Abrupt contraction flow of magnetorheological fluids

Contraction and expansion flows of magnetorheological fluids occur in a variety of smart devices. It is important therefore to learn how these flows can be controlled by means of applied magnetic fields. This paper presents a first investigation into the axisymmetric flow of a magnetorheological fluid through an orifice (so-called abrupt contraction flow). The effect of an external magnetic field, longitudinal or transverse to the flow, is examined. In experiments, the pressure-flow rate curves were measured, and the excess pressure drop (associated with entrance and exit losses) was derived from experimental data through the Bagley correction procedure. The effect of the longitudinal magnetic field is manifested through a significant increase in the slope of the pressure-flow rate curves, while no discernible yield stress occurs. This behavior, observed at shear Mason numbers 10<Mnshear<100, is interpreted in terms of an enhanced extensional response of magnetorheological fluids accompanied by shrinkage of the entrance flow into a conical funnel. At the same range of Mason numbers, the transverse magnetic field appears not to influence the pressure drop. This can be explained by a total destruction of magnetic particle aggregates by large hydrodynamic forces acting on them when they are perpendicular to the flow. To support these findings, we have developed a theoretical model connecting the microstructure of the magnetorheological fluid to its extensional rheological properties and predicting the pressure-flow rate relations through the solution of the flow equations. In the case of the longitudinal magnetic field, our model describes the experimental results reasonably well.