Theoretical analysis of field induced structure in E.R. and M.R. fluids

The rheological properties of E.R. and M.R. suspensions are determined by the strength of the structure built under the application of an electric (respectively magnetic) field. We present a general multipolar method which allows us to obtain the stress-strain curve for any sheared lattice. This is applied to infinite periodic chains of spheres arranged on three different lattices: simple cubic, simple hexagonal and body centered tetragonal. The predicted yield stresses and shear moduli are compared to the predictions of simpler models involving interactions between two or three particles. The field induced structures experimentally observed show that the chains of spheres aggregate into thick columns; we present a model which allows us to calculate the diameter of these aggregates, at least for M.R. fluids, on the basis of a minimization of the free energy.