Archive of Applied Mechanics

, Volume 89, Issue 1, pp 153–165 | Cite as

Magnetorheological gels in two and three dimensions: understanding the interplay between single particle motion, internal deformations, and matrix properties

  • Günter K. AuernhammerEmail author


Magnetic hybrid materials are intrinsically heterogeneous in their mechanical properties on different length scales. This gives rise to a number of challenges in the comparison of experimental results to modeling and simulation efforts. This review focused on recent advance on relating the mechanical properties of magnetic hybrid materials to the internal structure of these materials. Special emphasis is given to methods for observing the internal matrix deformations. For 3D and 2D magnetic hybrid materials, we discuss the possibilities and limitations of measuring internal motion and instabilities of the embedded magnetic particles. Although measuring internal matrix deformations in 3D systems is possible, the measurement time for 3D imaging is too long for truly dynamic studies. This limitation can be overcome with 2D imaging in 2D or 3D systems. In all presented systems, measuring the internal deformation also gives the possibility to use the magnetic particles to characterize the mechanical matrix properties locally. The presented experimental advances are put into relation to competing approaches.


Hybrid materials Magnetic particles Internal deformation Confocal microscopy Microgels Interfacial rheology 



It is my great pleasure to thank H. R. Brand, C. Holm, S. Huang, M. Kästner, R. von Klitzing, A. Menzel, H. Pleiner, S. Odenbach, and A. Tschöpe for many inspiring discussions. The work presented in this article was financially supported by the German Science Foundation (DFG) through the Project AU321/3 within the Priority Program 1681.


  1. 1.
    Klapcinski, T., Galeski, A., Kryszewski, M.: Polyacrylamide gels filled with ferromagnetic anisotropic powder: a model of a magnetomechanical device. J. Appl. Polym. Sci. 58, 1007 (1995)CrossRefGoogle Scholar
  2. 2.
    Zrínyi, M., Barsi, L., Büki, A.: Deformation of ferrogels induced by nonuniform magnetic fields. J. Chem. Phys. 104(21), 8750 (1996)CrossRefGoogle Scholar
  3. 3.
    Jolly, M.R., Carlson, J.D., Muñoz, B.C., Bullions, T.A.: The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix. J. Intell. Mater. Syst. Struct. 7(6), 613 (1996). CrossRefGoogle Scholar
  4. 4.
    Ilg, P.: Stimuli-responsive hydrogels cross-linked by magnetic nanoparticles. Soft Matter 9, 3465 (2013). CrossRefGoogle Scholar
  5. 5.
    Menzel, A.M.: Bridging from particle to macroscopic scales in uniaxial magnetic gels. J. Chem. Phys. 141(19), (2014).
  6. 6.
    Odenbach, S.: Microstructure and rheology of magnetic hybrid materials. Arch. Appl. Mech. 86(1), 269 (2016). CrossRefGoogle Scholar
  7. 7.
    Hanasoge, S., Hesketh, P.J., Alexeev, A.: Metachronal motion of artificial magnetic cilia. Soft Matter 14(19), 3689 (2018). CrossRefGoogle Scholar
  8. 8.
    Zrínyi, M.: Magnetic-field-sensitive polymer gels. Trends Polym. Sci. 5(9), 280 (1997)Google Scholar
  9. 9.
    Filipcsei, G., Csetneki, I., Szilagyi, A., Zrinyi, M.: Magnetic field-responsive smart polymer composites. Adv. Polym. Sci. 206, 137 (2007)CrossRefGoogle Scholar
  10. 10.
    Collin, D., Auernhammer, G.K., Gavat, O., Martinoty, P., Brand, H.R.: Frozen-in magnetic order in uniaxial magnetic gels: preparation and physical properties. Macromol. Rapid Commun. 24, 737 (2003)CrossRefGoogle Scholar
  11. 11.
    Ionov, L.: Hydrogel-based actuators: possibilities and limitations. Mater. Today 17(10), 494 (2014).
  12. 12.
    Drotlef, D.M., Blümler, P., del Campo, A.: Magnetically actuated patterns for bioinspired reversible adhesion (dry and wet). Adv. Mater. 26(5), 775 (2014). CrossRefGoogle Scholar
  13. 13.
    Maas, J., Uhlenbusch, D.: Experimental and theoretical analysis of the actuation behavior of magnetoactive elastomers. Smart Mater. Struct. 25(10), 104002 (2016).
