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ERF and MRF are characterized by a huge increase of their apparent viscosity under the influence of a electrical or accordingly a magnetic field.
Without the influence of a field they are in general real thin liquids whereas they behave as real solids, provided the field dependent yield stress is not exceeded, when the field becomes switched on.
They usually consist of a base fluid and solid particles. The volume fraction of the particles is between 20% and 60%. The build up of more or less branched particle chains is responsible for the increase of apparent viscosity. These particles are attracted to each other by electrical or accordingly magnetic forces. Shearing of the fluid first leads to a stretching and under higher stresses to a break up of the particle chains. Steady recombination of chain parts provides for increased viscosity even under high shear rates.
ERF and MRF belong to the group of Non Newtonian Fluids and their description as Bingham-Plastics is generally recognized. Hence, the following relation between shear stress and shear rate is appropriate:

      

with:

   -     shear stress [Pa]
  -      field induced shear stress [Pa]
    -    dynamic viscosity [Pa s] (some times called)
    -    shear rate []

As counterpart to the constant dynamic viscosityof Newtonian Fluids an apparent viscosity is defined for Bingham Plastics. It can be influenced by the electrical or magnetic field strength.
                                                

The dynamic viscosity is mostly determined by the base fluid. It is mainly temperature dependent.
The field induced shear stress depends on the electrical or magnetic field strength. For this dependence some theoretical models have been derived but neither one is yet able to reflect these relations properly. As a rule of thumb one can assume that increases quadratic with increasing electrical or magnetic field strength.
In the case of the shear stress being below, the fluid behaves as a solid and hence the shear stress is proportional to the shear strain (not to the shear rate). The proportionality factor is called shear modul G. When exceeding the yield stress the fluid becomes liquid. This liquid state is characterized by a linear increase of shear stress with shear rate. The proportionality factor is, as can be seen from the Bingham model, the static viscosity .
It is generally accepted that the transition from solid to liquid (increase of shear stress) occurs at a different shear stress than the transition from liquid to solid (reduction of shear stress). Both transitional shear stresses are in the same order of magnitude. The yield stress of the change from solid to liquid is called ' static yield stress' whereas the reverse characteristic yield stress is called 'dynamic yield stress'. The question which one is higher has to be answered different from fluid to fluid. The case however is the most likely to be encountered and it is to explained easier with the breakup behaviour of particle chains. Sorely for the most fluids are no measured values forand existant yet. Hence, one can obtain only one yield stress from the shear stress - shear rate-curves.
ERF are suspensions of electrically polarizable particles in a base fluid. This leads to a movement of particles to the poles under the impact of a direct voltage. Hence, it builds up a enriched zone next to the poles and a rarefied zone in the middle between them. This means that the particle concentration deviates everywhere from the optimum concentration, leading to a huge decrease of available yield stress. This process is called 'electrophoresis'. It can be prevented when using alternating fields.In this case one should also account for the influence of the field frequency on the yield stressand choose the optimum frequency, which is in the order of magnitude of several hundert Hertz. An analog effect for MRF was not encountered yet.
When using ERF or MRF special attention has to be drawn to the temperature dependence of their properties. Good fluids are already nowadays characterized by a good constancy of their properties. The dependence between yield stress and temperature is different from fluid to fluid. The biggest temperature problem for ERF results from the huge increase of current density with increasing temperature. Basic viscosity sligthly decreases with temperature for ERF as well as for MRF. For relative permeability  of MRF one can expect a very small decrease with increasing temperature.