The effect of particle concentration inhomogeneities on the steady flow of electro- and magneto-rheological materials
The yield stresses of electro-rheological (ER) and magneto-rheological (MR) suspensions increase by orders of magnitude when electric or magnetic fields are applied across them. In the absence of the field, the materials are essentially Newtonian fluids. When ER or MR materials flow through thin laminar ducts, the effect of the finite yield stress concentrates the material deformation gradients in the immediate vicinity of the duct walls. High shear rates in this region introduce drag and lift forces on the suspended particles, the net effect of which moves the particles away from the walls. Electro- or magneto-static image forces at the walls oppose this lift. The ensuing local changes in the particulate volume fraction gives rise to a local inhomogeneity in material properties adjacent to the walls. Four models for the material property inhomogeneities are presented in this paper. Three of these models admit analytical expressions for the relationship between pressure gradient and volumetric flow rate, but presume a piecewise constant particle concentration. The fourth model presumes a smooth relationship between the volume fraction and the shear rate, but requires a numerical solution. Results are presented in terms of the ratio of pressure gradients that can be produced by applying and removing the field. Experimental data collected for a variety of quasi-steady ER flows shows that the analytical solution corresponding to a flow of uniform particle concentration provides an upper bound to the pressure gradients. Each of the four models for inhomogeneous flow provides a lower bound over a sub-domain of the flow conditions. By combining these models heuristically, a single expression for the lower bound on the pressure gradients of ER and MR flows is presented. © 1997 Elsevier Science B.V.
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