  14. 14.
    Lum, G.Z., Ye, Z., Dong, X., Marvi, H., Erin, O., Hu, W., Sitti, M.: Shape-programmable magnetic soft matter. Proc. Natl. Acad. Sci. 113(41), E6007 (2016).
  15. 15.
    Yoshida, K., Onoe, H.: Functionalized core-shell hydrogel microsprings by anisotropic gelation with bevel-tip capillary. Sci. Rep. 7, 45987EP (2017). CrossRefGoogle Scholar
  16. 16.
    Moron, C., Cabrera, C., Moron, A., Garcia, A., Gonzalez, M.: Magnetic sensors based on amorphous ferromagnetic materials: a review. Sensors 15, 28340 (2015)CrossRefGoogle Scholar
  17. 17.
    Auernhammer, G.K., Collin, D., Martinoty, P.: Viscoelasticity of suspensions of magnetic particles in a polymer: effect of confinement and external field. J. Chem. Phys. 124, 204907 (2006)CrossRefGoogle Scholar
  18. 18.
    Chen, L., Gong, X.L., Li, W.H.: Microstructures and viscoelastic properties of anisotropic magnetorheological elastomers. Smart Mater. Struct. 16(6), 2645 (2007).
  19. 19.
    Monz, S., Tschöpe, A., Birringer, R.: Magnetic properties of isotropic and anisotropic cofe\_2o\_4-based ferrogels and their application as torsional and rotational actuators. Phys. Rev. E 78(2), 021404 (2008). CrossRefGoogle Scholar
  20. 20.
    Borin, D., Günther, D., Hintze, C., Heinrich, G., Odenbach, S.: The level of cross-linking and the structure of anisotropic magnetorheological elastomers. J. Magn. Magn. Mater. 324(21), 3452 (2012).
  21. 21.
    Puljiz, M., Huang, S., Auernhammer, G.K., Menzel, A.M.: Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions. Phys. Rev. Lett. 117(23), 238003 (2016). CrossRefGoogle Scholar
  22. 22.
    Menzel, A.M.: Force-induced elastic matrix-mediated interactions in the presence of a rigid wall. Soft Matter (2017).
  23. 23.
    Borbath, T., Günther, S., Borin, D.Y., Gundermann, T., Odenbach, S.: X\(\upmu \)ct analysis of magnetic field-induced phase transitions in magnetorheological elastomers. Smart Mater. Struct. 21(10), 105018 (2012).
  24. 24.
    Günther, D., Borin, D.Y., Günther, S., Odenbach, S.: X-ray micro-tomographic characterization of field-structured magnetorheological elastomers. Smart Mater. Struct. 21(1), 015005 (2012).
  25. 25.
    Frickel, N., Messing, R., Schmidt, A.M.: Magneto-mechanical coupling in CoFe2O4-linked paam ferrohydrogels. J. Mater. Chem. 21(23), 8466 (2011). CrossRefGoogle Scholar
  26. 26.
    Helminger, M., Wu, B., Kollmann, T., Benke, D., Schwahn, D., Pipich, V., Faivre, D., Zahn, D., Cölfen, H.: Synthesis and characterization of gelatin-based magnetic hydrogels. Adv. Funct. Mater. 24(21), 3187 (2014). CrossRefGoogle Scholar
  27. 27.
    Koetting, M.C., Peters, J.T., Steichen, S.D., Peppas, N.A.: Stimulus-responsive hydrogels: theory, modern advances, and applications. Mater. Sci. Eng. R Rep. 93, 1 (2015).
  28. 28.
    Messing, R., Schmidt, A.M.: Perspectives for the mechanical manipulation of hybrid hydrogels. Polym. Chem. 2(1), 18 (2011). CrossRefGoogle Scholar
  29. 29.
    Tschöpe, A., Birster, K., Trapp, B., Bender, P., Birringer, R.: Nanoscale rheometry of viscoelastic soft matter by oscillating field magneto-optical transmission using ferromagnetic nanorod colloidal probes. J. Appl. Phys. 116(18), (2014).
  30. 30.
    Velders, A.H., Dijksman, J.A., Saggiomo, V.: Hydrogel actuators as responsive instruments for cheap open technology (haricot). Appl. Mater. Today 9, 271 (2017).
  31. 31.
    Zhang, Y.S., Khademhosseini, A.: Advances in engineering hydrogels. Science 356(6337) (2017).
  32. 32.
    Kuo, A.C.M.: Poly(dimethylsiloxane) - PDMS. Oxford University Press Inc, Oxford (1999)Google Scholar
  33. 33.
    Chen, L., Auernhammer, G.K., Bonaccurso, E.: Short time wetting dynamics on soft surfaces. Soft Matter 7(19), 9084 (2011). CrossRefGoogle Scholar
  34. 34.
    Tordjeman, P., Fargette, C., Mutin, P.H.: Viscoelastic properties of a cross-linked polysiloxane near the sol-gel transition. J. Rheol. 45(4), 995 (2001). CrossRefGoogle Scholar
  35. 35.
    Huang, S., Pessot, G., Cremer, P., Weeber, R., Holm, C., Nowak, J., Odenbach, S., Menzel, A.M., Auernhammer, G.K.: Buckling of paramagnetic chains in soft gels. Soft Matter 12(1), 228 (2016). CrossRefGoogle Scholar
  36. 36.
    Chambon, F., Winter, H.H.: Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J. Rheol. 31(8), 683 (1987). CrossRefGoogle Scholar
  37. 37.
    Winter, H.H., Chambon, F.: Analysis of linear viscoelasticity of a crosslinking polymer at the gel point. J. Rheol. 30(2), 367 (1986). CrossRefGoogle Scholar
  38. 38.
    Chambon, F., Winter, H.H.: Stopping of crosslinking reaction in a pdms polymer at the gel point. Polym. Bull. 13(6), 499 (1985). CrossRefGoogle Scholar
  39. 39.
    Varga, Z., Fehér, J., Filipcsei, G., Zrínyi, M.: Smart nanocomposite polymer gels. Macromol. Symp. 200(1), 93 (2003). CrossRefGoogle Scholar
  40. 40.
    An, Y., Shaw, M.T.: Actuating properties of soft gels with ordered iron particles: basis for a shear actuator. Smart Mater. Struct. 12, 157 (2003)CrossRefGoogle Scholar
  41. 41.
    Aarts, D.G.A.L., Lekkerkerker, H.N.W.: Confocal scanning laser microscopy on fluid–fluid demixing colloid–polymer mixtures. J. Phys. Condens. Matter 16, S4231–S4242 (2004)CrossRefGoogle Scholar
  42. 42.
    Besseling, R., Isa, L., Weeks, E.R., Poon, W.C.K.: Quantitative imaging of colloidal flows. Adv. Colloid Interface Sci. 146(1–2), 1 (2009).
  43. 43.
    Derks, D., Wisman, H., Blaaderen, A.v., Imhof, A.: Confocal microscopy of colloidal dispersions in shear flow using a counter-rotating coneäìplate shear cell. J. Phys. Condens. Matter 16(38), 3917 (2004).
  44. 44.
    Dinsmore, A.D., Weeks, E.R., Prasad, V., Levitt, A.C., Weitz, D.A.: Three-dimensional confocal microscopy of colloids. Appl. Opt. 40(24), 4152 (2001)CrossRefGoogle Scholar
  45. 45.
    Dullens, R.P.A., de Villeneuve, V.W.A., Mourad, M.C.D., Petukhov, A.V., Kegel, W.K.: Confocal microscopy of geometrically frustrated hard sphere crystals. Eur. Phys. J. Appl. Phys. 44(1), 21 (2008). CrossRefGoogle Scholar
  46. 46.
    Jenkins, M.C., Egelhaaf, S.U.: Confocal microscopy of colloidal particles: towards reliable, optimum coordinates. Adv. Colloid Interface Sci. 136(1–2), 65 (2008).
  47. 47.
    Prasad, V., Semwogerere, D., Weeks, E.R.: Confocal microscopy of colloids. J. Phys. Condens. Matter 19(11) (2007).
  48. 48.
    Royall, C.P., Louis, A.A., Tanaka, H.: Measuring colloidal interactions with confocal microscopy. J. Chem. Phys. 127(4), 044507 (2007).
  49. 49.
    Roth, M., Schilde, C., Lellig, P., Kwade, A., Auernhammer, G.K.: Colloidal aggregates tested via nanoindentation and simultaneous 3d imaging. Eur. Phys. J. E 35, 124 (2012). CrossRefGoogle Scholar
  50. 50.
