Effects of magnetic field on the motion of multiphase fluids containing paramagnetic particles in porous media

When paramagnetic nanoparticles are adsorbed at the oil-water interface or dispersed in one of the fluid phases in reservoir rock pores, then exposed to an external magnetic field, the resultant particle movements displace the interface. Interfacial tension acts as a restoring force, leading to interfacial fluctuation and a pressure (sound) wave. Here we focus on the interface motion. We apply the theory of ferrofluids to the case of an interface in a cylindrical pore. The predictions are consistent with experiments with an aqueous suspension of iron oxide nanorods in which the interface motion is measured by optical coherence tomography. The relative densities of the fluid phases (air/aqueous and dodecane/aqueous in our case) strongly affect the displacement of the interface. Application of a magnetic field introduces pressure-like terms into the equation of fluid phase motion. We then recast the problem in terms of interface motion, extending a numerical interface-tracking model based on the level-set method to account for capillarity and magnetic pressures simultaneously. We use the model to illustrate the motion of an interface between inviscid fluids at the pore scale when magnetic forces are imposed on one fluid phase.