**2. Fundamentals of MRF and applications**

## **2.1. Composition of MRF**

Generally, MRF consists of non-colloidal suspensions, magnetically soft ferromagnetic, ferrimagnetic or paramagnetic elements and compounds in a non-magnetic medium. In practice, MRF usually consists of suitable magnetizable particles such as iron, iron alloys, iron oxides, iron nitride, iron carbide, carbonyl iron, nickel and cobalt [1, 2]. Among these, a preferred magnetic responsive particle that is commonly used to prepare MRF is carbonyl iron. The possible maximum yield stress induced by MR effect is mainly determined by the lowest coercivity and the highest magnitude of saturation magnetization of the dispersed particles. Therefore, soft magnetic material with high purity such as carbonyl iron powder appears to be the main magnetic phase for most of the practical MRF composition [3]. Other than carbonyl iron, Fe-Co alloys and Fe-Ni alloys can also be used as MR materials, whereby, Fe contributes to the high saturation magnetization. In contrary, some of the ferrimagnetic materials such as Mn-Zn ferrite, Ni-Zn ferrite and ceramic ferrites have low saturation magnetizations and are therefore suitable to be applied in low yield stress applications [1]. MR particles are typically in the range of 0.1 to 10μm [4, 5], which are about 1000 times bigger than those particles in the ferrofluids [6]. In the MRF, magnetic particles within a certain size distribution can give a maximum volume fraction without causing unacceptable increasing in zero-field viscosity. For instance, fluid composition that consists of 50% volume of carbonyl iron powder was used in the application of electromechanically controllable torque-applying device.

The carrier liquid forms the continuous phase of the MRF. Examples of appropriate fluids include silicone oils, mineral oils, paraffin oils, silicone copolymers, white oils, hydraulic oils, transformer oils, halogenated organic liquids, diesters, polyoxyalkylenes, fluorinated silicones, glycols, water and synthetic hydrocarbon oils [7, 2]. A combination of these fluids may also be used as the carrier component of the MRF. In the earlier patents, inventors were using magnetizable particles dispersed in a light weight hydrocarbon oil [8], either a liquid, coolant, antioxidant gas or a semi-solid grease [9] and either a silicone oil or a chlorinated or fluorinated suspension fluid [10]. However, when the particles settled down, the fieldinduced particle chains formed incompletely at best in which MR response was critically degraded. Later, in order to prevent further sedimentation, new compositions of MRF with consideration on viscoplastic [11] and viscoelastic continuous phases [12] were formulated, so that the stability could be improved immensely. In addition, a composite MRF has been prepared by Pan et al. [13] with a combination of iron particles powder, gelatine and carrier fluids. They showed that the MR effects were superior under low magnetic field strength, and had a better stability compared to pure iron carbonyl powder alone.

Surfactants, nanoparticles, nanomagnetizable or coating magnetizable particles can be added to reduce the sedimentation of the heavy particles in the liquid phase [14, 13]. The sedimentation phenomenon can cause a shear-thinning behaviour of the suspension [15]. With further sedimentation, with MRF under the influence of high stress and high shear rate over a long period of time, the fluid will thicken (in-use-thickening) [16, 17]. Sedimentation phenomenon will reduce the MR effect where the particles in the MRF are settled down and form a hard "cake" that consists of firmly bound primary particles due to incomplete chain formation [18]. Anti-settling agent such as organoclay can provide soft sedimentation. When the composition of MRF has relatively low viscosity, it does not settle hard and can easily redisperse [2]. Coating of the polymer layer also influences magnetic properties of the particles and cause them to easily re-disperse after the magnetic field is removed [19]. However, specific properties of MRF such as shear and yield stresses under the same conditions were enormously degraded inevitably by addition of the coating layer. This is due to the shielding of the polymer layer that affects the magnetic properties of the particles [19, 20]. In addition, some additives can improve the secondary properties like oxidation stability or abrasion resistance.

