Viscous micropump of immiscible fluids using magnetohydrodynamic effects and a power-law conducting fluid

Small-scale fluid transport methods have grown significantly in recent years, mainly in applications in microfluidic systems. Therefore, the present study analyzes the movement of two-layers of immiscible fluids within a parallel flat plates microchannel. The fluid layers are composed of a Newtonian fluid and a power-law fluid. The pumping is produced by magnetohydrodynamics effects that act on the non-Newtonian conducting fluid dragging the non-conducting Newtonian fluid by viscous forces. Under the consideration of a laminar, incompressible, and unidirectional flow, the dimensionless mathematical model is established by the momentum equations for each fluid, together with the corresponding boundary conditions at solid-liquid and liquid-liquid interfaces. The problem formulation is semi-analytically solved using the Newton-Raphson method. The results are presented as a function of the velocity profiles and flow rate, showing interesting behaviors that depend on the physical and electrical properties of each fluid and flow conditions via the dimensionless parameters such as the flow behavior index, a magnetic parameter related to Lorenz forces, the fluids viscosity ratios and the dimensionless liquid-liquid interface position. This work contributes to the understanding of the various immiscible non-conducting fluids pumping techniques that can be used in microdevices.