Kelvin-Helmholtz instability in viscoelastic fluids in presence of electro-magnetic fields

We investigate the root cause of Kelvin-Helmholtz instability with the aid of two simple models of energy exchange between the superposed fluids. We conclude that the density and surface tension of the fluids play a key role in determining the minimal relative speed that triggers the instability. We discuss the volume forces exerted by electric and magnetic field gradients on dielectric and ferro-fluids. We propose manipulating the field gradients to change the specific weight of fluids so that a flow of superposed fluids admits a greater relative velocity before the onset of Kelvin-Helmholtz instability. In order to include the effect of field gradients and viscosity in a closed form dispersion relation, we use the viscous potential flow approximation. It allows us to develop an analytical framework that works for dielectric fluids in presence of an electric field as well as ferro-fluid in presence of a magnetic field. The same framework is applicable to viscous as well as viscoelastic fluids described by the Oldroyd-B model. Our discussion of the Galilean transformation of the electromagnetic fields suggests ways to magnify the effects of field gradients. © 2011 American Institute of Physics