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A phenomenological model of electrorheological fluids

Authors:

Peter?O?Brunn Email author" target="_blank">Basim?Abu-Jdayil Email author

Institution:

(1) LSTM, University of Erlangen-Nürnberg, Cauerstr. 4, 91058 Erlangen, Germany;(2) Chemical Engineering Department, Jordan University of Science and Technology, P.O. Box: 3030, 22110 Irbid, Jordan

Abstract:

The fundamental assumption of the paper is that the extra stress tensor of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation ${\mathbf{\hat{n}}}$ and length N of the fibers formed by application of an electric field). The resulting constitutive equation for is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate $\dot{\gamma }$ is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for $\dot{\gamma } \to \infty$ the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of ${\mathbf{\hat{n}}}$ and N on $\dot{\gamma }$ leads to the Bingham behavior for $\dot{\gamma } \to 0$ and power law behavior for large shear rates.

Basim Abu-JdayilEmail:

Keywords:

Electrorheological fluids Phenomenological constitutive equation Plastic fluid " target="_blank">Bingham fluid for $\dot{\gamma } \to 0$ " target="_blank">gif" alt="$$ \dot{\gamma } \to 0 $$" align="middle" border="0"> " target="_blank">Power law behavior for $\dot{\gamma } \to \infty$ " target="_blank">gif" alt="$$ \dot{\gamma } \to \infty $$" align="middle" border="0">

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