Magnetorheological (MR) materials are a kind of smart materials whose mechanical properties can be altered in a controlled fashion by an external magnetic field. They traditionally include fluids, elastomers and foams. In this review paper we revisit the most outstanding advances on the rheological performance of MR fluids. Special emphasis is paid to the understanding of their yielding, flow and viscoelastic behaviour under shearing flows.

Magnetorheological fluids: a review

1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.

Colloidal Suspension Rheology

Co-continuous structures can be regarded as the coexistence of at least two continuous structures within the same volume. Blends with co-continuous structures may combine the properties of both components in a favorable way, for example, mechanical moduli. This review article deals with the identification, characterization, and properties of co-continuous structures as well as with the development of co-continuous structures during the melt blending process. Co-continuous structures usually can be formed within a composition region about the phase inversion composition, which mainly depends on the viscosity ratio. On the other hand, co-continuous structures can be found independent of composition as intermediate stages during the initial state of morphology development and during phase inversion process in blends in which the component finally forming the dispersed phase forms the matrix in early mixing states. In addition, even at low volume fractions of one component, stable co-continuous morph...

Formation of Co-continuous Structures in Melt-Mixed Immiscible Polymer Blends

The effects of different starch sources and plasticizers on film blowing of thermoplastic starch: Correlation among process, elongational properties and macromolecular structure

Rheology as a tool for evaluation of melt processability of innovative dosage forms.

Phase separation processes in mixtures of poly-α-methylstyrene-co-acrylonitrile (PαMSAN) and poly-methylmethacrylate (PMMA) with lower critical solution temperature (LCST) behavior have been studied, focusing on the manifestation of the interface in oscillatory shear measurements. By using blends of different composition, systems with a droplet-matrix morphology or a co-continuous structure are generated during the phase separation process. The feasibility of probing this morphology development by rheological measurements has been investigated. The development of a disperse droplet phase leads to an increase in the elasticity of the blend at low frequency, showing up as a shoulder in the plot of storage modulus versus frequency. Here, the droplet growth is unaffected by the shear amplitude up to strains of 0.2; therefore the resulting dynamic data are suitable for quantitative analysis. In contrast, for blends in which phase separation leads to a co-continuous structure, the storage modulus shows a power law behavior at low frequency and its value decreases as time proceeds. For the latter systems, effects of the dynamic measurement on the morphology development have been observed, even for strain amplitudes as low as 0.01. To probe the kinetics of morphology evolution in droplet-matrix systems, measurements of the time dependence of the dynamic moduli at fixed frequency should be performed (for a whole series of frequencies). Only from such measurements, curves of the frequency dependence of the moduli at a well defined residence time can be constructed. From fitting these curves to the emulsion model of Palierne, the droplet diameter distribution at that particular stage in the phase separation and growth process can be obtained. It is not appropriate to use a simplified version of the Palierne model containing only the average droplet size, because a morphology with too broad a size distribution is generated.

Manifestation of phase separation processes in oscillatory shear: droplet-matrix systems versus co-continuous morphologies

In high shear rate capillary rheometry the combined effect of pressure dependent viscosity and dissipative heating becomes significant. Analytical expressions are derived to treat curved Bagley plots and throttle experiments. End effects are taken into account by using an effective length over radius ratio. The non-adiabatic case is described using a lump heat transfer coefficient Λ following Hay et al. (1999). The latter enters into the dissipative heating coefficient % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacqaH1oqzdaWgaaWcbaGaemiCaahabeaakiabg2da % 9iabeg8aYnaaCaaaleqabaGaeyOeI0IaeGymaedaaOWaaeWaaeaacq % WGJbWydaWgaaWcbaGaemiCaahabeaakiabgUcaRmaalyaabaGaeu4M % dWeabaGafmyBa0MbaiaaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacq % GHsislcqaIXaqmaaaaaa!4D6C! $$ \varepsilon _p = \rho ^{ - 1} \left( {c_p + {\Lambda \mathord{\left/ {\vphantom {\Lambda {\dot m}}} \right. \kern-\nulldelimiterspace} {\dot m}}} \right)^{ - 1} $$
 
(ρ density, c

 p
 heat capacity, % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacuWGTbqBgaGaaaaa!3C5E! $$ \dot m $$
 
mass flow rate). A rigorous treatment is possible for incompressible melts, assuming a flat radial temperature profile. For compressible melts, the downstream density variation reduces the effective temperature and pressure coefficients of viscosity. In addition, it causes less dissipative heating. The applicability of the treatment was carefully checked for a well characterised LDPE melt and consistent results from throttle experiments and the Bagley plot curvature are found. The pure dissipation effect was treated by a viscous FEM simulation. A fit of the expected analytical expression to the simulated axial pressure profile allows to extract Λ. Throttle experiments allow a reliable determination of the pressure coefficient of viscosity β
 η
 from a fit of the analytical prediction for the measured pressure loss Δp as function of the die inlet pressure P

 i
 , provided the dissipation coefficient from the FEM simulation is used. An analytical solution for the Bagley plot was derived for the pure dissipation or pressure effect, respectively. In the parabola approximation, however, the two contributions may be superimposed. Whereas dissipative heating increases the curvature of the axial pressure profile in a die in the same direction as the pressure effect, it operates in the opposite direction for the Bagley plot curvature. Pressure coefficients solely determined from Bagley plots are not reliable. The effect of variable melt density on the temperature and pressure coefficients of the LDPE remains below 5%.

Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts

First and second normal stress differences of a 50 vol.% magnetorheological fluid (MRF) are investigated by using a commercial plate–plate magneto-rheometer (Anton Paar GmbH) with plate–plate and cone–plate geometry. The manufacturer modified the instrument to achieve higher normal force (60 N) and torque (295 mNm) capacity. An additional modification by us allows an online determination of the true magnetic flux density B in the MRF by means of a Hall probe. FEM Maxwell 2D simulations quantitatively verify the Hall probe results and give detailed insight into the radial flux density profile within the MRF sample. Without shear, the static normal force FN for plate–plate increases as a power law: FN ∝ B2.4. A similar magnitude is found for cone–plate geometry, in contrast to the expectation. For steady shear at 10 s−1, the plate–plate normal force built-up limits the experiments at high flux densities rather than the torque generated. The normal forces increase linearly with the shear stress at high flux density. The first normal stress difference N1 is positive and about five times larger than the shear stress. The second normal stress difference N2 is also positive. The experimentally derived N2/N1 ratio of 1/4 distinctly deviates from theoretical predictions (N2/N1 = −1) for a semi-dilute MRF. Improvements of the radial flux density profiles are required to verify the normal stress difference ratio and to support the conjecture that the positive but small N2 is a consequence of the densely packed MRF, which does not allow to create extended chain-like structures. As shown in the appendix, the experimentally determined N2/N1 ratio is favorable to stabilize concentricity in concentric cylinder arrangements, relevant for the MRF application in clutches.

Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T

Capillary rheometry provides an efficient access to high shear rate flow properties relevant for processing. An automated gas driven capillary rheometer developed at BASF enables accurate measurements at imposed wall shear stress, thus supplementing instruments operating at imposed flow rate. A simplified treatment of dissipative heating based on the assumption of a radially flat temperature profile is outlined and justified by means of finite element simulations. The combined treatment of dissipation and pressure dependent viscosity yields relations to treat throttling experiments at imposed flow rate. Throttle pressure coefficients from a long die and an orifice agree for LDPE but significantly differ for PαMSAN. The effect is explained on the basis of identical pressure coefficients for shear and elongational flows, with regard to a constant stress, however. The effect of melt compressibility is negligible in practical capillary rheometry if the temperature and pressure coefficients of the melt density are by an order of magnitude smaller than those of the viscosity. Gas pressure driven instruments allow an effective determination of wall slip velocities from Mooney plots. This is of advantage for the investigation of the mechanism of additives or processing aids. Furthermore, imposed pressure experiments are pertinent to investigate the spurt effect of HDPE and to demonstrate that two different slip processes contribute to the apparent flow curve above spurt.

Capillary rheometry for polymer melts revisited

The response of a magneto-rheological fluid (MRF) to a change of magnetic flux density is investigated by using a commercial plate–plate magneto-rheometer MCR501 (Anton Paar GmbH) at constant shear rate. The instrument was modified to allow an online determination of the transient flux density in the MRF. Both current and voltage imposition to the magneto-cell were applied by using a power operational amplifier to drive the electromagnet. Assuming a Maxwell behavior with switching time λ and a linear increase in shear stress with flux density, analytic relations for the transient shear stress are derived for sinusoidal and single exponential flux densities vs time. True switching times of a few milliseconds are only obtained if the low pass filter in the original MCR501 torque signal is surpassed by a firmware allowing a sampling rate of 0.1 ms. For a sinusoidal flux density, the switching time is derived from the modulation depth of the shear stress. An upper bound of λ < 3 ms for a flux density of 0.8 T was found. For step coil current imposition of 1 T magnitude, switching times of 2.8 ms (start-up) and 1.8 ms (shutdown) allowed to fit the transient torque signal more than 2/3 of the total change. Finally, the effect of a sigmoidal characteristic on the switching time determination is addressed.

Hans Martin Laun

Papers

Manifestation of phase separation processes in oscillatory shear: droplet-matrix systems versus co-continuous morphologies

Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts

Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T

Capillary rheometry for polymer melts revisited

Measurement modes of the response time of a magneto-rheological fluid (MRF) for changing magnetic flux density