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**Flow of electro-rheological materials.**
*(English)*
Zbl 0746.76095

Summary: An electro-rheological fluid is a material in which a particulate solid is suspended in an electrically non-conducting fluid such as oil. On the application of an electric field, the viscosity and other material properties undergo dramatic and significant changes. In this paper, the particulate imbedded fluid is considered as a homogeneous continuum. It is assumed that the Cauchy stress depends on the velocity gradient and the electric field vector. A representation for the constitutive equation is developed using standard methods of continuum mechanics. The stress components are calculated for a shear flow in which the electric field vector is normal to the velocity vector. The model predicts (i) a viscosity which depends on the shear rate and electric field and (ii) normal stresses due to the interaction between the shear flow and the electric field. These expressions are used to study several fundamental shear flows: the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device. Detailed solutions are presented when the shear response is that of a Bingham fluid whose yield stress and viscosity depends on the electric field.

### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

76T99 | Multiphase and multicomponent flows |

76A02 | Foundations of fluid mechanics |

74A20 | Theory of constitutive functions in solid mechanics |

### Keywords:

particulate solid; electrically non-conducting fluid; electric field; viscosity; homogeneous continuum; Cauchy stress; constitutive equation; shear flow; Couette flow; Bingham fluid
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\textit{K. R. Rajagopal} and \textit{A. S. Wineman}, Acta Mech. 91, No. 1--2, 57--75 (1992; Zbl 0746.76095)

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### References:

[1] | Truesdell, C., Toupin, R.: The classical field theories. Handbuch der Physik, Bd. IV/1. Berlin: Springer 1960. |

[2] | Spencer, A. J. M.: In: Continuum physics (Eringen, A. C., ed.), vol. 3. New York: Academic Press 1975. |

[3] | Filisko, F.: Private communication. |

[4] | Rajagopal, K. R., Wineman, A. S.: Flow of a BKZ fluid in an orthogonal rheometer. J. Rheol.27, 509-516 (1983). · Zbl 0535.76004 |

[5] | Rajagopal, K. R.: On the flow of a simple fluid in an orthogonal rheometer. Arch. Rational Mech. Anal.79, 39-47 (1982). · Zbl 0513.76002 |

[6] | Rajagopal, K. R., Renardy, M., Renardy, M., Wineman, A. S.: Flow of viscoelastic fluids between plates rotating about distinct axes. Rheol. Acta25, 459-467 (1986). · Zbl 0608.76007 |

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