Electro-magneto-hydrodynamics of non-linear viscoelastic fluids

Abstract

A combined mechanical, electrical and magnetic field driven flow of a charged viscoelastic fluid is analyzed here. Body forces on the fluid are exerted due to the multifold interactions between electrical charges in the electrical double layer (EDL), the electric field, the magnetic field as well as the electrical currents. The fluid is assumed to obey the non-linear Phan-Thein-Tanner (PTT) constitutive behavior. We analyze combined electroosmotic and pressure driven flows, along with the streaming potential resulting from a purely pressure driven flow in presence of a magnetic field. The analysis is carried out for a slit type channel closed along the width. Flows in confinements open sideways, may be treated as a special case of our analysis. Our results reveal that, while viscoelasticity tends to augment the flow rate, the magnetic field can both aid and oppose the flow through its interactions with the electrical currents, depending on the actuating mechanism. We argue that the electro-magneto-hydrodynamic (EMHD) flow of viscoelastic fluids (or, any fluids, for that matter) is inherently multi-dimensional, because of the 3-dimensional nature of the Lorentz forces and this introduces an element of anisotropy in the fluid motion as well as the induced streaming potentials. We demonstrate that presence of non-linear viscoelasticity generally augments the streaming potential, whereas, the influence of magnetic field is more complex and depends on the primary driving factor behind the induced electric field. The anisotropy, on the other hand, mainly depends on the strength of the applied magnetic field and is largely independent of the fluid properties.