#### **2.2. Magnetic properties of MRF**

348 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**2. Fundamentals of MRF and applications** 

**2.1. Composition of MRF** 

controllable torque-applying device.

design methodology of MRF-based mechanisms is considered. In this section, firstly the necessity of optimal design and the state of the art are discussed. Then the magnetic circuit analysis and the modeling of MRF devices are considered. In addition, the optimization problem of MRF devices is figured out and the methods to solve the problem are investigated. Section 5 is devoted to deal with a case study of MR valve optimal design. In this case study, several valve configurations such as single-coil, multiple-coil and annular-

Generally, MRF consists of non-colloidal suspensions, magnetically soft ferromagnetic, ferrimagnetic or paramagnetic elements and compounds in a non-magnetic medium. In practice, MRF usually consists of suitable magnetizable particles such as iron, iron alloys, iron oxides, iron nitride, iron carbide, carbonyl iron, nickel and cobalt [1, 2]. Among these, a preferred magnetic responsive particle that is commonly used to prepare MRF is carbonyl iron. The possible maximum yield stress induced by MR effect is mainly determined by the lowest coercivity and the highest magnitude of saturation magnetization of the dispersed particles. Therefore, soft magnetic material with high purity such as carbonyl iron powder appears to be the main magnetic phase for most of the practical MRF composition [3]. Other than carbonyl iron, Fe-Co alloys and Fe-Ni alloys can also be used as MR materials, whereby, Fe contributes to the high saturation magnetization. In contrary, some of the ferrimagnetic materials such as Mn-Zn ferrite, Ni-Zn ferrite and ceramic ferrites have low saturation magnetizations and are therefore suitable to be applied in low yield stress applications [1]. MR particles are typically in the range of 0.1 to 10μm [4, 5], which are about 1000 times bigger than those particles in the ferrofluids [6]. In the MRF, magnetic particles within a certain size distribution can give a maximum volume fraction without causing unacceptable increasing in zero-field viscosity. For instance, fluid composition that consists of 50% volume of carbonyl iron powder was used in the application of electromechanically

The carrier liquid forms the continuous phase of the MRF. Examples of appropriate fluids include silicone oils, mineral oils, paraffin oils, silicone copolymers, white oils, hydraulic oils, transformer oils, halogenated organic liquids, diesters, polyoxyalkylenes, fluorinated silicones, glycols, water and synthetic hydrocarbon oils [7, 2]. A combination of these fluids may also be used as the carrier component of the MRF. In the earlier patents, inventors were using magnetizable particles dispersed in a light weight hydrocarbon oil [8], either a liquid, coolant, antioxidant gas or a semi-solid grease [9] and either a silicone oil or a chlorinated or fluorinated suspension fluid [10]. However, when the particles settled down, the fieldinduced particle chains formed incompletely at best in which MR response was critically degraded. Later, in order to prevent further sedimentation, new compositions of MRF with consideration on viscoplastic [11] and viscoelastic continuous phases [12] were formulated, so that the stability could be improved immensely. In addition, a composite MRF has been

radial MR valves are considered. The chapter is then closed by the conclusion

The static magnetic properties of MRF are important to design any MRF-based devices and generally can be characterized by B-H and M-H hysteresis. Through the magnetic properties, the dependence of the MRF response on the applied current in the device can be predicted. Under the influence of the magnetic field, a standard model for the structure is used to predict the behaviour of the particle of MRF [21]. The model is based on a cubic network of infinite chains of the particles arranged in a line with respect to the direction of the magnetic field as shown in Figure 1.

**Figure 1.** Schematic presentation of the affine deformation of a chain of spherical particles

The chains are considered to deform with the same distance between any pair of neighbours in the chains and increase at the same rate with the strain when the MRF is strained. This model is quite simple since the chains, in actual case, are formed into some more compact aggregates of spheres in which can be constituted in the form of cylinders. Under shear stress, these aggregates might deform and eventually break. Even though the particles

develop into different complicated structures under different conditions [22], the standard model still can be used in order to give a valid prediction of the yield stress [21]. The equation of motion of each particle under a magnetic field is required in order to evaluate the bulk property of MRF. At a very low magnetic field, the magnetic force tensor *Fij* is obtained as point-dipole similar to the pair interaction, the magnetic dipole moment induced by other particles and surrounding walls for an unmagnetized and isolated sphere under a uniform magnetic field is given by [23]:

$$F\_{ij} = \frac{3}{4\pi\mu\_p\mu\_0} \left| m^2 \frac{r\_{ij}}{r\_{ij}^5} - \text{5(}mr\_{ij}\text{)}^2 \frac{r\_{ij}}{r\_{ij}^7} + \text{2(}mr\_{ij}\text{)}m\frac{1}{r\_{ij}^5} \right| \tag{1}$$

where *Fij* is the magnetic force tensor acts on particle *i* from *j*, *μp* is the specific permeability of particles, *μ0* is the vacuum permeability, *rij* is position from particle *j* to *i* and *m* is magnetic dipole moment induced in particles within MRF given by [24],

$$
\hbar m = 4\pi \mu\_f \mu\_0 \beta a^3 H \tag{2}
$$

where *H* is the uniform magnetic field, *a* is the diameter of the particles and *β* is given by,

$$\beta = \frac{\mu\_f - \mu\_p}{\mu\_f - 2\,\mu\_p} \tag{3}$$

where *μf* is the specific permeability of carrier liquid.