    Zhao, J., Papadopoulos, P., Roth, M., Dobbrow, C., Roeben, E., Schmidt, A., Butt, H.J., Auernhammer, G.K., Vollmer, D.: Colloids in external electric and magnetic fields: colloidal crystals, pinning, chain formation, and electrokinetics. Eur. Phys. J. Spec. Top. 222(11), 2881 (2013). CrossRefGoogle Scholar
  51. 51.
    Wenzl, J., Seto, R., Roth, M., Butt, H.J., Auernhammer, G.: Measurement of rotation of individual spherical particles in cohesive granulates. Granul. Matter 15(4), 391 (2013). CrossRefGoogle Scholar
  52. 52.
    Minski, M.: Memoir on inventing the confocal scanning microscope. Scanning 10, 128 (1988)CrossRefGoogle Scholar
  53. 53.
    Minsky, M.: Microscopy apparatus. US Patent Office US 3 013 467 (1957)Google Scholar
  54. 54.
    Crocker, J.C., Grier, D.G.: Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298 (1996)CrossRefGoogle Scholar
  55. 55.
    Weeks, E.R., Crocker, J.C., Levitt, A.C., Schofield, A., Weitz, D.A.: Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287, 627 (2000)CrossRefGoogle Scholar
  56. 56.
    Schümann, M., Borin, D., Huang, S., Auernhammer, G.K., Müller, R., Odenbach, S.: A characterization of the magnetically induced movement of ndfeb-particles in magnetorheological elastomers. Smart Mater. Struct. 26, 095018 (2017). CrossRefGoogle Scholar
  57. 57.
    Sanchez, P.A., Gundermann, T., Dobroserdova, A., Kantorovich, S.S., Odenbach, S.: Importance of matrix inelastic deformations in the initial response of magnetic elastomers. Soft Matter 14(11), 2170 (2018). CrossRefGoogle Scholar
  58. 58.
    Saffman, P.G., Delbrück, M.: Brownian motion in biological membranes. Proc. Natl. Acad. Sci. 72(8), 3111 (1975)CrossRefGoogle Scholar
  59. 59.
  60. 60.
    Stone, H.A., Ajdari, A.: Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth. J. Fluid Mech. 369, 151 (1998)zbMATHGoogle Scholar
  61. 61.
    Danov, K., Aust, R., Durst, F., Lange, U.: Influence of the surface viscosity on the hydrodynamic resistance and surface diffusivity of a large brownian particle. J. Colloid Interface Sci. 175(1), 36 (1995).
  62. 62.
    Fischer, T.M., Dhar, P., Heinig, P.: The viscous drag of spheres and filaments moving in membranes or monolayers. J. Fluid Mech. 558, 451 (2006). CrossRefzbMATHGoogle Scholar
  63. 63.
    Stone, H.A., Masoud, H.: Mobility of membrane-trapped particles. J. Fluid Mech. 781, 494 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Ngai, T., Auweter, H., Behrens, S.H.: Environmental responsiveness of microgel particles and particle-stabilized emulsions. Macromolecules 39(23), 8171 (2006). CrossRefGoogle Scholar
  65. 65.
    Destribats, M., Lapeyre, V., Wolfs, M., Sellier, E., Leal-Calderon, F., Ravaine, V., Schmitt, V.: Soft microgels as pickering emulsion stabilisers: role of particle deformability. Soft Matter 7(17), 7689 (2011). CrossRefGoogle Scholar
  66. 66.
    Richtering, W.: Responsive emulsions stabilized by stimuli-sensitive microgels: emulsions with special non-pickering properties. Langmuir 28(50), 17218 (2012). CrossRefGoogle Scholar
  67. 67.
    Monteux, C., Marlière, C., Paris, P., Pantoustier, N., Sanson, N., Perrin, P.: Poly(n-isopropylacrylamide) microgels at the oil-water interface: interfacial properties as a function of temperature. Langmuir 26(17), 13839 (2010). CrossRefGoogle Scholar
  68. 68.
    Zhang, J., Pelton, R.: Poly(n-isopropylacrylamide) microgels at the air–water interface. Langmuir 15, 8032 (1999)CrossRefGoogle Scholar
  69. 69.
    Deshmukh, O.S., Maestro, A., Duits, M.H., van den Ende, D., Stuart, M.C., Mugele, F.: Equation of state and adsorption dynamics of soft microgel particles at an air–water interface. Soft Matter 10(36), 7045 (2014).
