in Physics, vol 763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85387-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85387-9_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85386-2

  • Online ISBN: 978-3-540-85387-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation