Annular Poiseuille flow of electrorheological and magnetorheological materials

Electro- (ER) and magnetorheological (MR) materials exhibit substantial inc reases in yield stress when subjected to strong electric or magnetic fields . The applied electric/magnetic field satisfies Laplace's equations in the ER/MR material. In annular geometries, the resulting spatial variation of t he electric/magnetic field results in a yield stress inhomogeneity. The ana lysis of annular Poiseuille flow of ER/MR materials herein assumes a power- law relationship between the field and the yield stress, and includes the e ffects of the inhomogeneous yield stresses and hyperbolic shear stress dist ributions. The approximation of the solution to this problem by flow throug h an appropriately defined rectangular duct tin which the yield stress is c onstant and the shear stresses are linearly distributed) can be remarkably accurate, even for nonslender ducts. (C) 2001 The Society of Rheology.