## Rheology and Microstructure of Magneto-Rheological Fluids

Simulation studies of microstructural dynamics in sheared MRFs

## Magneto-rheological Fluids

Magneto-rheological fluids (MRFs) are a type of smart fluid. When subjected to a magnetic field, the fluid greatly increases its apparent viscosity, to the point of becoming a viscoelastic solid. The yield stress (amount of stress needed to make the fluid flow within a given timeframe) of the fluid when “activated” can be controlled very accurately by varying the magnetic field strength. The force it can transmit can be controlled externally, giving rise to its many possible control-based applications. These applications include, among others, shock absorbers (for instance in cars or bridge suspensions, rotator dampers, clutches, and brakes but also haptic feedback devices.

Fig 1: High-fidelity simulation of a sheared magneto-rheological fluid consisting of polydisperse paramagnetic carbonyl iron particles (BASF CC) suspended in oil (AeroShell Fluid41). Shear rate is 100/s, external magnetic field is 105 A/m. Shown are the particle magnetization (red arrows) and the magnitude of flow field in a slice. The discontinuities in the rearrangement of the particle chains in shear flow lead to short localized high flow velocities. (Note: The system is split into four layers each having their own reference frame moving with the shear flow. In the visulaization these layers don't move, giving the false impression that particle chain would break at their interfaces.)

MRFs consist of paramagnetic particles (carbonyl iron, cobalt, nickel) suspended in a fluid (e.g. mineral or silicone oils). Sometimes other constituents are added as for instance a dispersant to minimize particle coagulation, or gel-forming additives. In figure 2A an electron microscopy image is shown of the particles that where used in our simulation research (courtesy of the Soft Matter group of the Intitute of Physics at the University of Amsterdam). These are Carbonyl Iron particles with an average size of about 4.5 μm. Without a magnetic field, these particles move freely through the fluid (fig. 2C). When an external magnetic field is applied, however, the particles become magnetized (fig. 2B). The magnetic interactions that then occur between the particles cause them to form long system spanning chains which are responsible for the measured increase in viscosity (fig. 2D). In figure 1, the chain formation of the particles in the simulations is illustrated in a movie. When the fluid is subjected to flow, chains break and reform. The activation of an MRF is very fast: it only takes around twenty thousandths of a second. The effect this activation has on the MRF flow properties can vary dramatically depending on the composition of the fluid, the size, shape, and magnetic properties of the particles, and the strength of the magnetic field. The viscosity curve of an MRF can thus be adjusted by finding the optimal combination of these properties.

Fig 2: Carbonyl Iron Powder particles (CIP) (A) and their mass magnetization as a function of the magnetic field (B). CIP particles are paramagnetic with a saturation magnetization. Microstructure of an MRF without (C) and with (D) an external magnetic field. The field induces a magnetic moment in the particles. The resulting magnetic interactions cause chain formation of the particles.

## Validation

We have simulated the shear flow of a realistic MRF consisting of BASF carbonyl iron powder CC suspended in AeroShell Fluid41 over a range of shear rates $\dot{\gamma}$. Special care has been taken to accurately simulate the hydrodynamic interactions (spanning scales from sample size down to the lubrication limit), the kinetic and static friction between the particles, and an accurate paramagnetic response of the particle material. The following properties have been used:

 Properties AeroShell Fluid41 density $\rho_\textrm{f}$ 872.0 kg/m$^\textrm{3}$ (Newtonian) kinematic viscosity $\nu$ 2.8 $\times$ 10$^\textrm{-5}$
 Properties BASF CIP CC density $\rho_\textrm{p}$ 7874.0 kg/m$^\textrm{3}$ shape spherical mean size (normal distribution $\mu$ 4.5 $\times$ 10$^\textrm{-6}$ m variance (normal distribution) $\sigma$ 1.0 $\times$ 10$^\textrm{-6}$ m kinetic friction $\mu_\textrm{k}$ 0.2 static friction $\mu_\textrm{s}$ 0.5 magnetic susceptibility $\chi_0$ (at H=0 A/m) 6.875 $\times$ 10$^\textrm{-4}$ m$^\textrm{3}$/kg saturation magnetization $\sigma_\textrm{max}$ 200.0 Am$^\textrm{2}$/kg magnetization relaxation time scale $\tau_\sigma$ 10 μs

In figure 3 the simulation results for an MRF with a particle volume fraction of $\phi=$ 0.2 are shown (in green). The viscosity is given as a function of shear rate $\dot{\gamma}$ as obtained by exposing the MRF to an external magnetic field of 127 kA/m in strength. The experimentally measured viscosity for this particular MRF is also given (in blue). As can be seen, our simulations reproduce the shear-thinning behaviour of the MRF very well. For both the experimental as well as the simulated system the viscosity decays as $\sim\dot{\gamma}^{-0.95}$.

Fig 3: Viscosity of the MRF as a function of shear rate for a particle volume fraction of $\phi=$ 0.2 and a magnetic field strength of $H=$ 127 kA/m. Experimental data from Ioniqa B.V.

Although the simulated values for the viscosity are very close to the measured quantities, they still differ by a factor of approximately 2. In the simulations, we used spheres to represent the carbonyl iron particles. In the microscopy image of figure 2, however, you can see that most particles are not purely spherical but consist of agglomerates of two or more spheres. To test the effect of the particle shape, simulations were done using beetle-shaped particles: agglomerates of three spheres. A single simulation was done for a particle volume fraction of $\phi=$ 0.2, a shear rate of 1000/s and a magnetic field strenght of 127 kA/m. The resulting viscosity is also shown in figure 3 (in red) which is now a factor of 2 higher than the experimental value. The particle shape thus has a profound effect on the viscosity of the MRF.

This can also be seen in figure 4, which shows a slice through the simulation box of the MRF while it is being sheared for both particle shapes. The shape of the particle chains is different for the different particle shapes. The beetle-shaped particles align with their long axis in the direction of flow leading to dense packing of the particles in the chains.

Fig 4: Chain dynamics in MRFs of spherical (left) and beetle-shaped (right) magnetizable particles in flow while exposed to an external magnetic field. Red and green areas indicate particles while blue areas indicate fluid.

## Virtual Prototyping

We are now in the process of exploring the effect of:

• particle shape
• particle concentration
• magnetic field strenght and direction
• particle coating

By exploring these parameters and their effect on the viscosity as a function of shear rate as well as their influence on the MRF activation time, optimized parameters can be obtained for different MRF applications.