Gravity effects on mixing with magnetic micro-convection in microfluidics.

Mixing remains an important problem for the development of successful microfluidic and lab-on-a-chip devices, where simple and predictable systems are particularly interesting. One is magnetic micro-convection, an instability happening on the interface of miscible magnetic and non-magnetic fluids in a Hele-Shaw cell under applied field. Previous work proved that the Brinkman model quantitatively explains the experiments. However, a gravity-caused convective motion complicated the tests. Here we first improve the experimental system to exclude the parasitic convection. Afterwards, we experimentally observe the magnetic micro-convection, by finding and quantifying how gravity and laminar flow stabilizes the perturbations that create it. Accordingly, we improve our theoretical model for a zero-flow condition and perform a linear analysis. Two dimensionless quantities --magnetic and gravitational Rayleigh numbers-- are used to compare the experimental observations and theoretical predictions for the critical field of instability and the characteristic size of the emerging pattern. Finally, we discuss the conditions at which gravity plays an important role in microfluidic systems.