Multilayer analysis of immiscible power-law fluids under magnetohydrodynamic and pressure-driven effects in a microchannel

In the present study, the combined magnetohydrodynamic and pressure-driven flow of multilayer immiscible fluids into a parallel flat plate microchannel is semi-analytically solved. Due to the handling of complex fluids in various microfluidic platform applications, the fluid transport reviewed here considers the power-law model. The movement of electrically conductive fluid layers is due to Lorentz forces that arise from the interaction between an electric current and a magnetic field. To find a solution for the flow field, the momentum equation and the rheological model for each fluid layer, together with the corresponding boundary conditions at the liquid-liquid and solid-liquid interfaces, are solved simultaneously through a closed system of nonlinear equations. The graphical results show the influence of the dimensionless parameters that arise from the mathematical modeling on the velocity profiles and flow rate. These are the magnetic parameters, the fluid layers thickness, the viscosity coefficients, the ratios between pressure forces and magnetic forces, and the flow behavior indexes. This theoretical work contributes to the design of microfluidic devices for flow-focusing tasks in chemical, clinical, and biological areas.