Magnetohydrodynamic flow with slippage in an annular duct for microfluidic applications

In this paper, we investigate theoretically the 3D laminar flow of an electrolyte in an annular duct driven by a Lorentz force. The duct is formed by two concentric electrically conducting cylinders limited by insulating bottom and top walls. A uniform magnetic field acts along the axial direction, while a potential difference is applied between the cylinders so that a radial electric current traverses the fluid. The interaction of the current and the magnetic field produces a Lorentz force that drives an azimuthal flow. The steady flow is solved using a Galerkin method with Bessel–Fourier series in the radial direction and trigonometric series along the vertical direction, allowing different combinations of slip conditions at the walls. The orthogonality of both series with the general boundary conditions of the third kind is used to find an analytic approximation. Velocity patterns and flow rates are explored by varying the aspect ratio of the duct and the gap between the cylinders, as well as the slippage at the walls. Results can provide useful information for optimization and design of annular microfluidic devices.