Lorentz force induced shear waves in a layer of a Maxwell fluid*

We numerically analyze the generation of shear waves in a two-dimensional region where an electrically conducting viscoelastic fluid is confined. By imposing a Lorentz force caused by the interaction of a unidirectional alternating electric current with a steady magnetic field produced by one or several magnetic dipoles, superimposed shear waves are created in an oscillating vortex pattern. The viscoelastic behavior of the fluid layer is modeled using the linearized Maxwell model, while it is assumed that the fluid has a low electrical conductivity, so that the induced electromagnetic effects are negligible. A vorticity – stream function formulation is used to solve the governing equations, assuming a low Reynolds number flow. The Womersley and Deborah numbers, along with the Lorentz force parameter, characterize the dynamics of the flow. According to the magnetic field configurations and the value of the dimensionless parameters, different vorticity maps are obtained which resemble electromagnetic radiation patterns. It is found that shear waves can cross the whole system and cause interference leading to constructive resonances that substantially increase the amplitude of the velocity profiles. The use of this system for mixing enhancement purposes is explored.