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Determining the Flow Curves for an Inverse Ferrofluid

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Determining the Flow Curves for an Inverse Ferrofluid Korea-Australia Rheology Journal Vol. 20, No. 1, March 2008 pp. 35-42 Determining the flow curves for an inverse ferrofluid C. C. Ekwebelam and H. See* The School of Chemical and Biomolecular Engineering, The University of Sydney, Australia. NSW 2006 (Received Oct. 9, 2007; final revision received Jan. 30, 2008) Abstract An inverse ferrofluid composed of micron sized polymethylmethacrylate particles dispersed in ferrofluid was used to investigate the effects of test duration times on determining the flow curves of these materials under constant magnetic field. The results showed that flow curves determined using low duration times were most likely not measuring the steady state rheological response. However, at longer duration times, which are expected to correspond more to steady state behaviour, we noticed the occurrence of plateau and decreasing flow curves in the shear rate range of 0.004 s−1 to ~ 20 s−1, which suggest the presence of non- homogeneities and shear localization in the material. This behaviour was also reflected in the steady state results from shear start up tests performed over the same range of shear rates. The results indicate that care is required when interpreting flow curves obtained for inverse ferrofluids. Keywords : inverse ferrofluid, flow curve, shear localization 1. Introduction An IFF comprises a magnetisable carrier liquid, otherwise known as a ferrofluid, which is a colloidal dispersion of Field-responsive fluids are suspensions of micron-sized nano-sized magnetite particles. Into this we disperse particles which show a dramatic increase in flow resistance micron-sized non-magnetic solid particles, thereby pro- upon application of external magnetic or electrical fields. ducing an IFF. The difference in particle size between the The two main types are electrorheological fluids (ERF) larger non-magnetic particles and those comprising the fer- which respond under electric fields and magnetorheolog- rofluid carrier means that the larger particles would behave ical fluids (MRF) which respond under magnetic fields. In as if they were in a continuum. Under a magnetic field, the both cases, the reason for this behaviour is that application non-magnetic particles are observed to form chains in the of the external field leads to the formation of field-aligned field direction (Skjeltorp, 1983), and this is due to essen- dipoles within each particle. The subsequent dipole-dipole tially the same induced dipolar interactions as arises in interactions between the particles then leads to the for- ERF and MRF. Due to these interactions and structures, mation of elongated aggregates or clusters in the direction IFF show a field-induced increase in shear resistance anal- of the applied field, and this in turn brings about the ogous to ERF and MRF (Bossis and Lemaire, 1991; Pop- increase in the flow resistance. There are review articles plewell et al., 1995; de Gans et al., 1999a, 1999b, 2000; available providing more details on these physical mech- Volkova et al., 2000; Saldivar-Guerrero et al., 2005; Ekwe- anisms and materials (Block and Kelly, 1988; Parthasar- belam and See, 2007). A significant advantage of this kind athy and Klingenberg, 1996; See, 1999). The tunable flow of system is that it allows us to probe the effects of using properties of these fluids lend themselves to a variety of a wide range of particle sizes and geometries-these studies engineering applications, including damping and high pre- will be reported in future. This work is an attempt to estab- cision polishing devices (Klingenberg, 2001; Magnac et lish the basic rheological behaviour of these systems, and al., 2006; Stanway et al., 1996; Bombard et al., 2002). so we have focused on the simplest IFF comprising mon- As a model of these suspensions, the “inverse ferrofluid” odisperse spherical particles in a ferrofluid and examined (abbreviated to IFF), has recently been receiving some the response under steady shear flow. attention (Skjeltorp, 1983; Bossis and Lemaire, 1991; Pop- In general, the rheological behaviour under steady shear- plewell et al., 1995; de Gans et al., 1999a, 1999b, 2000; ing of many materials is described by a plot of shear stress Volkova et al., 2000; Saldivar-Guerrero et al., 2005; Ekwe- versus shear rate, otherwise known as a flow curve. For belam and See, 2007), and will be the focus of this work. MRF and ERF it is found that the flow curves under an external field will take the form of a ‘Bingham fluid’ described by the following equation: *Corresponding author: [email protected] © 2008 by The Korean Society of Rheology Korea-Australia Rheology Journal March 2008 Vol. 20, No. 1 35 C. C. Ekwebelam and H. See · ττ= y +ηpγ (1) The structure of this