## Magnetorheological fluid – Catharine Lo

Remember the ferrofluid that Luyu introduced during the camp.  It is made up of nanoparticles of ferromaterials that become magnetised under a magnetic field.  Now let us look at another type of fluid.

A magnetorheological fluid (MR fluid) is another type of smart fluid, usually a type of oil. It contains particles much larger than that of ferrofluid, at the micrometre scale.  When a magnetic field is applied, the viscosity of the fluid greatly increases, and the fluid becomes a viscoelastic solid.  By varying the strength of the magnetic field, the yield stress of the fluid can be controlled accurately.

How it works

Under normal conditions (with no magnetic field), the magnetic particles in the fluid are suspended within the medium in a random way as shown below:

However, when a magnetic field is applied the magnetic particles align themselves in the direction of the magnetic flux.  When the magnetic field is applied across the sides of the container, the particles form chains linking between the two sides of the container, restricting the movement of the fluid in the direction perpendicular to the direction of the magnetic flux.  Hence its viscosity increases:

Behaviour of the Material

To better understand the behaviour of this fluid, let us model it mathematically.

As mentioned above, MR fluids have a low viscosity in the absence of an applied magnetic field, but become quasi-solid when such a field is applied.  The properties of the quasi-solid is in fact, comparable to a solid, unless shearing occurs.  The yield stress (or apparent yield stress) is the maximum stress before deformation occurs.  It is dependent on the magnetic field applied, but reaches a maximum when the fluid is magnetically saturated, after which increasing the magnetic flux density yields no changes.  Hence, MR fluids can be considered similar to a Bingham plastic.

Thus we can model MR fluid as:

,

where τ = shear stress; τy = yield stress; H = Magnetic field intensity η = Newtonian viscosity;  is the velocity gradient in the z-direction.

Shear strength

Low shear strength acts as a obstacle for application.  However, when pressure is applied in the direction of the magnetic field, the shear strength is raised from about 100kPa to 1100kPa.  Shear strength can also be increased by replacing the particles with elongated particles.

Particle sedimentation

Due to the inherent density difference between the particles and the medium, the ferroparticles tend to settle out of the suspension over time.  To prevent this, surfactants are used, but at the cost of the fluid’s magnetic saturation, and hence the maximum yield stress.  Common surfactants include oleic acid, citric acid and tetramethylammonium hydroxide.

Surfactants have a polar head and a non-polar tail.  The polar head absorbs to the nanoparticle, while the non-polar tail sticks out into the medium, forming a micelle around the particle.  This increases the effective particle diameter.  As the particle is apparently larger, steric repulsion between the larger particles prevents the particles from congregating during settling.

Spherical ferromagnetic nanoparticles can also be added to prevent settling.  Due to the random Brownian motion of the nanoparticles, they interfere with the settling of the fluid particles to delay settling.

However, addition of other particles decreases the packing density of the fluid particles, thus decreasing the viscosity of the fluid, reducing its apparent yield stress.

Modes of operation

The MR fluid can operate in three main modes: the flow mode, shear mode and the squeeze-flow mode.

In the flow mode, the fluid flows as a result of pressure gradient between the two plates.  This mode is commonly used in dampers and shock absorbers, where the movement is controlled by fluid through channels, across which a magnetic field is applied.

In the shear mode, the fluid moves because the two plates move relative to one another horizontally.  Shear mode is used in clutches and brakes to control rotational motion.

In the squeeze-flow mode, the fluid moves due to a plate moving perpendicularly with respect to the other.  It is most suitable for controlling small, millimeter-order movements but involving large forces.

Limitations

1. High density of ferromagnetic particles such as iron makes them heavy.
2. High-quality fluids are expensive.
3. Fluids are subjected to thickening after prolonged use.  Hence, they need to be replaced regularly.

Applications

1. Mechanical engineering: dampers, e.g. heavy motor damping, operator seat/cab damping in construction vehicles and even seismic dampers which operate within the building’s resonance frequency, absorbing detrimental shock waves and oscillations within the structure to increase the resistance of the building to earthquakes
2. Military: bullet resistant body armour
3. Optics: Magnetorheological Finishing is an optical polishing method that is highly precise.  It was used in the construction of the Hubble Space Telescope’s corrective lens.
4. Medical: dampers to absorb shock in semi-active human prosthetic legs