Analysis of an Annular MHD Stirrer for Microfluidic Applications

An annular magnetohydrodynamic (MHD) device that may be used for the stirring of electrically conducting fluids in microfluidic applications is analyzed theoretically. A thin fluid layer is contained in the gap between two coaxial conducting cylinders connected to a potential difference under a uniform axial magnetic field. The imposed radial electric current that circulates in the fluid layer interacts with the magnetic field to produce an azimuthal Lorentz force that drives the fluid. A quasi-two-dimensional model that considers a linear friction due to the boundary layer attached to the insulating bottom wall is implemented and analytical solutions for the azimuthal flow are obtained for two different cases. The first case corresponds to a high conductivity fluid (a liquid metal) where the electric potential is coupled to the fluid velocity. The second case considers a low conductivity fluid (an electrolyte) where the electric potential is uncoupled from the fluid motion. The effect of slip boundary conditions at the walls of inner and outer cylinders, as well as the space between them, is explored.