  70. 70.
    Li, Z., Geisel, K., Richtering, W., Ngai, T.: Poly(n-isopropylacrylamide) microgels at the oil–water interface: adsorption kinetics. Soft Matter 9(41), 9939 (2013). CrossRefGoogle Scholar
  71. 71.
    Richardson, R.M., Pelton, R., Cosgrove, T., Zhang, J.: A neutron reflectivity study of poly(n-isopropylacrylamide) at the air–water interface with and without sodium dodecyl sulfate. Macromolecules 33(17), 6269 (2000). CrossRefGoogle Scholar
  72. 72.
    Servant, A., Rogers, S., Zarbakhsh, A., Resmini, M.: Polymeric organic nanogels: structural studies and correlation between morphology and catalytic efficiency. N. J. Chem. 37(12), 4103 (2013). CrossRefGoogle Scholar
  73. 73.
    Huang, S., Gawlitza, K., von Klitzing, R., Gilson, L., Nowak, J., Odenbach, S., Steffen, W., Auernhammer, G.K.: Microgels at the water/oil interface: in situ observation of structural aging and two-dimensional magnetic bead microrheology. Langmuir 32(3), 712 (2016). CrossRefGoogle Scholar
  74. 74.
    Huang, S., Gawlitza, K., von Klitzing, R., Steffen, W., Auernhammer, G.K.: Structure and rheology of microgel monolayers at the water/oil interface. Macromolecules 50(9), 3680 (2017). CrossRefGoogle Scholar
  75. 75.
    Wiese, S., Antje, C.S., Richtering, W.: Microgelstabilized smart emulsions for biocatalysis. Angew. Chem. 125(2), 604 (2012). CrossRefGoogle Scholar
  76. 76.
    Destribats, M., Wolfs, M., Pinaud, F., Lapeyre, V., Sellier, E., Schmitt, V., Ravaine, V.: Pickering emulsions stabilized by soft microgels: influence of the emulsification process on particle interfacial organization and emulsion properties. Langmuir 29(40), 12367 (2013). CrossRefGoogle Scholar
  77. 77.
    Pinaud, F., Geisel, K., Masse, P., Catargi, B., Isa, L., Richtering, W., Ravaine, V., Schmitt, V.: Adsorption of microgels at an oil-water interface: correlation between packing and 2d elasticity. Soft Matter 10(36), 6963 (2014). CrossRefGoogle Scholar
  78. 78.
    Deshmukh, O.S., van den Ende, D., Stuart, M.C., Mugele, F., Duits, M.H.G.: Hard and soft colloids at fluid interfaces: adsorption, interactions, assembly & rheology. Adv. Colloid Interface Sci. 222, 215 (2015).
  79. 79.
    Geisel, K., Henzler, K., Guttmann, P., Richtering, W.: New insight into microgel-stabilized emulsions using transmission x-ray microscopy: nonuniform deformation and arrangement of microgels at liquid interfaces. Langmuir 31(1), 83 (2015). CrossRefGoogle Scholar
  80. 80.
    Cohin, Y., Fisson, M., Jourde, K., Fuller, G., Sanson, N., Talini, L., Monteux, C.: Tracking the interfacial dynamics of pnipam soft microgels particles adsorbed at the air–water interface and in thin liquid films. Rheol. Acta 52(5), 445 (2013). CrossRefGoogle Scholar
  81. 81.
    Destribats, M., Eyharts, M., Lapeyre, V., Sellier, E., Varga, I., Ravaine, V., Schmitt, V.: Impact of pnipam microgel size on its ability to stabilize pickering emulsions. Langmuir 30(7), 1768 (2014). CrossRefGoogle Scholar
  82. 82.
    Dickinson, E.: Microgels—an alternative colloidal ingredient for stabilization of food emulsions. Trends Food Sci. Technol. (2015).
  83. 83.
    Plateau, J.: Liv. experimental and theoretical researches into the figures of equilibrium of a liquid mass without weight—eighth series. Lond. Edinb. Dublin Philos. Mag. J. Sci. 38(257), 445 (1869). CrossRefGoogle Scholar
  84. 84.
    Reynaert, S., Brooks, C.F., Moldenaers, P., Vermant, J., Fuller, G.G.: Analysis of the magnetic rod interfacial stress rheometer. J. Rheol. 52(1), 261 (2008). CrossRefGoogle Scholar
  85. 85.
    Buttinoni, I., Zell, Z.A., Squires, T.M., Isa, L.: Colloidal binary mixtures at fluid-fluid interfaces under steady shear: structural, dynamical and mechanical response. Soft Matter 11(42), 8313 (2015). CrossRefGoogle Scholar
  86. 86.
    Rey, M., Fernandez-Rodriguez, M.A., Steinacher, M., Scheidegger, L., Geisel, K., Richtering, W., Squires, T.M., Isa, L.: Isostructural solid–solid phase transition in monolayers of soft core-shell particles at fluid interfaces: structure and mechanics. Soft Matter 12(15), 3545 (2016). CrossRefGoogle Scholar
  87. 87.
    Wilhelm, C.: Out-of-equilibrium microrheology inside living cells. Phys. Rev. Lett. 101(2), 028101 (2008). CrossRefGoogle Scholar
  88. 88.
    Masschaele, K., Fransaer, J., Vermant, J.: Direct visualization of yielding in model two-dimensional colloidal gels subjected to shear flow. J. Rheol. 53(6), 1437 (2009). CrossRefGoogle Scholar
  89. 89.
    Israelachvili, J.N., Pashley, R.M.: Molecular layering of water at surfaces and origin of repulsive hydration forces. Nature 306, 249 (1983). CrossRefGoogle Scholar
  90. 90.
    Christov, N.C., Danov, K.D., Zeng, Y., Kralchevsky, P.A., von Klitzing, R.: Oscillatory structural forces due to nonionic surfactant micelles: data by colloidal-probe AFM vs theory. Langmuir 26(2), 915 (2010). CrossRefGoogle Scholar
  91. 91.
    Fuller, G.G., Vermant, J.: Complex fluid-fluid interfaces: rheology and structure. Annu. Rev. Chem. Biomol. Eng. 3(1), 519 (2012). CrossRefGoogle Scholar
  92. 92.
    Samaniuk, J.R., Vermant, J.: Micro and macrorheology at fluid–fluid interfaces. Soft Matter 10(36), 7023 (2014). CrossRefGoogle Scholar
  93. 93.
    Maestro, A., Bonales, L.J., Ritacco, H., Fischer, T.M., Rubio, R.G., Ortega, F.: Surface rheology: macro- and microrheology of poly(tert-butyl acrylate) monolayers. Soft Matter 7(17), 7761 (2011). CrossRefGoogle Scholar
  94. 94.
    Ortega, F., Ritacco, H., Rubio, R.G.: Interfacial microrheology: particle tracking and related techniques. Curr. Opin. Colloid Interface Sci. 15(4), 237 (2010).
  95. 95.
    Monroy, F., Ortega, F., Rubio, R.G., Velarde, M.G.: Surface rheology, equilibrium and dynamic features at interfaces, with emphasis on efficient tools for probing polymer dynamics at interfaces. Adv. Colloid Interface Sci. 134–135, 175 (2007).
  96. 96.
    Mendoza, A.J., Guzmán, E., Martínez-Pedrero, F., Ritacco, H., Rubio, R.G., Ortega, F., Starov, V.M., Miller, R.: Particle laden fluid interfaces: dynamics and interfacial rheology. Adv. Colloid Interface Sci. 206, 303 (2014).
  97. 97.
    Karbaschi, M., Lotfi, M., Krägel, J., Javadi, A., Bastani, D., Miller, R.: Rheology of interfacial layers. Curr. Opin. Colloid Interface Sci. 19(6), 514 (2014).
  98. 98.
    Lotfi, M., Karbaschi, M., Javadi, A., Mucic, N., Krägel, J., Kovalchuk, V.I., Rubio, R.G., Fainerman, V.B., Miller, R.: Dynamics of liquid interfaces under various types of external perturbations. Curr. Opin. Colloid Interface Sci. 19(4), 309 (2014). CrossRefGoogle Scholar
  99. 99.
    Miller, R., Liggieri, L.: Interfacial rheology–the response of two-dimensional layers on external perturbations. Curr. Opin. Colloid Interface Sci. 15(4), 215 (2010).
  100. 100.
    Sollich, P., Lequeux, F., Hébraud, P., Cates, M.E.: Rheology of soft glassy materials. Phys. Rev. Lett. 78(10), 2020 (1997). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Leibniz Institute for Polymer ResearchDresdenGermany

Personalised recommendations