paper is as follows: the materials, experimental methods and procedures used are described Here τ is the instantaneous stress (units of Pa), τ is the next; the tests carried out are flow curve and shear start up y · yield stress (Pa), ηp is the plastic viscosity (Pa ·s), and γ is tests. In the following section we display the results from the applied shear rate (s−1). That is, these materials show a these two rheological tests, and discuss the implications of yield stress, corresponding to the minimum shear stress these results. The results are plotted in the form of ‘shear necessary to rupture the aggregates produced under the stress versus shear rate’ (i.e., flow curves) and ‘shear stress given applied field. Numerous examples of flow curves versus shear strain’ curves. The paper ends with a con- exist in literature for ERF (Klingenberg and Zukoski, clusion section. 1990; Park and Park, 2001; Sung et al., 2004; Park et al., 2005; Espin et al., 2006) and MRF (Bombard et al., 2002; 2. Experimental Ashour et al., 1996; Rankin et al., 1999; Stanway, 2004; Claracq et al., 2004; Choi et al., 2005; Wereley et al., 2.1. Material 2006). In all of these works, curves similar to the Bingham The ferrofluid was supplied by Ferrotec Inc. USA, (type fluid curve were observed. It should also be noted that for EFH1), and consisted of a mineral based fluid into which flow curves to provide unambiguous characterization of were dispersed nano-sized magnetite particles. The fluid had the rheological properties of a fluid, they ideally should be a viscosity of 6×10−3 Pas at 27oC, a density of 1.21 g/ml, measuring the response of the material at steady state at and a remanent magnetism of 400 gauss. Into this fer- each shear rate (Coussot, 2005). rofluid we dispersed polymethylmethacrylate (PMMA) The rheological behaviour under steady shearing of IFF spherical particles with an average particle size of 4.6 µm, under magnetic fields has been reported by several work- to a volume fraction of 30%, thereby making up the ers, including Popplewell et al. (1995), de Gans et al. inverse ferrofluid (IFF). This ferrofluid and the PMMA (1999a, 1999b, 2000), and Saldivar-Guerrero et al. (2005). were used in Paper 1 for studies on the yielding behaviour For example, de Gans et al. (2000) determined the flow of bidisperse mixtures of IFF (Ekwebelam and See, 2007). curves of an IFF composed of nanometer-sized non-mag- It is noted that the density of the PMMA particles is less netic particles, but their small size means that they would than that of the disperse phase (~ 1.08 g/cc), and as such, be susceptible to considerable thermal motion effects, and there is the potential for flotation of the particles in sus- hence the behaviour would be expected to differ from the pension. However, the IFF was observed under a micro- micron-sized systems we study in this work. Popplewell et scope before and after each test, and showed no apparent al. (1995) explored the effect of shear rates of up to 400 s−1 signs of flotation. Further, there was also no apparent sign on an IFF which consisted of composites of hollow glass of any chemical reaction having taken place. beads dispersed in a ferrofluid. Saldivar-Guerrero et al. (2005) also explored the field dependence of polystyrene 2.2. Equipment particles dispersed in a ferrofluid under steady shear flow. A Paar Physica MCR300 rheometer was used with the These workers all report field-induced Bingham-type 20MR magnetorheological cell. This employs parallel behaviour in their flow curves. However, none of these plates of diameter 20 mm, and a constant gap of 1 mm was workers have reported the time allowed for the test, despite used. A uniform magnetic field, generated by coils under this being an essential consideration when interpreting the bottom plate, was applied perpendicularly to the plates. flow curves (Coussot, 2005). The sample was enclosed in a chamber consisting of soft To date, there seem to be no reports which explore in detail whether the flow curve measurements for IFF based on micron-sized particles, are indeed being taken at steady state. It is expected that the system will approach steady state as we increase the duration time of the test. The main point of this work, therefore, will be to explore the effects of the duration times (or equivalently, the ramp-up rate of the shear rate) used for determining the flow curves of IFF. In an earlier paper (Ekwebelam and See, 2007; herein- after referred to as Paper 1), we reported on the behaviour of essentially the same IFF system under oscillatory shear flow, with particular focus on the effects of mixing two particle sizes. This present paper extends our investigations of this IFF system to the behaviour under steady shear Fig. 1. Schematic diagram of the magnetic rheological test cell flow, particularly as large strains are reached. (Anton Paar Physica MCR300).
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