9334 DOI: 10.1021/la100252g Langmuir 2010, 26(12), 9334–9341 Published on Web 03/26/2010 pubs.acs.org/Langmuir © 2010 American Chemical Society Small-Amplitude Oscillatory Shear Magnetorheology of Inverse Ferrofluids Jose Ramos, Juan de Vicente,* and Roque Hidalgo-  Alvarez Biocolloid and Fluid Physics Group, Department of Applied Physics, Faculty of Sciences, University of Granada, C/ Fuentenueva s/n, 18071-Granada, Spain Received January 18, 2010. Revised Manuscript Received March 5, 2010 A comprehensive investigation is performed on highly monodisperse silica-based inverse ferrofluids under small- amplitude oscillatory shear in the presence of external magnetic fields up to 1 T. The effect of particle volume fraction and continuous medium Newtonian viscosity is thoroughly investigated. Experimental results for storage modulus are used to validate existing micromechanical magnetorheological models assuming different particle-level field-induced structures. 1. Introduction Magnetorheological (MR) fluids are smart materials whose mechanical properties can be externally controlled through mag- netic fields. They are typically prepared by dispersing micrometer- sized spherical magnetic particles in nonmagnetic media. Cur- rently, new trends in magnetorheology involve the use of non- spherical particles instead of their spherical counterparts both in rotational 1 and oscillatory 2 regimes. Even though much effort is being focused now on the use of magnetic particles having different geometries, a profound understanding of the MR properties of even classical sphere-based MR fluids is still missing. The reason for this is basically the lack of monodisperse magnetic particles to validate existing analytical or numerical magnetor- heological models. To overcome this problem, inverse ferrofluids (IFFs) are known to be promising workbench candidates to test MR models even though their magnetic driven response is orders of magni- tude lower than conventional MR fluids. 3 An IFF is formed by dispersing micrometric nonmagnetic particles in a ferrofluid which basically consists of a stable suspension of nanometric magnetite particles. As a consequence, the nonmagnetic particles experience a medium that is magnetic and hydrodynamically continuous. By exposing the IFF to an external magnetic field, dipolar interactions appear between nonmagnetic particles. 3 The strength of this interaction can be controlled by varying the strength of the magnetic field and/or the saturation magnetization of the ferrofluid. The interest in using IFFs comes from the fact that nonmagnetic particles are available that are highly mono- disperse and susceptible to surface modification. In spite of the interest in using IFFs as models for magnetor- heology, little research has been focused on the understanding of their magnetorheological properties if compared to investigations on classical MR fluids. In this sense, the most outstanding works are briefly reviewed next. A comparative study between classical MR fluids and IFFs in steady shear flow was performed by Volkova and co-workers 10 years ago. 4 In their paper, the authors reported the existence of two different yield stresses, one asso- ciated to the solid friction with the plates and the other associated to the rupture of the aggregates. Unfortunately, particle size was not well controlled and viscoelastic properties were not discussed. Inverse ferrofluids have been used in the past as model systems for investigating the influence of particle size and particle size distribution. Highly monodisperse IFFs were investigated first by de Gans and co-workers. 5,6 Functionalized silica spheres were used having mean diameters in the range from 106 to 380 nm. A very complete characterization was carried out including steady-state and dynamic oscillatory tests. Furthermore, a micro- structural rheological model was proposed. For small enough particles, a strong increase of MR properties with particle size was observed. This finding was explained in terms of the average length of the aggregates under the field. Polydisperse IFFs were investigated by Lemaire et al. 7 in simple steady shear and Saldivar-Guerrero et al. 8 in small-amplitude oscillatory shear. Lemaire et al. did not find any difference in the flow curves between mono- and polydisperse IFFs. In contrast, Saldivar-Guerrero et al. observed an enhanced storage modulus in polydisperse systems compared to monodisperse systems in the linear regime of magnetization. In the case of polydisperse IFFs, there was not a quantitative agreement with the micromechanical model by de Gans et al. 5 They found a slow increase of storage modulus with magnetic field strength that was attributed to the existence of thick columnar structures (instead of single-width particle chains), hydrodynamic interactions, and the “poisoning effect”. More recently, Ekwebelam and See 9 investigated the effect of particle size distribution on the MR response of IFFs subjected to large amplitude oscillatory shear flow. The ratio of the first to the third harmonic was found to become more pronounced with decreasing particle size as well as with increasing proportion of small particles in bidisperse mixtures. *To whom correspondence should be addressed. E-mail: jvicente@ugr.es. (1) Bell, R. C.; Karli, J. O.; Vavreck, A. N.; Zimmerman, D. T.; Ngatu, G. T.; Wereley, N. M. Smart Mater. Struct. 2008, 17, 015028–1-6. (2) de Vicente, J.; Segovia-Guti errez, J. P.; Andablo-Reyes, E.; Vereda, F.; Hidalgo-  Alvarez, R. J. Chem. Phys. 2009, 131, 194902–1-10. (3) Skjeltorp, A. T. Phys. Rev. Lett. 1983, 51, 2306–2309. (4) Volkova, O.; Bossis, G.; Guyot, M.; Bashtovoi, V.; Reks, A. J. Rheol. 2000, 44, 91–104. (5) de Gans, B. J.; Blom, C.; Philipse, A. P.; Mellema, J. Phys. Rev. E 1999, 60, 4518–4527. (6) de Gans, B. J.; Duin, N. J.; van den Ende, D.; Mellema, J. J. Chem. Phys. 2000, 113, 2032–2042. (7) Lemaire, E.; Meunier, A.; Bossis, G. J. Rheol. 1995, 39, 1011–1020. (8) Saldivar-Guerrero, R.; Richter, R.; Rehberg, I.; Aksel, N.; Heymann, L.; Rodriguez-Fernandez, O. S. J. Chem. Phys. 2006, 125, 084907–1-7. (9) Ekwebelam, C. C.; See, H. Korea-Aust. Rheol. J. 2007, 19, 35–42.