Network theory of electro-rheological fluid and its hydrodynamic characteristics in a parallel duct

We proposed a shear rheological relation based on a network theory regarding a suspension-type electro-rheological fluid (ERF) containing smectite particles. The theoretical constitutive equations concerning ERF under a D. C. electric field were derived using Rodge's network theory. The equations have creative and destructive functions expressing behavior as aggregated particles influenced by shear flow and an electric field. The theoretical results regarding viscosity based on the theoretical equations were compared with experimental data concerning the static shear stress in relation to shear rate obtained using a rotating concentric cylindrical rheometer. The viscosity behaves as a non-affine motion at a small shear rate range and as affine motion at large one. We investigated the parameters in the equations of the network theory. Next, we applied the proposed network theory to a rectangular duct ERF flow problem. The theoretical result can explain quantitatively the experimental data regarding pressure difference at a large given flow velocity. At a small given flow velocity range, the mechanical model containing the Maxwell model by Shimada can explain the experimental data quantitatively.