At high magnetic fields, the magnitude of the moment can be considered as independent point dipoles as magnetization of particles reaches saturation. In this case, the magnetic moment is given by [25].

$$
\mu m = \frac{4}{3} \pi a^3 \mu\_s M\_s \tag{4}
$$

where *μsMs* is the saturation magnetization of the particle, which is about 1.7 x 106*A/m* for bulk iron and 0.48x106*A/m* for the magnetite.

#### **2.3. Fundamentals of rheological properties**

Rheology is the response of materials to an applied stress [26]. Rheology is an interdisciplinary field and is used to describe the properties of a wide variety of materials such as oil, food, ink, polymers, clay, concrete, asphalt and others. Rheology measurements and parameters can be used to determine the processing behaviour of non-Newtonian materials, viscoelastic behaviour as a function of time, the degree of stability of a formulation at rest condition or during transport, and zero shear viscosity or the maximum viscosity of the fluid phase to prevent sedimentation [27]. The viscosity equation on the basis of a hydrodynamic theory for dilute dispersions of spherical particles has been developed by Einstein about 100 years ago [28]. The equation has been derived as

$$
\eta\_r = 1 + 2.5\phi \tag{5}
$$

where *ηr* is the relative viscosity of the suspension and *φ* is the volume fraction of the suspended solutes or particles assumed to be spherical. The addition of the solid particles to a liquid will increase the amount of particles and consequently increases the volume fraction of the particles. Therefore, as the volume fraction of particles increases, there will be an increase in the fluid's viscosity. Shook [29] has suggested that the maximum concentration of the particles *φ*max should be incorporated in the relationship between viscosity and concentration as

350 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

0

magnetic dipole moment induced in particles within MRF given by [24],

πμ μ

where *μf* is the specific permeability of carrier liquid.

bulk iron and 0.48x106*A/m* for the magnetite.

**2.3. Fundamentals of rheological properties** 

moment is given by [25].

under a uniform magnetic field is given by [23]:

develop into different complicated structures under different conditions [22], the standard model still can be used in order to give a valid prediction of the yield stress [21]. The equation of motion of each particle under a magnetic field is required in order to evaluate the bulk property of MRF. At a very low magnetic field, the magnetic force tensor *Fij* is obtained as point-dipole similar to the pair interaction, the magnetic dipole moment induced by other particles and surrounding walls for an unmagnetized and isolated sphere

2 2

3 1 5( ) 2( ) <sup>4</sup> *ij ij ij ij ij*

= −+

where *Fij* is the magnetic force tensor acts on particle *i* from *j*, *μp* is the specific permeability of particles, *μ0* is the vacuum permeability, *rij* is position from particle *j* to *i* and *m* is

> <sup>0</sup> 4 *m aH <sup>f</sup>* = πμ μ β

> > 2 *f p f p* <sup>−</sup> <sup>=</sup> <sup>−</sup> μ μ

 μ

where *H* is the uniform magnetic field, *a* is the diameter of the particles and *β* is given by,

μ

At high magnetic fields, the magnitude of the moment can be considered as independent point dipoles as magnetization of particles reaches saturation. In this case, the magnetic

> 4 <sup>3</sup> 3 *m aMs s* = π μ

where *μsMs* is the saturation magnetization of the particle, which is about 1.7 x 106*A/m* for

Rheology is the response of materials to an applied stress [26]. Rheology is an interdisciplinary field and is used to describe the properties of a wide variety of materials such as oil, food, ink, polymers, clay, concrete, asphalt and others. Rheology measurements and parameters can be used to determine the processing behaviour of non-Newtonian materials, viscoelastic behaviour as a function of time, the degree of stability of a formulation at rest condition or during transport, and zero shear viscosity or the maximum viscosity of the fluid phase to prevent sedimentation [27]. The viscosity equation on the basis of a hydrodynamic theory for dilute dispersions of spherical particles has been

developed by Einstein about 100 years ago [28]. The equation has been derived as

β

*r r F m mr mr m*

*p ij ij ij*

57 5

(1)

