Flow of Electrorheological Fluid under Conditions of Slip on the Boundary

Electrorheological fluids are smart materials that are concentrated suspensions of polarizable particles in a nonconducting dielectric liquid. In moderately large electric fields the particles form chains along the field lines and these chains then aggregate into the form of columns. These chainlike and columnar structures yield dramatic changes in the rheological properties of the suspensions. The fluid becomes anisotropic, the apparent viscosity (the resistance to flow) in the direction, orthogonal to that of the electric field, abruptly increases, while the apparent viscosity in the direction of the electric field changes not so drastically. LetΩ⊂Rn be a bounded domain, in which a fluid flows, n∈ {2,3}. Let the boundary S ofΩ be Lipschitz continuous. As it is well known, the stationary movement of any fluid is described by the equation in Cauchy form: