In general, electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to an electric field, the particles form structures which have essentially the direction of the electric field, resulting in a higher effective viscosity. Of considerable interest is the dependence of this effect on the direction of the electric field. Towards this end, we propose a micropolar theory including appropriate balance and constitutive equations for these suspensions essentially based on the works of Eringen. An appropriate non-dimensionalization is carried out which combines procedures of Eringen for micropolar fluids, on the one hand, and Eckart and Růžička for electrorheological fluids on the other. We then derive constitutive equations for the Cauchy stress and the couple stress and discuss the restrictions imposed on them by the second law of thermodynamics using scaling arguments. To illustrate the enhanced possibilities of micropolar electrorheology, a simple constitutive model which is linear in the strain rate is discussed in a study of a viscometric flow. We finally show that the velocity profile (hence the flow rate) may strongly depend on the direction of the electric field.
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We address some issues regarding the use of the Lagrangian description and convected frames in describing fluid motions. We also discuss the implications of Brownian motion on modeling the macroscopic motion of fluids and the schemes of filtered simulations. The relevance of these issues to the modeling of turbulence is discussed in detail.
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