(2)

(3)

(4)

*rr r*

3

$$\eta\_r = \frac{\phi}{(1-\phi)^{2.5\phi\_{\text{max}}}} \tag{6}$$

However, these equations do not depend on the particle size but instead depend on the particle shape and solid concentration. Thus, Toda and Furuse [30] extended the equation in order to satisfy the viscosity behaviour of concentrated dispersion for small and large particles, respectively given by,

$$\eta\_r = \frac{1 - 0.5\phi}{(1 - \phi)^3} \tag{7}$$

$$\eta\_r = \frac{1 + 0.5\kappa\phi - \phi}{(1 - \kappa\phi)^3(1 - \phi)}\tag{8}$$

where *κ* is the correction factor that may depend on the size and concentration of the particles. The viscosity of the fluid can be increased with additional amounts of the solid particles. However, at the same time, the fluid behaviour will change and diverge from a Newtonian fluid. Generally, shear stress τ increases with the shear rate *du/dy* which often can be represented by the relationship

$$
\pi = \pi\_y + \eta (\frac{du}{dy})^n \tag{9}
$$

where *τy, η* and *n* are constants, *τ<sup>y</sup>* is the yield stress and *η* is the dynamic viscosity. Newtonian fluids occur when the fluids show no yield stress or *τy* is equal to zero and *n* is equal to one. The viscosity of a Newtonian fluid is independent of time and shear rate. Figure 2 show the classification of fluids based on rheological properties. As shown in the figure, the behaviour of the fluids can be classified into Newtonian fluids and non-Newtonian fluids such as plastic, Bingham plastic, pseudo-plastic and dilatant fluids [31]. Fluids are said to be plastic when the shear stress must reach a certain minimum value before it begins to flow. If *n*, in Eq. (9), is equal to one, the material is known as a Bingham plastic. For the pseudo-plastic or shearthinning fluid, the dynamic viscosity decreases as the shear rate increases. On the other hand, a shear-thickening or dilatant fluid exhibits the converse property of pseudo-plastic for which the dynamic viscosity increases as the shear rate increases. The shear thickening fluid is represented by *n* > 1 and shear thinning fluid by *n* < 1.

**Figure 2.** Classification of time-independent non-Newtonian fluid

#### **2.4. Rheology of MRF**

MRF responds to the external field, where the particles are held together to form chains parallel to the applied field. The interaction between the particles impedes to a certain level of the shear stress without breaking and simultaneously increases the viscosity of the fluids [32]. In many cases, the effect of MRF is described by Bingham Plastic model [33]. A modified or extended Bingham model, or a combination of Bingham model with other models such as viscous and coulomb friction have also been used to describe the behaviour of MRF [34]. In the absence of an external field, MRF behave like a normal fluid which is known as Newtonian fluid. There are many factors that influence the rheological properties of controllable MRF such as concentration and density of particles, particle size and shape distribution, properties of the carrier fluid [35], additional additives, applied field and temperature. The relationships of all these factors are very complex and are important in establishing methodology to improve efficiency of these fluids for suitable applications. Excellent MRF must have low viscosity and coercivity of particles without the influence of an external magnetic field and can achieve maximum yield stress in the presence of the external magnetic field. Gross [8] in his invention related to the valve for magnetic fluids, found that the advantage of large particle sizes or heavy suspensions can increase the size of the gap which also increases the flow of the fluid. Conversely, the large particles of the magnetically active phase of MRF lead to a strong tendency for particles to settle out of the liquid phase [19].

Some of the techniques are typically necessary in order to increase the yield stress; either by increasing the volume fraction of MR particles or by increasing the strength of the applied magnetic field. However, neither of these techniques is desirable since a higher volume fraction of the MR particles can add significant weight to the MR devices as well as increases the overall off-state viscosity of the material. In that connection, restricting the size and geometry of the MR device capable of utilizing that material, and a higher magnetic field significantly increases the power requirement of the device. To overcome this difficulty, Carlson [36] in his patent introduced alloy-particles material that was used as a solid particle instead of the common carbonyl iron. This MRF independently increases the yield stress without requiring increment of either the volume fraction of particles or magnetic field strength.
